Question

I have a matrix 5×5 (25 nodes). Is there a formula that I can find the shortest distance between 2 node i and j in the matrix ?

Note: distance between 1 node and its neighbor is 1 unit.

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In my observation, there are many paths with the same distance between those 2 nodes i and j
so i’m not sure if there is a formula to calculate the shortest one? I appreciate if anybody can help. Thanks.

Ex:

* * * i *
* * * * *
* * * * *
* * * * *
* j * * *

Shortest distance between i and j is 6 units.

Answer 1

I believe what you need is the L1 distance, also called the Manhattan distance. So if your two nodes have matrix indices (i1,j1) and (i2,j2), then the shortest distance between them is |i1-i2|+|j1-j2|.

This is of course, assuming you can’t move diagonally.