Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. If a binary search algorithm returns -1, what does it indicate?

A. The element is found
B. The element is not in the array
C. The array is empty
D. The array is sorted

Solution

A return value of -1 typically indicates that the searched element is not present in the array.

Correct Answer: B — The element is not in the array

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Q. If a binary search is performed on a sorted array of size n, what is the space complexity?

A. O(1)
B. O(n)
C. O(log n)
D. O(n log n)

Solution

The space complexity of binary search is O(1) when implemented iteratively, as it uses a constant amount of space.

Correct Answer: A — O(1)

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Q. If a binary search is performed on an array of 32 elements, how many iterations will it take in the worst case?

A. 4
B. 5
C. 6
D. 7

Solution

The worst-case number of iterations is log2(32) = 5.

Correct Answer: C — 6

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Q. If a binary search is performed on an array of size 16, how many comparisons are needed in the worst case?

A. 4
B. 5
C. 6
D. 7

Solution

The maximum number of comparisons needed is log2(16) = 4, but since we start counting from 0, it takes 5 comparisons.

Correct Answer: D — 7

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Q. If a binary search is performed on an array of size 16, how many comparisons will be made in the worst case?

A. 4
B. 8
C. 16
D. 5

Solution

In the worst case, binary search will make log2(16) = 4 comparisons.

Correct Answer: D — 5

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Q. If a binary search is performed on an array of size 16, how many comparisons will it take in the worst case?

A. 4
B. 8
C. 16
D. 5

Solution

In the worst case, binary search will take log2(16) = 4 comparisons, but since we start counting from 0, it will take 5 comparisons.

Correct Answer: D — 5

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Q. If a binary tree has 'n' nodes, what is the maximum height of the tree?

A. n
B. log n
C. n/2
D. n-1

Solution

The maximum height of a binary tree occurs when the tree is skewed (like a linked list), resulting in a height of n.

Correct Answer: A — n

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Q. If a binary tree has 15 nodes, what is the maximum height of the tree?

A. 15
B. 4
C. 3
D. 5

Solution

The maximum height of a binary tree with 15 nodes occurs when the tree is skewed, which can have a height of 15.

Correct Answer: D — 5

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Q. If a binary tree has a height of 'h', what is the minimum number of nodes it can have?

A. h
B. h + 1
C. 2^h - 1
D. 2^h

Solution

The minimum number of nodes in a binary tree of height h is h + 1, which occurs in a skewed tree.

Correct Answer: B — h + 1

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Q. If a binary tree has a height of h, what is the maximum number of nodes it can have?

A. 2^h - 1
B. 2^h
C. h^2
D. h!

Solution

The maximum number of nodes in a binary tree of height h is 2^h - 1, which occurs in a complete binary tree.

Correct Answer: A — 2^h - 1

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Q. If a binary tree has n nodes, what is the maximum number of leaf nodes it can have?

A. n
B. n/2
C. n/3
D. n/2 + 1

Solution

In a binary tree, the maximum number of leaf nodes can be n, which occurs in a degenerate tree.

Correct Answer: A — n

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Q. If a binary tree is balanced, what is the maximum height of the tree in terms of the number of nodes 'n'?

A. O(n)
B. O(log n)
C. O(n log n)
D. O(1)

Solution

In a balanced binary tree, the maximum height is O(log n), as the tree is structured to minimize height.

Correct Answer: B — O(log n)

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Q. If a graph has 5 vertices and 10 edges, what is the maximum number of edges it can have?

A. 5
B. 10
C. 20
D. 25

Solution

In a simple undirected graph, the maximum number of edges is given by the formula V(V-1)/2, which for 5 vertices is 5(5-1)/2 = 10.

Correct Answer: C — 20

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Q. If a graph has 5 vertices and 10 edges, what is the maximum number of iterations Dijkstra's algorithm will perform?

A. 5
B. 10
C. 15
D. 20

Solution

Dijkstra's algorithm will perform at most V iterations, where V is the number of vertices. In this case, it will perform 5 iterations.

Correct Answer: A — 5

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Q. If a graph has 5 vertices and 10 edges, what is the maximum time complexity of Dijkstra's algorithm using an adjacency matrix?

A. O(10)
B. O(5^2)
C. O(5 log 5)
D. O(10 + 5^2)

Solution

Using an adjacency matrix, the time complexity of Dijkstra's algorithm is O(V^2), which in this case is O(5^2) or O(25).

Correct Answer: B — O(5^2)

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Q. If a graph has 5 vertices and 7 edges, what is the maximum number of edges in a simple undirected graph?

A. 10
B. 12
C. 15
D. 20

Solution

In a simple undirected graph, the maximum number of edges is given by the formula V(V-1)/2. For 5 vertices, it is 5(5-1)/2 = 10.

Correct Answer: A — 10

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Q. If a graph has 5 vertices and 7 edges, what is the maximum number of edges in a complete graph with 5 vertices?

