{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":61280,"title":"Project Aether: Non-Linear Temporal Flow Optimization","description":"Ⅰ. Description\r\nIn the year 2450, you are the Chief Architect of the Neo-Elysium defense grid. You must manage energy distribution between stations in 3D space. This is not a simple flow problem because:\r\nKinematics: Every station moves with a constant velocity . Their positions change every second.\r\nTemporal Rifts: Spherical anomalies appear and disappear, disabling any station trapped inside.\r\nDynamic Cost: The cost of sending 1 unit of energy between station  is the squared Euclidean distance at the exact moment of the query.\r\nCapacity Constraints: Each station has a maximum storage capacity, and each link has a maximum throughput.\r\nⅡ. Task\r\nWrite a function [max_flow, min_cost] = solve_aether(stations, events) that processes a sequence of events and returns the results for all optimization queries.\r\nInput:\r\nstations: An  matrix: [x, y, z, vx, vy, vz, capacity]\r\nevents: A cell array where each element is a vector representing an event:\r\n                * [1, id, vx, vy, vz]: Update velocity of station id.\r\n                * [2, u, v, k]: Create a directed link from  with capacity .\r\n                * [3, x, y, z, R, duration]: A rift appears at  with radius  for a certain duration.\r\n                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\r\nOutput:\r\nA  matrix where Q is the number of Types 4 events. Each row is [TotalMaxFlow, TotalMinCost].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 638.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 333.5px 319.25px; transform-origin: 333.5px 319.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅠ. Description\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the year 2450, you are the Chief Architect of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNeo-Elysium\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e defense grid. You must manage energy distribution between \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003estations in 3D space. This is not a simple flow problem because:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 171.767px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 85.8833px; transform-origin: 316.5px 85.8833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 49.1667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 24.5833px; text-align: left; transform-origin: 288.5px 24.5833px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKinematics\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Every station moves with a constant velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"28\" style=\"width: 17px; height: 28px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Their positions change every second.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTemporal Rifts\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Spherical anomalies appear and disappear, disabling any station trapped inside.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDynamic Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The cost of sending 1 unit of energy between station \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the s\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003equared Euclidean distance\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the exact moment of the query.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCapacity Constraints\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Each station has a maximum storage capacity, and each link has a maximum throughput.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅡ. Task\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[max_flow, min_cost] = solve_aether(stations, events)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that processes a sequence of events and returns the results for all optimization queries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003estations\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix: [x, y, z, vx, vy, vz, capacity]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eevents\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A cell array where each element is a vector representing an event:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [1, id, vx, vy, vz]: Update velocity of station id.