PREVIOUS YEAR SOLVED PAPERS - August 2016 Paper 3

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31. Consider the problem of a chain < A₁, A₂, A₃, A₄> of four matrices. Suppose that the dimensions of the matrices A₁, A₂, A₃ and A₄ are 30 × 35, 35 × 15, 15 × 5 and 5 × 10 respectively. The minimum number of scalar multiplications needed to compute the product A₁A₂A₃A₄ is ____.

Answer
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Array

Option : C
Explanation :

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32. Consider a hash table of size m = 10000, and the hash function h(K) = floor (m(KA mod 1)) for A = ( √(5) – 1)/2. The key 123456 is mapped to location ______.

Answer
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Option : B
Explanation :
Given hash function: h(K) = floor (m (K*A mod 1)) where A = ( √(5) – 1)/2
h(123456) = floor(10000 * (123456 * (√5 − 1) / 2) mod 1)
= floor(10000 * (76300.004115 mod 1)
= floor(10000 * (.004115))
= 41.15
= 41
So, option (B) is correct.

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33. Consider a weighted complete graph G on the vertex set {ν₁, ν₂, .... ν_n} such that the weight of the edge (ν_i, ν_j) is 4 | i – j|. The weight of minimum cost spanning tree of G is :

Answer
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Option : C
Explanation :

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34. A priority queue is implemented as a max-heap. Initially, it has five elements. The level-order traversal of the heap is as follows:
20, 18, 15, 13, 12
Two new elements ‘10’ and ‘17’ are inserted in the heap in that order. The level-order traversal of the heap after the insertion of the element is:

Answer
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Option : D
Explanation :
Initially we have:

When we insert 10 and 17:

We have to maintain max-heap, so:

The level-order traversal of the heap after the insertion of the element is 20, 18, 17, 13, 12, 10, 15 So, option (D) is correct.

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35. If there are n integers to sort, each integer has d digits, and each digit is in the set {1, 2, ..., k}, radix sort can sort the numbers in:

Answer
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Option : B
Explanation :
If there are n integers to sort, each integer has d digits, and each digit is in the set {1, 2, ..., k}, radix sort can sort the numbers in O(d (n + k)). For more information Refer:Radix Sort Option (B) is correct.

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