Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. In a complete binary tree, what is the maximum number of nodes at level 'h'?

A. 2^h
B. 2^(h+1) - 1
C. h^2
D. h!

Solution

In a complete binary tree, the maximum number of nodes at level 'h' is 2^h.

Correct Answer: A — 2^h

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Q. In a complete binary tree, what is the relationship between the number of nodes and the height of the tree?

A. Nodes = 2^height
B. Nodes = 2^(height + 1) - 1
C. Nodes = height^2
D. Nodes = height!

Solution

In a complete binary tree, the number of nodes is given by the formula Nodes = 2^(height + 1) - 1.

Correct Answer: B — Nodes = 2^(height + 1) - 1

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Q. In a complete binary tree, what is the relationship between the number of nodes and the height?

A. Height = log(n)
B. Height = n
C. Height = n/2
D. Height = n^2

Solution

In a complete binary tree, the height is approximately log(n), where n is the number of nodes.

Correct Answer: A — Height = log(n)

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Q. In a complete binary tree, what is the time complexity of DFS?

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

Solution

In a complete binary tree, the time complexity of DFS is O(n) as it visits every node once.

Correct Answer: B — O(n)

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Q. In a depth-first search, what happens when a node is visited?

A. It is added to the queue.
B. It is marked as visited and all its adjacent nodes are explored.
C. It is removed from the graph.
D. It is added to the stack.

Solution

In DFS, when a node is visited, it is marked as visited and all its adjacent nodes are explored.

Correct Answer: B — It is marked as visited and all its adjacent nodes are explored.

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Q. In a double-ended queue (deque), which operations can be performed at both ends?

A. Enqueue only
B. Dequeue only
C. Enqueue and Dequeue
D. None

Solution

A double-ended queue (deque) allows both enqueue and dequeue operations to be performed at both ends, making it more flexible than a standard queue.

Correct Answer: C — Enqueue and Dequeue

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Q. In a doubly linked list, how do you delete a node given only a pointer to that node?

A. Set next and previous pointers
B. Traverse from head
C. Use a stack
D. Not possible

Solution

In a doubly linked list, you can delete a node by adjusting the next and previous pointers of the adjacent nodes.

Correct Answer: A — Set next and previous pointers

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Q. In a doubly linked list, how many pointers does each node contain?

A. One
B. Two
C. Three
D. Four

Solution

Each node in a doubly linked list contains two pointers: one to the next node and one to the previous node.

Correct Answer: B — Two

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Q. In a doubly linked list, what is the time complexity for deleting a node given a pointer to that node?

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

Solution

Deletion of a node in a doubly linked list can be done in O(1) time if you have a pointer to the node.

Correct Answer: A — O(1)

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Q. In a doubly linked list, what is the time complexity of deleting a node given a pointer to that node?

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

Solution

If you have a pointer to the node to be deleted, you can adjust the pointers of the adjacent nodes in constant time, so the time complexity is O(1).

Correct Answer: A — O(1)

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Q. In a doubly linked list, what is the time complexity of inserting a new node after a given node?

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

Solution

Inserting a new node after a given node in a doubly linked list involves changing a few pointers, which takes constant time, hence O(1).

Correct Answer: A — O(1)

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Q. In a dynamic programming approach, what is the primary technique used to optimize recursive solutions?

A. Memoization
B. Backtracking
C. Greedy Method
D. Divide and Conquer

Solution

Memoization is the technique used in dynamic programming to store the results of expensive function calls and reuse them when the same inputs occur again.

Correct Answer: A — Memoization

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Q. In a dynamic programming solution for the Longest Common Subsequence (LCS), what does the DP table represent?

A. The length of the LCS
B. The characters of the LCS
C. The indices of the LCS
D. The number of subsequences

Solution

The DP table in LCS represents the length of the longest common subsequence between two strings.

Correct Answer: A — The length of the LCS

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Q. In a graph represented as an adjacency list, what is the space complexity of storing the graph?

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

Solution

The space complexity of storing a graph in an adjacency list is O(V + E), where V is the number of vertices and E is the number of edges.

Correct Answer: C — O(V + E)

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Q. In a graph represented as an adjacency list, what is the space complexity?

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

Solution

The space complexity of a graph represented as an adjacency list is O(V + E), where V is the number of vertices and E is the number of edges.

Correct Answer: A — O(V + E)

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Q. In a graph represented by an adjacency list, what is the space complexity?

