Question 1 : What will be the worst case time complexity of code to find sum in given query range (l,r) in an array of size n with q number of such queries?
1. O(n)
2. O(q)
3. O(n*q)
4. O(n+q)
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Question 2 : Total how many iterations are required to find the sum of elements in a given range of (l,r) in an array of size n when we use square root optimization?
1. vn
2. 2*vn
3. 3*vn
4. n*vn
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Question 3 : What will be the worst case time complexity of finding the sum of elements in a given range of (l,r) in an array of size n when we use square root optimization?
1. O(n)
2. O(l+r)
3. O(vn)
4. O(r-l)
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Question 4 : What will be the worst case time complexity of finding the sum of elements in a given range of (l,r) in an array of size n?
1. O(n)
2. O(l+r)
3. O(l-r)
4. O(r-l)
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Question 5 : What will be the output if quickselect algorithm is applied to the array arr={1,5,4,3,7} with k given as 4?
1. 1
2. 3
3. 4
4. 5
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Question 6 : Most Efficient Time Complexity of Topological Sorting is? (V – number of vertices, E – number of edges)
1. O(V + E)
2. O(V)
3. O(E)
4. None of the mentioned
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Question 7 : Which of the following is false?
1. The spanning trees do not have any cycles
2. MST have n – 1 edges if the graph has n edges
3. Edge e belonging to a cut of the graph if has the weight smaller than any other edge in the same cut, then the edge e is present in all the MSTs of the graph
4. Removing one edge from the spanning tree will not make the graph disconnected
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Question 8 : Consider the graph shown below. Which of the following are the edges in the MST of the given graph?
1. (a-c)(c-d)(d-b)(d-b)
2. (c-a)(a-d)(d-b)(d-e)
3. (a-d)(d-c)(d-b)(d-e)
4. (c-a)(a-d)(d-c)(d-b)(d-e)
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Question 9 : If all the weights of the graph are positive, then the minimum spanning tree of the graph is a minimum cost subgraph.
1. True
2. False
3.
4.
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Question 10 : Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?
1. Every minimum spanning tree of G must contain CD
2. If AB is in a minimum spanning tree, then its removal must disconnect G
3. No minimum spanning tree contains AB
4. G has a unique minimum spanning tree
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