Guys this problem generated lot of discussion in computer science as ist 
Euler Problem 
 
as it  involves maths stuff rather then considering tree (it wont work check 
below link for detail ) or applying computer science . Also  problem is 
already famous (Euler problem ) as we have to find the maximum sum in 
triangle we have given a big triangle which has many small triangle only 
thing u need to know a triangle has 3 vertexes so that you can approach :) 

and a detailed description,explaination & solution you can find here using 
bottom up iterative approach :)

http://shashank7s.blogspot.com/2011/04/project-euler-problem-67-finding.html

let me know if i missed something or any other approach to solve it 
Shashank Mani 
Computer Science
Birla Institute of Technlogy,Mesra
 

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