A. O(V)
B. O(E)
C. O(V + E)
D. O(V * E)

Solution

The space complexity of a graph represented by an adjacency list is O(V + E), where V is the number of vertices and E is the number of edges.

Correct Answer: C — O(V + E)

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Q. In a graph with V vertices and E edges, what is the time complexity of DFS?

A. O(V)
B. O(E)
C. O(V + E)
D. O(V * E)

Solution

DFS has a time complexity of O(V + E) as it visits each vertex and edge once.

Correct Answer: C — O(V + E)

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Q. In a graph, if all edges have the same weight, which algorithm can be used to find the shortest path?

A. Dijkstra's algorithm
B. Breadth-First Search (BFS)
C. Depth-First Search (DFS)
D. A* Search

Solution

When all edges have the same weight, Breadth-First Search (BFS) can be used to find the shortest path.

Correct Answer: B — Breadth-First Search (BFS)

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Q. In a graph, if there are multiple paths to a node, how does Dijkstra's algorithm determine which path to take?

A. It chooses the path with the most edges
B. It chooses the path with the least weight
C. It randomly selects a path
D. It chooses the first path it encounters

Solution

Dijkstra's algorithm always chooses the path with the least cumulative weight to ensure the shortest path is found.

Correct Answer: B — It chooses the path with the least weight

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Q. In a graph, if there are multiple paths to reach a node, how does Dijkstra's algorithm choose the path?

A. It chooses the path with the maximum weight
B. It chooses the path with the minimum weight
C. It chooses the first path it encounters
D. It randomly selects a path

Solution

Dijkstra's algorithm always chooses the path with the minimum weight to ensure the shortest path is found.

Correct Answer: B — It chooses the path with the minimum weight

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Q. In a graph, if you want to check for cycles, which traversal method is more suitable?

A. BFS
B. DFS
C. Both are equally suitable
D. Neither can check for cycles

Solution

DFS is more suitable for cycle detection as it can track back edges effectively.

Correct Answer: B — DFS

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Q. In a graph, if you want to check if there is a path between two nodes, which traversal method would be more suitable?

A. BFS
B. DFS
C. Both are equally suitable
D. Neither is suitable

Solution

Both BFS and DFS can be used to check if there is a path between two nodes, but BFS is generally preferred for finding the shortest path.

Correct Answer: C — Both are equally suitable

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Q. In a graph, if you want to find the shortest path in an unweighted graph, which traversal method would you use?

A. DFS
B. BFS
C. Dijkstra's Algorithm
D. A* Search

Solution

BFS is used to find the shortest path in an unweighted graph because it explores all nodes at the present depth before moving on.

Correct Answer: B — BFS

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Q. In a graph, which traversal method uses a queue data structure?

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

Solution

BFS (Breadth-First Search) uses a queue to keep track of the next vertex to visit.

Correct Answer: B — BFS

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Q. In a linked list, what is the time complexity of inserting an element at the beginning?

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

Solution

Inserting at the beginning of a linked list is a constant time operation, hence O(1).

Correct Answer: C — O(1)

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Q. In a priority queue implemented with a binary heap, what is the time complexity for inserting an element?

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

Solution

Inserting an element into a binary heap takes O(log n) time due to the need to maintain the heap property after the insertion.

Correct Answer: B — O(log n)

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Q. In a priority queue implemented with a binary heap, what is the time complexity of inserting an element?

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

Solution

Inserting an element into a priority queue implemented with a binary heap has a time complexity of O(log n) due to the need to maintain the heap property.

Correct Answer: B — O(log n)

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Q. In a queue implemented using a linked list, what operation is performed to add an element?

A. Push
B. Enqueue
C. Pop
D. Dequeue

Solution

The operation to add an element to a queue is called 'enqueue'.

Correct Answer: B — Enqueue

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Q. In a queue implemented using a linked list, what operation is performed to remove an element?

A. Pop
B. Dequeue
C. Shift
D. Remove

Solution

In a queue, the operation to remove an element is called 'dequeue', which removes the front element.

Correct Answer: B — Dequeue

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Q. In a queue implemented using an array, what happens when the array is full?

A. Overflow error
B. Underflow error
C. Elements are overwritten
D. Queue shrinks

Solution

When a queue implemented using an array is full, it results in an overflow error as no more elements can be added.

Correct Answer: A — Overflow error

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Data Structures & Algorithms

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