Question

How many different paths are there between the node in the lower left corner and the...

How many different paths are there between the node in the lower left corner and the node in
the upper right corner of a square mesh with n nodes in each row and column? Justify your answer.

Homework Answers

Answer #1

Solution for the problem is provided below, please comment if any doubts:

Answer:

Explanation:

The given problem is to find the number of roots between lower left corner and the upper right corner node.

Each side has “n” nodes thus each side has “n-1” edges.

Thus the shortest distance between the given source and destination is “2*(n-1)”.

Now to reach from lower left to upper right, we need to follow two directions, either right or up, it is clear that we need to take “n-1” right steps and “n-1” up steps.

Now in the “2*(n-1)” length paths there should be “n-1” right and “n-1” up moves.

The number of possible combination of such nodes is:

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