A. 10
B. 12
C. 15
D. 20

Solution

In a complete graph with V vertices, the maximum number of edges is given by V*(V-1)/2. For 5 vertices, it is 5*(5-1)/2 = 10.

Correct Answer: A — 10

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Q. If a graph has 5 vertices and 7 edges, what is the maximum number of edges it can have?

A. 10
B. 15
C. 20
D. 25

Solution

In a simple undirected graph, the maximum number of edges is given by the formula V(V-1)/2, which for 5 vertices is 5(5-1)/2 = 10.

Correct Answer: B — 15

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Q. If a graph has 5 vertices and 7 edges, what is the maximum number of iterations Dijkstra's algorithm will perform?

A. 5
B. 7
C. 10
D. 12

Solution

Dijkstra's algorithm will perform at most V iterations, where V is the number of vertices. In this case, it will perform 5 iterations.

Correct Answer: A — 5

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Q. If a graph has a cycle, which traversal method can detect it?

A. Only BFS
B. Only DFS
C. Both BFS and DFS
D. Neither BFS nor DFS

Solution

DFS can detect cycles in a graph by keeping track of visited nodes and checking for back edges.

Correct Answer: B — Only DFS

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Q. If a graph has negative edge weights, which algorithm can be used instead of Dijkstra's algorithm?

A. Prim's Algorithm
B. Kruskal's Algorithm
C. Bellman-Ford Algorithm
D. Floyd-Warshall Algorithm

Solution

The Bellman-Ford algorithm can be used instead of Dijkstra's algorithm when the graph has negative edge weights, as it can handle such cases.

Correct Answer: C — Bellman-Ford Algorithm

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Q. If a graph has negative weight edges, which algorithm can be used instead of Dijkstra's?

A. Prim's algorithm
B. Kruskal's algorithm
C. Bellman-Ford algorithm
D. A* algorithm

Solution

The Bellman-Ford algorithm can handle graphs with negative weight edges, unlike Dijkstra's algorithm.

Correct Answer: C — Bellman-Ford algorithm

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Q. If a graph has negative weight edges, which algorithm should be used instead of Dijkstra's algorithm?

A. Prim's algorithm
B. Kruskal's algorithm
C. Bellman-Ford algorithm
D. Floyd-Warshall algorithm

Solution

The Bellman-Ford algorithm should be used instead of Dijkstra's algorithm when the graph has negative weight edges, as it can handle such cases.

Correct Answer: C — Bellman-Ford algorithm

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Q. If a graph has negative weight edges, which algorithm should be used instead of Dijkstra's?

A. Prim's algorithm
B. Kruskal's algorithm
C. Bellman-Ford algorithm
D. A* algorithm

Solution

The Bellman-Ford algorithm can handle graphs with negative weight edges, unlike Dijkstra's algorithm.

Correct Answer: C — Bellman-Ford algorithm

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Q. If a graph has V vertices and E edges, what is the space complexity of Dijkstra's algorithm using an adjacency list?

A. O(V)
B. O(E)
C. O(V + E)
D. O(V^2)

Solution

The space complexity of Dijkstra's algorithm using an adjacency list is O(V + E) due to the storage of vertices and edges.

Correct Answer: C — O(V + E)

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Q. If a graph has V vertices and E edges, what is the space complexity of Dijkstra's algorithm?

A. O(V)
B. O(E)
C. O(V + E)
D. O(V^2)

Solution

The space complexity of Dijkstra's algorithm is O(V + E) due to the storage of the graph's adjacency list and the distance array.

Correct Answer: C — O(V + E)

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Q. If a graph has V vertices and E edges, what is the worst-case time complexity of Dijkstra's algorithm using an adjacency matrix?

A. O(V^2)
B. O(E log V)
C. O(V + E)
D. O(V^3)

Solution

When using an adjacency matrix, the worst-case time complexity of Dijkstra's algorithm is O(V^2) because it requires checking all vertices for the minimum distance.

Correct Answer: A — O(V^2)

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Q. If a graph is represented using an adjacency matrix, what is the time complexity of BFS?

A. O(V + E)
B. O(V^2)
C. O(E)
D. O(V log V)

Solution

For an adjacency matrix representation, BFS has a time complexity of O(V^2) due to the need to check all possible edges.

Correct Answer: B — O(V^2)

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Q. If a queue is implemented using two stacks, what is the time complexity of dequeue operation in the worst case?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

In the worst case, the dequeue operation can take O(n) time because all elements may need to be transferred from one stack to another.

Correct Answer: B — O(n)

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Q. If a sorted array has 16 elements, how many comparisons will binary search make in the worst case?

A. 4
B. 5
C. 16
D. 8

Solution

In the worst case, binary search will make log2(16) = 4 comparisons.

Correct Answer: B — 5

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Data Structures & Algorithms

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