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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 -

Tag(s) : Graph Theory

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# Path Search in a Pyramid Triangle

## Path search in a Pyramid of Numbers

### Counting

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.

### 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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