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Path Search in a Pyramid Triangle

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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Path Search in a Pyramid Triangle - dCode

Tag(s) : Graph Theory

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Path Search in a Pyramid Triangle

Path search in a Pyramid of Numbers

See also: Pascal's Triangle — Calculator

Answers to Questions

How to find the shortest path?

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

Example: ...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 (from top to bottom) 5->4->5->2 (which is 16 long) or 2->5->4->5 (from bottom to top)

How to find the longest path?

Go through the pyramid from top to bottom, as for the shortest path, but by adding values that gave the highest total.

How to count possible paths?

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

Source code

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