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [2, u, v, k]: Create a directed link from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with capacity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [3, x, y, z, R, duration]: A rift appears at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for a certain duration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAAkCAYAAADB7MdlAAAHWElEQVR4AeyZaWxUVRTHZzptQVppSgFrpXtDookYU2UJfFAjJBLEWPkAKCEEV1CJCCiCaFwgJqAYNkEMARUUDYIYSaBRYyJGpSYgaNC0nZqy2c1Ci0qX8fcf3htn5s178wapQjPNOXPucu555/7vuWtTPMk/1wgkwXINlceTBCsJVgIIJKCajKwkWAkgkIBqMrJ6GCxfUVHRCHhdcXFxLdwJB+Cz8P6SkpJ7+L4PvlTJi5/D8H8r8iQs30/j96elpaW34bSt74lEllfGMH7Y6/V+lZKSkoucWFtb2weWnZF8KC0QCHyIzh6cySV/SVF5eXkavi3CqSp8n4K8ChZdid93dHd378XvVdJTYTSrk9FllvygQYMyMfKWjFF5DTylpqamAv6BdBccALBDyEk48SNyLHILo5VF+pKhpqamCpx5BmC205fRcB5+ytedlKsfPvIPojeTvIXigqUOZ2RkvI+RGbQ+JwkwH5AOwBFEeR0ObDYKx5J+yEj/74JZMZjZsABHnvP7/ffV1dXth08w4JWwQFxIXRAw5DT1GxlBjmCpAR3eCkDjjVYrMLzDSMcUOLSfinbYQ7t7hw4dOlBpB9YaMonIXWAX/jZt1W4202oa9V7YkejHSCKqpa2tbR2K0QMdwNcN1H9Dnfwu7urqylM6nJ3AkgOPYMQE6iBArKJx9Ico+ofQ/4PcOViUz0cLlbBjBqScug20W9rS0rLIJWACah7tXhcbNkjaE0DcCm9saGhoi6VFELTiwxdGXd/U1NR+RjokbMFixMZgXKEpZYXn8urq6t+UcWLaXEF9OizKZkQtI6QKk3GyijZzyZ9DLnYBmK+kpOQp9JfBajNXNkg7ElPvCfg9JyW+32rU/w5wp4x0SMQEa8iQIerwk2j1h0WHiaq9SrjgwehkwG4pQCc24+gsGqjzToD5iKL56L5k6M5SW9KO0U69KwKgLEPxSGdnZ6ORDomYYKWlpY1BYxwcJIzsdBNVUqYjmlZKilsA+bgScdgNYD0KFGtmX3wcBnfRh3cZhD9JR1BMsNCYACu6EJ4WwNqtRDwO+6Cp2sA0rDczcaQTYBFAYWc+ndGue1EiCnsen89XhhwOV7a3t3+CtJAFrIKCgmy0RsAmHWKx+9nMOEmAyaP+BjhIjNABjhNNwYy7Hwtgzc3NSxiExdgKTj3MzMfmWuRFAwpbXjYi82y1xG4TsIBFFOnkXYABkw4ePXr0jJlxkky5sdTnwyJtCorITmUS4AjAaLcYn55HaoftCaA8bGa3843p8CwG4lu+FZMsYBFF2jI1f4MNGFGdyINppx9tCoB1V5jOdx0dHfvC8okkBdg7fHtbWKMdTJWN5C9mRAkoHW1exe4ydlXnMyRKjgTabhZojzYFOneLYUxnrWXHjh1LZAoaTYNCa9Q8vj09mDv/M5lpvtDlOex8izi/7Kza/TagtoWIWo50HAhLZLFlnqWRZSegzJYUVVTOhs1N4e0BAwbsIX8hJKBCxwMMPAZoWk/iHStQdU8CisHdju2v8XUlLR2Bot76Bk+oH8dIrSrFGDPPWsrGZKJKzzLaQVW/jzYLqqqqOpRJkKOB0hq1humxCZ/cnMNcfc4Aaj02q7Ozs1+28dWXl5enJSlk0xJZONbK2hNaazCopxdvqEVUgsVR2+0KivUOVMk6NVk2yCdKsYAydz2tYW4Pro7f1QsKfdK1rTUnJ2eODVAeduBJ6enpuneG7FnAUg2RIScPKg1XlJWVXYe0UGFh4SgKP4JzcGATl9S76+vrm8knSrrrzcWG0/HgXwOm5SIzM/M1vpPBUeGVxsbGgfTh6nBm8AuJPF2/nkUv4tYSEyyd1llM9Th2mF7nYXgHBm8kHYwwnjvyQX4tEfglZaeR4/x+/0y78wk6TiSgdCkO3vVQ1NTTYMVaQy4YMG0MLBcrsX8/wVDBclON38ejmXo/IK1A53OecPzkQxQTLNWi+BORMoqGc8inY/R7UG+FTwPkEfJFlFewOA4D3M9Ix+ocxc6EPV0xdA91e46KBuxRDq4aSMcPcUF/EQVtFIi4pHe7XWhF9MkWLBQ9ihS/37+GtEb6DMA9wBabBfdnXRqP3G035wnlLI0mbR0JG3r6mYrSHNL6ToSDlMeiIGCMvjo/g3a2B0mzMf4+jV4q7HXBfdCvNNua0hEszXGm22qUXwAonaT13uPYBl1Nq4no72HEdf2hyJkUmXTgTbTcAIVakAJ0aBvtdEsIFvT0j23HtS4xx3cxeg/jRF+kHtr035C/mDq/EDlvIO9ET08yWst8rGvXUrYe/dXoP05H6kj3GooFlhcgJrAuVdFLrSc1yF9h846nI0IZkaP39Y/ROwVA3XAn65j+gZFP3XBG/QBtehVZwCI6culsMb28nsjIhUvhQhbyfkTLzZQvpV5Ahl9lTlG2DR6N7njWuZPo9TqygMUueIIOr4IjnlW1kCtaKF8EGDchB8LmYplL2VRYD/6JrDuXFaAWsC4r7/9jZ5NgJQB4EqwEwPobAAD//2VZDXMAAAAGSURBVAMA95fjdpm6nyMAAAAASUVORK5CYII=\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix where Q is the number of Types 4 events. Each row is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[TotalMaxFlow, TotalMinCost]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solve_aether(stations,events)\r\n  result = 'binary_search';\r\nend","test_suite":"%% --- Test Case Setup ---\r\nstations = [ ...\r\n    0, 0, 0,  1, 0, 0, 10; ... % St 1: starts at origin, moves right\r\n   10, 0, 0, -1, 0, 0, 10; ... % St 2: moves left\r\n    0, 10, 0, 0,-1, 0, 10; ... % St 3: moves down\r\n   10, 10, 0, 0, 0, 0, 10; ... % St 4: static\r\n    5, 5, 5,  0, 0, 0, 10];    % St 5: Hub (static)\r\n\r\nevents = { ...\r\n    [2, 1, 5, 5], ...        % Event 1: Link 1-\u003e5, Cap 5\r\n    [2, 2, 5, 5], ...        % Event 2: Link 2-\u003e5, Cap 5\r\n    [2, 3, 5, 5], ...        % Event 3: Link 3-\u003e5, Cap 5\r\n    [4, 3, 1, 2, 3, 1, 5], ... % Event 4: Query Sources {1,2,3} to Sink {5} at T=4\r\n    [3, 5, 5, 5, 2, 10], ...   % Event 5: Rift at (5,5,5) Radius 2, duration 10\r\n    [4, 3, 1, 2, 3, 1, 5] ...  % Event 6: Same Query at T=6 (Station 5 should be disabled)\r\n};\r\nexpected = [15.0, 765.0; 0.0, 0.0];\r\nactual = solve_aether(stations, events);\r\n\r\nassert(max(abs(actual(:) - expected(:))) \u003c 1e-6);\r\ndisp('Test Passed!');\r\n\r\n%%\r\nstations = [...\r\n   13.8016   64.3856   75.3146    0.2430   -4.9817   -1.0341   44.0000\r\n   65.3592    7.8309   69.3887   -4.8116   -1.2985    2.6095   41.0000\r\n    2.5492   38.0750   13.6881   -2.3655   -0.6388   -3.3722   29.0000\r\n   23.3686   43.7689   90.6962    4.9859    1.3320   -0.3190   44.0000\r\n   97.8782   40.6951   37.8877    2.1054   -3.5322    0.9364   48.0000\r\n   94.3021   27.3786   52.9622   -2.8191    0.6537   -4.1467   10.0000\r\n   98.1064   23.1351   98.8615    1.4161   -0.9688   -0.0286   39.0000\r\n    6.6964   73.7898   95.8209   -3.7893   -4.4602    2.7690   29.0000\r\n   19.5257   87.9400   81.7646    0.5668   -3.6402   -3.6618   34.0000\r\n   42.3406   77.2488   42.3895    2.8797   -1.0949    2.0019   50.0000\r\n   53.7076    3.5833   81.7977   -0.8550   -0.4244    3.3073   44.0000\r\n   46.3277   55.4316   44.4496   -4.1634   -1.6809    0.1315   50.0000\r\n   62.5909   58.8174   38.0260    0.8711    3.5733   -4.9519   24.0000\r\n   50.2559   24.6189   70.7235    1.3927    1.0716   -1.4329   21.0000\r\n   79.1777   39.8386   23.8916   -3.7485   -3.0288    4.7302   22.0000\r\n   71.0352   80.6780   17.5765    3.6526   -3.5648   -3.5534   23.0000\r\n   56.9405   30.1836   23.8147   -0.1222    2.6738    2.7477   32.0000\r\n   15.7099   48.9634   28.3592   -2.2398    1.5272   -1.3902   21.0000\r\n   62.5603   78.1287    4.0649   -1.8853   -1.5772   -2.1842   47.0000\r\n   92.5833   44.9977   55.1417    1.6657   -4.4339    0.4341   37.0000\r\n   98.3197   83.3240   94.2499    0.0010   -0.7964   -0.9276   42.0000\r\n   72.3174   67.6675   78.7837   -0.5586   -0.3914    4.2030   17.0000\r\n   18.7558    8.6629   24.1432   -1.7442    0.3550   -1.4310   15.0000\r\n   86.0132   98.0718   69.5976    0.6592    3.2842   -3.8749   12.0000\r\n   12.9060   56.6428    1.5258   -4.8478    4.9837   -2.4492   35.0000\r\n   74.3472   20.7679   76.8548    0.5283   -1.1759   -3.4432   34.0000\r\n    4.7878    9.5609   33.1893    4.3582   -3.0992    3.1311   25.0000\r\n   64.9699    6.2521   32.2330   -0.1823    4.9239    1.2964   10.0000\r\n    5.9537    2.5782   76.5437   -1.7152    1.7994    1.5937   16.0000\r\n   91.9762   33.4127   38.4165    3.0308    4.3490    1.6412   30.0000\r\n   17.1725   55.6807   21.8627   -3.5653    1.3641    0.4728   42.0000\r\n    8.8046   84.5939   56.3322   -4.2138    1.4870   -2.1405   41.0000\r\n   30.4543   62.6754   22.0633   -0.5459   -1.1739   -4.0269   48.0000\r\n   67.1595   59.9864   16.2637   -0.3449   -4.7213    3.3122   42.0000\r\n   20.4443   21.0636   39.9640    2.3668    0.9307   -1.8498   28.0000\r\n   97.4810   25.3915    2.0395    1.9904    2.3131    0.9878   24.0000\r\n    3.9560   65.1974   42.3270    0.3309    1.5312   -0.3123   15.0000\r\n   49.1791   32.8917    0.3273   -2.9368   -4.3804    1.5821   33.0000\r\n   64.0933   52.3174    4.4860   -3.4303   -3.4696   -2.3900   18.0000\r\n   40.5016   12.4717   18.9124   -0.9776    2.5565   -2.1547   14.0000\r\n    5.7082   45.2696   20.1336   -0.6242   -0.0417    1.9106   41.0000\r\n   63.0337   99.2596   60.0350    4.7506   -1.1563    4.7348   28.0000\r\n   21.4581   39.9229   23.1722    4.2674   -2.1168   -2.1744   39.0000\r\n   62.9709    6.1912   56.6548   -1.9194   -3.1363    3.5399   14.0000\r\n   39.4561   29.2961   55.0750    3.6258    4.4734    4.0133   28.0000\r\n   79.6108   55.2272   33.8006    0.6023   -1.0194    3.3775   32.0000\r\n   87.9037   74.0127   98.9924    0.4416   -3.6085    2.5228   45.0000\r\n   78.0077   31.8404   14.8359    3.4228    0.4137   -2.4087   47.0000\r\n   70.2483   49.3858   85.1288    2.8797   -4.6948    4.4714   24.0000\r\n   42.0672   62.8669   78.7180    0.3637    0.4845    3.4713   25.0000];\r\nevents = {...