GATE CS 2014 Set 3 — Question 49
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Question
Suppose we have a balanced binary search tree holding numbers. We are given two numbers and and wish to sum up all the numbers in that lie between and . Suppose there are such numbers in . If the tightest upper bound on the time to compute the sum is , the value of is _____.
Correct answer
110 to 110
Solution
To sum all numbers between and in a standard balanced Binary Search Tree (BST) without augmentation (like subtree sums):
Calculation:
.
1.Search for : This takes time to find the first node .
2.Traverse: Perform an in-order traversal from that node until we reach a node . Since there are nodes in the range, we will visit nodes. In a BST, finding the successor takes amortized constant time, or simply traversing nodes takes time (the accounts for the initial search and the path back up/down).
The total time complexity is .Matching this with the given form :- The term corresponds to , so .
- The term corresponds to , so .
Calculation:
.
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