Printing Pyramid Puzzle

Question

Derive an algorithm for printing a pyramid with all possible combination such that lightest and smallest person lie on top of pyramid and heaviest and biggest person as a base

For Example :

Person A 80kg 140 cms

Person B 90kg 150 cms

Person C 100kg 160 cms

Person D 100kg 170 cms

Person E 150kg 180 cms

Person F 160kg 185 cms

  A
 B C
D E F

Note: Person with height and weight larger than other person cannot lie on top of that person Its not mandotory for every person to be part of pyramid structure

Answer 1

Here's a rough idea.

Construct a graph in a way that an directed edge goes from node X to Y if X > Y (both components) and there's no such Z that X > Z > Y, for your example

       / C \
F -> E       B -> A
       \ D /

Then construct all trees of hight 1, and recursively construct the rest like so:

Mark all used nodes in the tree (initially, just one node) For putting a person X under another 2 persons Y Z you can only use persons that in the graph are under Y Z

use all permutations and recursively repeat until you can construct no more