\r\n    [1.0000   33.0000   -2.8119    3.6643   -1.0660],\r\n    [2 10 4 17],\r\n    [4 4 32 9 2 7 6 16 36 38 7 37 8],\r\n    [3.0000 7.8557 39.3866 81.5830 13.0000 10.0000],\r\n    [2 29 10 11],\r\n    [4     4    35     2    24    32     6    21     8    27    45    47    46],\r\n    [     4     5    44    38     8     4    24     6     5    22    15    18    46    40],\r\n    [     4     4    42    34    29    11     3    27     3    21],\r\n    [    1.0000   17.0000    4.3766    3.4737   -2.4302],\r\n    [2 37 40 5],\r\n    [    1.0000    4.0000    2.0565    3.7593   -2.2252],\r\n    [    3.0000   13.9014   37.4769   83.5878   16.0000    9.0000],\r\n    [     4     4    15    47    38    39     5    37    39    20     7     8],\r\n    [     4     3    42    47    23     5     4    26    10    15    45],\r\n    [    1.0000   39.0000   -1.5862   -0.2590   -3.9976],\r\n    [    1.0000   44.0000   -4.2913    3.8280   -1.0616],\r\n    [2 18 2 16],\r\n    [2 33 39 15],\r\n    [2 41 4 5],\r\n    [2 8 41 5],\r\n    [    1.0000   22.0000   -2.6489    4.5630   -1.2851],\r\n    [2 14 29 13],\r\n    [     4     5     5    21     2    29    34     6    35     3    33    15    17    48],\r\n    [    1.0000   13.0000   -0.6107    0.8718   -1.9299],\r\n    [2 16 46 15],\r\n    [    1.0000   33.0000   -4.6471    2.8261   -4.9820],\r\n    [2 34 2 11],\r\n    [    1.0000   30.0000   -3.0896   -1.1636    3.8218],\r\n    [    1.0000   35.0000   -2.1749    3.2141   -2.0589],\r\n    [2 48 42 19],\r\n    [     4     3    36    31    41     4    12    16    11     2],\r\n    [    3.0000   28.6149    3.0791   28.4451    6.0000    5.0000],\r\n    [    3.0000    1.0961   84.3501    6.6062   12.0000    5.0000],\r\n    [2 44 33 20],\r\n    [2 21 39 19],\r\n    [    3.0000   17.1376   31.9782   27.1206    8.0000    9.0000],\r\n    [2 49 44 14],\r\n    [     4     4    32    15    28     6     5    40    43    32     3    44],\r\n    [    1.0000   13.0000   -1.2488   -0.8647   -3.3482],\r\n    [     4     3    33    16     6     6    48    41     8    19    22    34]\r\n};\r\nexpected = [39.000 0; 0 0; 0 0 ;0 0; 18 0; 0 0; 0 0 ; 0 0; 41 0 ; 0 0];\r\nactual = solve_aether(stations,events)\r\nassert(all(abs(actual(:)-expected(:))\u003c1e-6))\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4945722,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-18T06:10:31.000Z","updated_at":"2026-03-22T18:30:25.000Z","published_at":"2026-03-18T06:10:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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Description\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the year 2450, you are the Chief Architect of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNeo-Elysium\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defense grid. You must manage energy distribution between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003estations in 3D space. This is not a simple flow problem because:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKinematics\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Every station moves with a constant velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{v}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Their positions change every second.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTemporal Rifts\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Spherical anomalies appear and disappear, disabling any station trapped inside.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDynamic Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The cost of sending 1 unit of energy between station \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu \\\\text{ and } v\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the s\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equared Euclidean distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e at the exact moment of the query.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCapacity Constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Each station has a maximum storage capacity, and each link has a maximum throughput.