Circus Sorting Problem

gistfile1.txt

A circus is designing a tower routine consisting of people standing atop one another’s shoulders. For 
practical and aesthetic reasons, each person must be both shorter and lighter than the person below him or 
her. Given the heights and weights of each person in the circus, write a method to compute the largest 
possible number of people in such a tower.

EXAMPLE:
Input (ht, wt): (65, 100) (70, 150) (56, 90) (75, 190) (60, 95) (68, 110)
Output: The longest tower is length 6 and includes from top to bottom: (56, 90) (60,95) (65,100) (68,110) 
(70,150) (75,190)

Proposed Algorithm:
 The proposed algorithm is as follows
 1. Create a Directed graph from the given list of persons
 2. Each vertex will represent a Person and there will be an edge between two vertices iff source  
 vertex(person) can stand on destination vertex(person)
 3. Once a graph is created, now find the longest path in the graph. This should give the solution for the
 problem. 

 To implement a graph, we can make use of adjacency matrix
 Check the link: http://en.wikipedia.org/wiki/Adjacency_matrix