Dynamic Programming for MATLAB

Dynamic Programming has been implemented in MATLAB using two illustrative example

Matlab Dynamic Programming

Dynamic Programming has been demostrated by two examples:

1. Fibonacci sequence
2. Find number of path in the Grid Map with obstacles

Example 1: Fibonacci squence

Just run the Fibonacci/EVAL_fibo.m file to compare run-time of the following three methods:

1. Fibo using Recursive method
2. Fibo using Dynamic programming
3. Fibo using Matrix Exponentiation (Fastest method)

MATLAB function

1. Fibonacci/Fibo_R.m: Fibonacci with Recursive approach:

   • Time Complexity: O(2^n)
   • Space Complexity: O(2^n)

2. Fibonacci/Fibo_DP.m: Fibonacci with Dynamic programming (Memoization):

   • Time Complexity: O(n)
   • Space Complexity: O(n)

3. Fibonacci/Fibo_M.m: Fibonacci with Matrix Exponentiation:

   • Time Complexity: O(log(n))

Example 2: Find number of path in the Grid Map with obstacles

Just run the Grid Path/EVAL_grid_path.m file to compare run-time of the following two methods:

1. Count number of path using Recursive method
2. Count number of path using Dynamic Programming

Usage:

clc, clear

% Define Map (Grid Path)
Map = zeros(15,10);
Map(3,5) = 1;
Map(6,7) = 1;
Map(7,3) = 1;

% Visualize Map (Grid Path)
MapView(Map)
%%
tic;
N1 = GridPath_R(Map, 1,1)
toc;

tic;
N2 = GridPath_DP(Map, 1,1)
toc;

Grid map is as follows:

N1 = 475550
Elapsed time is 8.417751 seconds.

N2 = 475550
Elapsed time is 0.002251 seconds.

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