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅡ. Task\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[max_flow, min_cost] = solve_aether(stations, events)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that processes a sequence of events and returns the results for all optimization queries.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN \\\\times 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e matrix: [x, y, z, vx, vy, vz, capacity]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eevents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A cell array where each element is a vector representing an event:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [1, id, vx, vy, vz]: Update velocity of station id.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [2, u, v, k]: Create a directed link from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu \\\\text{ to } v\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with capacity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [3, x, y, z, R, duration]: A rift appears at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x, y, z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for a certain duration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ \\\\times 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e matrix where Q is the number of Types 4 events. Each row is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[TotalMaxFlow, TotalMinCost]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":61280,"title":"Project Aether: Non-Linear Temporal Flow Optimization","description":"Ⅰ. Description\r\nIn the year 2450, you are the Chief Architect of the Neo-Elysium defense grid. You must manage energy distribution between stations in 3D space. This is not a simple flow problem because:\r\nKinematics: Every station moves with a constant velocity . Their positions change every second.\r\nTemporal Rifts: Spherical anomalies appear and disappear, disabling any station trapped inside.\r\nDynamic Cost: The cost of sending 1 unit of energy between station  is the squared Euclidean distance at the exact moment of the query.\r\nCapacity Constraints: Each station has a maximum storage capacity, and each link has a maximum throughput.\r\nⅡ. Task\r\nWrite a function [max_flow, min_cost] = solve_aether(stations, events) that processes a sequence of events and returns the results for all optimization queries.\r\nInput:\r\nstations: An  matrix: [x, y, z, vx, vy, vz, capacity]\r\nevents: A cell array where each element is a vector representing an event:\r\n                * [1, id, vx, vy, vz]: Update velocity of station id.\r\n                * [2, u, v, k]: Create a directed link from  with capacity .\r\n                * [3, x, y, z, R, duration]: A rift appears at  with radius  for a certain duration.\r\n                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\r\nOutput:\r\nA  matrix where Q is the number of Types 4 events. Each row is [TotalMaxFlow, TotalMinCost].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 638.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 333.5px 319.25px; transform-origin: 333.5px 319.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅠ. Description\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the year 2450, you are the Chief Architect of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNeo-Elysium\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e defense grid. You must manage energy distribution between \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003estations in 3D space. This is not a simple flow problem because:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 171.767px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 85.8833px; transform-origin: 316.5px 85.8833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 49.1667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 24.5833px; text-align: left; transform-origin: 288.5px 24.5833px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKinematics\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Every station moves with a constant velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"28\" style=\"width: 17px; height: 28px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Their positions change every second.