Problem 45426. The Tortoise and the Hare - 02

Created by Asif Newaz

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{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Previous problem</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\"><w:r><w:t>&lt;https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01</w:t></w:r></w:hyperlink><w:r><w:t>&gt;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Suppose in an infinitely long line, the tortoise is standing in position 0.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>From that place, it can move in both +ve and -ve direction. The condition is that, in i-th jump, it can move i step forward or backward.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>So one possible scenario can be -</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 0 [i=1] --- 1 step forward\n 1 [i=2] --- 2 step forward\n 3 [i=3] --- 3 step forward\n 6 [i=4] --- 4 step backward\n 2 [i=5] --- 5 step forward\n 7 [i=6] --- 6 step backward\n 1 [i=7] --- 7 step forward\n 8]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If you look carefully, you'll find that -- If the tortoise moves this way, it'll always be able to reach any destination (x).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The question is what is the minimum number of moves it'll take to reach destination x.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For example --</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ if x=8\n >> in the above example, it takes 7 steps\n >> but if it moves this way -- [0,-1,1,4,8] -- steps required = 4.]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>So 4 is the optimum way.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Previous problem <a href = "https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01">https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01</a>Suppose in an infinitely long line, the tortoise is standing in position 0.From that place, it can move in both +ve and -ve direction. The condition is that, in i-th jump, it can move i step forward or backward.So one possible scenario can be -<pre> 0 [i=1] --- 1 step forward
 1 [i=2] --- 2 step forward
 3 [i=3] --- 3 step forward
 6 [i=4] --- 4 step backward
 2 [i=5] --- 5 step forward
 7 [i=6] --- 6 step backward
 1 [i=7] --- 7 step forward
 8</pre>If you look carefully, you'll find that -- If the tortoise moves this way, it'll always be able to reach any destination (x).The question is what is the minimum number of moves it'll take to reach destination x.For example --<pre> if x=8
 &gt;&gt; in the above example, it takes 7 steps
 &gt;&gt; but if it moves this way -- [0,-1,1,4,8] -- steps required = 4.</pre>So 4 is the optimum way.

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Problem 45426. The Tortoise and the Hare - 02

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