Design and Analysis of Algorithm MCQ

Correct Answer: A. Ω (Omega) notation describes the best-case performance of an algorithm.

Correct Answer: A. Binary search divides the search space into two equal parts at each step.

Correct Answer: A. Quick Sort is an example of a divide and conquer algorithm.

Correct Answer: B. The time complexity of merge sort is O(n log n).

Correct Answer: A. Choosing a pivot is a key step in the Quick Sort algorithm.

Correct Answer: A. Prim’s algorithm makes the greedy choice by selecting the vertex with the smallest edge cost.

Correct Answer: C. The 0/1 knapsack problem is solved using dynamic programming, not the greedy approach.

Correct Answer: A. Kruskal’s algorithm selects the smallest edge that does not form a cycle.

Correct Answer: A. Matrix Chain Multiplication is a problem that can be solved using dynamic programming.

Correct Answer: A. Memoization is a technique used to store the results of subproblems to avoid recalculating them.

Correct Answer: A. The Longest Common Subsequence algorithm is based on dynamic programming.

Correct Answer: C. The dynamic programming solution to the 0/1 knapsack problem has a time complexity of O(nW), where W is the capacity of the knapsack.

Correct Answer: A. The N-Queens Problem is often solved using the backtracking technique.

Correct Answer: A. Backtracking explores all possible solutions by recursively trying each possibility.

Correct Answer: A. The Travelling Salesman Problem can be solved using the branch and bound technique.

Correct Answer: A. Branch and bound prunes the solution space by eliminating branches that do not provide better solutions.

Correct Answer: A. Randomized Quick Sort is an example of a randomized algorithm.

Correct Answer: A. In the best-case scenario, the time complexity of linear search is O(1), when the target element is the first in the list.

Correct Answer: A. Recurrence relations help analyze the time complexity of recursive algorithms.

Correct Answer: A. The Travelling Salesman Problem is a classic example of an NP-Complete problem.

Correct Answer: A. The Cook-Levin theorem was the first proof that SAT is NP-Complete.

Correct Answer: A. P is the class of problems that are both in NP and can be solved in polynomial time.

Correct Answer: A. Approximation algorithms are typically used for NP-Hard problems where finding an exact solution is computationally infeasible.

Correct Answer: A. Bubble Sort repeatedly swaps adjacent elements if they are in the wrong order.

Correct Answer: B. The best-case time complexity of insertion sort is O(n), which occurs when the input array is already sorted.

Correct Answer: A. Merge sort has a time complexity of O(n log n) because it divides the array and then merges the sorted subarrays.

Correct Answer: A. Counting Sort is a non-comparative sorting algorithm, as it sorts elements by counting occurrences rather than comparing elements.

Correct Answer: A. Binary search has O(log n) complexity because the search space is halved with each comparison.

Correct Answer: A. AVL trees are self-balancing, which ensures that operations like search, insert, and delete take logarithmic time.

Correct Answer: A. Breadth-First Search (BFS) explores all adjacent vertices before moving to the next level.

Correct Answer: A. In DFS, the graph is traversed by exploring as far as possible along each branch before backtracking.

Correct Answer: A. Kruskal’s algorithm selects the smallest edge that does not form a cycle.

Correct Answer: A. The time complexity of Prim’s algorithm when implemented using a binary heap is O(E log V), where E is the number of edges and V is the number of vertices.

Correct Answer: A. The Bellman-Ford algorithm can handle graphs with negative weight edges.

Correct Answer: A. The time complexity of the Floyd-Warshall algorithm is O(V^3), where V is the number of vertices.

Correct Answer: A. The Edmonds-Karp algorithm improves the Ford-Fulkerson method by using breadth-first search to find augmenting paths.

Correct Answer: A. The goal of maximum bipartite matching is to pair vertices from two sets such that the number of edges is maximized.

Correct Answer: A. Network flow algorithms are often used in optimization problems such as logistics and traffic flow.

Correct Answer: A. In a max heap, the largest element is always at the root.

Correct Answer: A. Fibonacci heaps allow faster decrease-key operations compared to binary heaps.

Correct Answer: A. Union by rank helps to reduce the height of the tree in union-find operations.

Correct Answer: A. In a trie, each node represents a character of a string.

Correct Answer: A. A Binary Indexed Tree (BIT) is used for performing efficient range sum queries.

Correct Answer: A. The Traveling Salesman Problem is often solved using approximation algorithms due to its NP-Hard nature.

Correct Answer: A. The performance ratio is the ratio of the approximate solution’s value to the optimal solution’s value.

Correct Answer: A. Las Vegas algorithms always produce a correct result but may take a variable amount of time.

Correct Answer: A. NP problems can be verified in polynomial time, even though they may not be solvable in polynomial time.

Correct Answer: A. Grover’s algorithm is used to search an unsorted database in O(√n) time.

Correct Answer: A. Quantum algorithms, such as Grover’s, offer significant speedups in problems involving large-scale data search.

Correct Answer: A. In evolutionary algorithms, a population of solutions evolves over time through processes like selection, crossover, and mutation.