Problem 1049. Path of least resistance

Created by Paul Peeling

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Find the length of the shortest path through the matrix from the top left to bottom right corner. You may move right, down, or diagonally right-down one element at a time. The length of the path is the sum of the elements you pass through.

E.g.

 M = [*8      6      10      10     4     7     7      7
       9     *1      10      5      9     0     8      2
       1      3     *2       8      8     8     7      7
       9      5      10     *1     *10   *9    *4     *0 ];

>> shortest_path(M)

ans =

The shortest path through this matrix has length 35. Each element along the path is marked with a *

Solve

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Last Solution submitted on Mar 18, 2020

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Zikobrelli on 10 Feb 2014

Cool problem. Optimal solutions sometimes appear if moving up is enabled.

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Solution 167237

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Vitaly Lavrukhin on 23 Nov 2012

functional programming approach

Jean-Marie Sainthillier on 8 Sep 2013

Congratulations.
Honestly, I have difficulties with this kind of algorithm. I have the feeling that you only increment i or j, but at the end you check all the matrix.

Vitaly Lavrukhin on 9 Sep 2013

Thanks, Jean-Marie. This solution uses recursive calls of the function. So all elements of the matrix are processed.
If you would like to learn more about functional programming principles, I recommend 'Functional Programming Principles in Scala' course by Martin Odersky at Coursera. It starts soon. Actually, I wrote this solution after taking the course a year ago. It is very interesting to look at the same problem from different points of view.

Jean-Marie Sainthillier on 10 Sep 2013

Thanks for your advice.

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Problem 1049. Path of least resistance

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Problem 1049. Path of least resistance

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