Circus arrangment

A circus is designing an act consisting of a tower 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 her. Given the heights and weights of each person in the circus, what is the largest possible number of people in such a tower?

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)


  1. Denote each person as a vertex in a graph G. There is a directed edge from vertex u to vertex v if person u can stand on top of v. Problem now reduces to finding the longest path in G.


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