binary search tree - What is the worst case complexity of the given program? -

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program takes input balanced binary search tree n leaf nodes , computes value of function g(x) each node x. if cost of computing g(x) min{no. of leaf-nodes in left-subtree of x, no. of leaf-nodes in right-subtree of x} worst-case time complexity of program is

my solution :

for each internal node maximum cost n/2. every leaf node cost zero.

and number of internal nodes balanced binary tree : leaf nodes - 1

so total cost :

n/2 * (n-1)

o(n^2)

am right?

i have different solution. worst case tree happen complete tree got right , therefore number of leaf nodes n/2.

but case root node.

for nodes @ level 1: total cost 2*n/4=n/2

for nodes @ level 2: total cost 4*n/8=n/2

and on till last level log(n) , cost again = n/2

total cost therefore in worst case =n/2*log (n) = o(n*logn), in complete tree can happen last level not filled in asymptotic analysis ignore such intricate details.


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