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTemporal Rifts\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Spherical anomalies appear and disappear, disabling any station trapped inside.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDynamic Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The cost of sending 1 unit of energy between station \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the s\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003equared Euclidean distance\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the exact moment of the query.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCapacity Constraints\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Each station has a maximum storage capacity, and each link has a maximum throughput.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eⅡ. Task\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[max_flow, min_cost] = solve_aether(stations, events)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that processes a sequence of events and returns the results for all optimization queries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003estations\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix: [x, y, z, vx, vy, vz, capacity]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eevents\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A cell array where each element is a vector representing an event:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [1, id, vx, vy, vz]: Update velocity of station id.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [2, u, v, k]: Create a directed link from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with capacity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [3, x, y, z, R, duration]: A rift appears at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for a certain duration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix where Q is the number of Types 4 events. Each row is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[TotalMaxFlow, TotalMinCost]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solve_aether(stations,events)\r\n  result = 'binary_search';\r\nend","test_suite":"%% --- Test Case Setup ---\r\nstations = [ ...\r\n    0, 0, 0,  1, 0, 0, 10; ... % St 1: starts at origin, moves right\r\n   10, 0, 0, -1, 0, 0, 10; ... % St 2: moves left\r\n    0, 10, 0, 0,-1, 0, 10; ... % St 3: moves down\r\n   10, 10, 0, 0, 0, 0, 10; ... % St 4: static\r\n    5, 5, 5,  0, 0, 0, 10];    % St 5: Hub (static)\r\n\r\nevents = { ...\r\n    [2, 1, 5, 5], ...        % Event 1: Link 1-\u003e5, Cap 5\r\n    [2, 2, 5, 5], ...        % Event 2: Link 2-\u003e5, Cap 5\r\n    [2, 3, 5, 5], ...        % Event 3: Link 3-\u003e5, Cap 5\r\n    [4, 3, 1, 2, 3, 1, 5], ... % Event 4: Query Sources {1,2,3} to Sink {5} at T=4\r\n    [3, 5, 5, 5, 2, 10], ...   % Event 5: Rift at (5,5,5) Radius 2, duration 10\r\n    [4, 3, 1, 2, 3, 1, 5] ...  % Event 6: Same Query at T=6 (Station 5 should be disabled)\r\n};\r\nexpected = [15.0, 765.0; 0.0, 0.0];\r\nactual = solve_aether(stations, events);\r\n\r\nassert(max(abs(actual(:) - expected(:))) \u003c 1e-6);\r\ndisp('Test Passed!');\r\n\r\n%%\r\nstations = [...\r\n   13.8016   64.3856   75.3146    0.2430   -4.9817   -1.0341   44.0000\r\n   65.3592    7.8309   69.3887   -4.8116   -1.2985    2.6095   41.0000\r\n    2.5492   38.0750   13.6881   -2.3655   -0.6388   -3.3722   29.0000\r\n   23.3686   43.7689   90.6962    4.9859    1.3320   -0.3190   44.0000\r\n   97.8782   40.6951   37.8877    2.1054   -3.5322    0.9364   48.0000\r\n   94.3021   27.3786   52.9622   -2.8191    0.6537   -4.1467   10.0000\r\n   98.1064   23.1351   98.8615    1.4161   -0.9688   -0.0286   39.0000\r\n    6.6964   73.7898   95.8209   -3.7893   -4.4602    2.7690   29.0000\r\n   19.5257   87.9400   81.7646    0.5668   -3.6402   -3.6618   34.0000\r\n   42.3406   77.2488   42.3895    2.8797   -1.0949    2.0019   50.0000\r\n   53.7076    3.5833   81.7977   -0.8550   -0.4244    3.3073   44.0000\r\n   46.3277   55.4316   44.4496   -4.1634   -1.6809    0.1315   50.0000\r\n   62.5909   58.8174   38.0260    0.8711    3.5733   -4.9519   24.0000\r\n   