Follow questions have been asked in GATE CS exam.

**1 In a heap with n elements with the smallest element at the root, the 7th smallest element can be found in time (GATE CS 2003)**

a) Θ(n log n)

b) Θ(n)

c) Θ(log n)

d) Θ(1)

Answer(d)

The 7th smallest element must be in first 7 levels. Total number of nodes in any Binary Heap in first 7 levels is at most 1 + 2 + 4 + 8 + 16 + 32 + 64 which is a constant. Therefore we can always find 7th smallest element in Θ(1) time.

2. Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree? (GATE CS 2003)

a) 7 5 1 0 3 2 4 6 8 9

b) 0 2 4 3 1 6 5 9 8 7

c) 0 1 2 3 4 5 6 7 8 9

d) 9 8 6 4 2 3 0 1 5 7

Answer (c)

In-order traversal of a BST gives elements in increasing order. So answer c is correct without any doubt.

3. Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operation take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m >= 1, define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S. The average stack-life of an element of this stack is (GATE CS 2003)

a) n(X+ Y)

b) 3Y + 2X

c) n(X + Y)-X

d) Y + 2X

Answer(c)

We can easily arrive at the result by taking few examples.

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