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.
Path Search in a Pyramid Triangle - dCode
Tag(s) : Graph Theory
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Path Search in a Pyramid Triangle
Path search in a Pyramid of Numbers
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?
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
dCode retains ownership of the source code of the script Path Search in a Pyramid Triangle online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Path Search in a Pyramid Triangle script for offline use on PC, iPhone or Android, ask for price quote on contact page !
Questions / Comments
Version Française
or 