50.2559   24.6189   70.7235    1.3927    1.0716   -1.4329   21.0000\r\n   79.1777   39.8386   23.8916   -3.7485   -3.0288    4.7302   22.0000\r\n   71.0352   80.6780   17.5765    3.6526   -3.5648   -3.5534   23.0000\r\n   56.9405   30.1836   23.8147   -0.1222    2.6738    2.7477   32.0000\r\n   15.7099   48.9634   28.3592   -2.2398    1.5272   -1.3902   21.0000\r\n   62.5603   78.1287    4.0649   -1.8853   -1.5772   -2.1842   47.0000\r\n   92.5833   44.9977   55.1417    1.6657   -4.4339    0.4341   37.0000\r\n   98.3197   83.3240   94.2499    0.0010   -0.7964   -0.9276   42.0000\r\n   72.3174   67.6675   78.7837   -0.5586   -0.3914    4.2030   17.0000\r\n   18.7558    8.6629   24.1432   -1.7442    0.3550   -1.4310   15.0000\r\n   86.0132   98.0718   69.5976    0.6592    3.2842   -3.8749   12.0000\r\n   12.9060   56.6428    1.5258   -4.8478    4.9837   -2.4492   35.0000\r\n   74.3472   20.7679   76.8548    0.5283   -1.1759   -3.4432   34.0000\r\n    4.7878    9.5609   33.1893    4.3582   -3.0992    3.1311   25.0000\r\n   64.9699    6.2521   32.2330   -0.1823    4.9239    1.2964   10.0000\r\n    5.9537    2.5782   76.5437   -1.7152    1.7994    1.5937   16.0000\r\n   91.9762   33.4127   38.4165    3.0308    4.3490    1.6412   30.0000\r\n   17.1725   55.6807   21.8627   -3.5653    1.3641    0.4728   42.0000\r\n    8.8046   84.5939   56.3322   -4.2138    1.4870   -2.1405   41.0000\r\n   30.4543   62.6754   22.0633   -0.5459   -1.1739   -4.0269   48.0000\r\n   67.1595   59.9864   16.2637   -0.3449   -4.7213    3.3122   42.0000\r\n   20.4443   21.0636   39.9640    2.3668    0.9307   -1.8498   28.0000\r\n   97.4810   25.3915    2.0395    1.9904    2.3131    0.9878   24.0000\r\n    3.9560   65.1974   42.3270    0.3309    1.5312   -0.3123   15.0000\r\n   49.1791   32.8917    0.3273   -2.9368   -4.3804    1.5821   33.0000\r\n   64.0933   52.3174    4.4860   -3.4303   -3.4696   -2.3900   18.0000\r\n   40.5016   12.4717   18.9124   -0.9776    2.5565   -2.1547   14.0000\r\n    5.7082   45.2696   20.1336   -0.6242   -0.0417    1.9106   41.0000\r\n   63.0337   99.2596   60.0350    4.7506   -1.1563    4.7348   28.0000\r\n   21.4581   39.9229   23.1722    4.2674   -2.1168   -2.1744   39.0000\r\n   62.9709    6.1912   56.6548   -1.9194   -3.1363    3.5399   14.0000\r\n   39.4561   29.2961   55.0750    3.6258    4.4734    4.0133   28.0000\r\n   79.6108   55.2272   33.8006    0.6023   -1.0194    3.3775   32.0000\r\n   87.9037   74.0127   98.9924    0.4416   -3.6085    2.5228   45.0000\r\n   78.0077   31.8404   14.8359    3.4228    0.4137   -2.4087   47.0000\r\n   70.2483   49.3858   85.1288    2.8797   -4.6948    4.4714   24.0000\r\n   42.0672   62.8669   78.7180    0.3637    0.4845    3.4713   25.0000];\r\nevents = {...\r\n    [1.0000   33.0000   -2.8119    3.6643   -1.0660],\r\n    [2 10 4 17],\r\n    [4 4 32 9 2 7 6 16 36 38 7 37 8],\r\n    [3.0000 7.8557 39.3866 81.5830 13.0000 10.0000],\r\n    [2 29 10 11],\r\n    [4     4    35     2    24    32     6    21     8    27    45    47    46],\r\n    [     4     5    44    38     8     4    24     6     5    22    15    18    46    40],\r\n    [     4     4    42    34    29    11     3    27     3    21],\r\n    [    1.0000   17.0000    4.3766    3.4737   -2.4302],\r\n    [2 37 40 5],\r\n    [    1.0000    4.0000    2.0565    3.7593   -2.2252],\r\n    [    3.0000   13.9014   37.4769   83.5878   16.0000    9.0000],\r\n    [     4     4    15    47    38    39     5    37    39    20     7     8],\r\n    [     4     3    42    47    23     5     4    26    10    15    45],\r\n    [    1.0000   39.0000   -1.5862   -0.2590   -3.9976],\r\n    [    1.0000   44.0000   -4.2913    3.8280   -1.0616],\r\n    [2 18 2 16],\r\n    [2 33 39 15],\r\n    [2 41 4 5],\r\n    [2 8 41 5],\r\n    [    1.0000   22.0000   -2.6489    4.5630   -1.2851],\r\n    [2 14 29 13],\r\n    [     4     5     5    21     2    29    34     6    35     3    33    15    17    48],\r\n    [    1.0000   13.0000   -0.6107    0.8718   -1.9299],\r\n    [2 16 46 15],\r\n    [    1.0000   33.0000   -4.6471    2.8261   -4.9820],\r\n    [2 34 2 11],\r\n    [    1.0000   30.0000   -3.0896   -1.1636    3.8218],\r\n    [    1.0000   35.0000   -2.1749    3.2141   -2.0589],\r\n    [2 48 42 19],\r\n    [     4     3    36    31    41     4    12    16    11     2],\r\n    [    3.0000   28.6149    3.0791   28.4451    6.0000    5.0000],\r\n    [    3.0000    1.0961   84.3501    6.6062   12.0000    5.0000],\r\n    [2 44 33 20],\r\n    [2 21 39 19],\r\n    [    3.0000   17.1376   31.9782   27.1206    8.0000    9.0000],\r\n    [2 49 44 14],\r\n    [     4     4    32    15    28     6     5    40    43    32     3    44],\r\n    [    1.0000   13.0000   -1.2488   -0.8647   -3.3482],\r\n    [     4     3    33    16     6     6    48    41     8    19    22    34]\r\n};\r\nexpected = [39.000 0; 0 0; 0 0 ;0 0; 18 0; 0 0; 0 0 ; 0 0; 41 0 ; 0 0];\r\nactual = solve_aether(stations,events)\r\nassert(all(abs(actual(:)-expected(:))\u003c1e-6))\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4945722,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-18T06:10:31.000Z","updated_at":"2026-03-22T18:30:25.000Z","published_at":"2026-03-18T06:10:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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Description\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the year 2450, you are the Chief Architect of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNeo-Elysium\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defense grid. You must manage energy distribution between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003estations in 3D space. This is not a simple flow problem because:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKinematics\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Every station moves with a constant velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{v}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Their positions change every second.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTemporal Rifts\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Spherical anomalies appear and disappear, disabling any station trapped inside.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDynamic Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The cost of sending 1 unit of energy between station \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu \\\\text{ and } v\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the s\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equared Euclidean distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e at the exact moment of the query.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCapacity Constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Each station has a maximum storage capacity, and each link has a maximum throughput.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eⅡ. Task\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[max_flow, min_cost] = solve_aether(stations, events)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that processes a sequence of events and returns the results for all optimization queries.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN \\\\times 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e matrix: [x, y, z, vx, vy, vz, capacity]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eevents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A cell array where each element is a vector representing an event:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [1, id, vx, vy, vz]: Update velocity of station id.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [2, u, v, k]: Create a directed link from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu \\\\text{ to } v\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with capacity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [3, x, y, z, R, duration]: A rift appears at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x, y, z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for a certain duration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                * [4, num_sources, sourcess..., num_sinks, sinks...]: Optimization query.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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