Tool to search path in a number pyramid. Path search in a pyramid triangle allows to find the shortest path or the longest path by traversing the graph (tree) from the root to its leaves or from the bottom to the top.

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Tool to search path in a number pyramid. Path search in a pyramid triangle allows to find the shortest path or the longest path by traversing the graph (tree) from the root to its leaves or from the bottom to the top.

Answers to Questions

How to find the shortest path?

One has to traverse the pyramid (or the triangle) from top to bottom, adding values that gave a the smallest total respecting a single rule : one can only go to one of the two numbers immediately below.

...5... ..4.8.. .9.5.2. 1.2.7.6

2nd line: 5+4 = 9 or 5+8 = 13, choose the lowest, the path 5->4.

3rd line: 4+9 = 13 or 4+5 = 9, choose the lowest, the path 4->5.

4th line: 5+2 = 7 or 5+7 = 12, choose the lowest, the path 5->2.

Finally, the shortest path route is 5->4->5->2 (which is 16 long).

How to find the longest path?

One has to traverse the pyramid from top to bottom, as for the shortest pah, but by adding values that gave the highest total.

How to count possible paths?

Total number of path in a pyramid of height \( H \) is given by the formula : $$ 2^{H-1} $$

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Source code

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