Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. In binary search, what happens to the search space after each comparison?

A. It doubles
B. It halves
C. It remains the same
D. It increases linearly

Solution

After each comparison, the search space is halved, which is the key to its efficiency.

Correct Answer: B — It halves

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Q. In binary search, what is the formula to find the middle index?

A. (low + high) / 2
B. (low + high) / 2 + 1
C. (low + high) / 2 - 1
D. low + high

Solution

The middle index is calculated using (low + high) / 2.

Correct Answer: A — (low + high) / 2

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Q. In binary search, what is the purpose of calculating the mid index?

A. To find the maximum element
B. To divide the array into two halves
C. To check for duplicates
D. To sort the array

Solution

The mid index is calculated to divide the array into two halves for further searching.

Correct Answer: B — To divide the array into two halves

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Q. In Depth-First Search (DFS), which data structure is primarily used to keep track of the vertices to be explored?

A. Queue
B. Stack
C. Array
D. Linked List

Solution

DFS uses a stack (either explicitly or via recursion) to keep track of the vertices.

Correct Answer: B — Stack

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Q. In Depth-First Search (DFS), which data structure is primarily used?

A. Queue
B. Stack
C. Array
D. Hash Table

Solution

DFS uses a stack to keep track of the nodes to be explored, either explicitly or through recursion.

Correct Answer: B — Stack

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Q. In DFS, what is the maximum depth of recursion for a graph with V vertices?

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

Solution

The maximum depth of recursion in DFS can go up to O(V) in the worst case, where V is the number of vertices.

Correct Answer: A — O(V)

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Q. In Dijkstra's algorithm, how is the next node to process selected?

A. By selecting the node with the highest degree
B. By selecting the node with the lowest tentative distance
C. By selecting the node that was added last
D. By selecting a random node

Solution

The next node to process in Dijkstra's algorithm is selected based on the lowest tentative distance, ensuring the shortest path is explored first.

Correct Answer: B — By selecting the node with the lowest tentative distance

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Q. In Dijkstra's algorithm, what condition must be met for a vertex to be added to the set of visited vertices?

A. It must have the smallest edge weight
B. It must be the last vertex processed
C. It must be connected to the source
D. It must have the highest degree

Solution

In Dijkstra's algorithm, a vertex is added to the set of visited vertices when it has the smallest tentative distance from the source vertex.

Correct Answer: A — It must have the smallest edge weight

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Q. In Dijkstra's algorithm, what data structure is commonly used to keep track of the nodes to be explored?

A. Array
B. Stack
C. Priority Queue
D. Linked List

Solution

A priority queue is used in Dijkstra's algorithm to efficiently retrieve the next node with the smallest tentative distance.

Correct Answer: C — Priority Queue

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Q. In Dijkstra's algorithm, what data structure is commonly used to keep track of the minimum distance to each vertex?

A. Array
B. Stack
C. Priority Queue
D. Linked List

Solution

A priority queue is used in Dijkstra's algorithm to efficiently retrieve the vertex with the smallest distance.

Correct Answer: C — Priority Queue

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Q. In Dijkstra's algorithm, what data structure is commonly used to select the next node to process?

A. Stack
B. Queue
C. Priority Queue
D. Array

Solution

A priority queue is used in Dijkstra's algorithm to efficiently select the node with the smallest tentative distance.

Correct Answer: C — Priority Queue

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Q. In Dijkstra's algorithm, what data structure is commonly used to select the next node with the smallest tentative distance?

A. Array
B. Stack
C. Priority Queue
D. Linked List

Solution

A priority queue is used in Dijkstra's algorithm to efficiently retrieve the node with the smallest tentative distance.

Correct Answer: C — Priority Queue

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Q. In Dijkstra's algorithm, what data structure is primarily used to keep track of the shortest path estimates?

A. Array
B. Linked List
C. Stack
D. Priority Queue

Solution

A priority queue is used in Dijkstra's algorithm to efficiently retrieve the vertex with the smallest distance estimate.

Correct Answer: D — Priority Queue

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Q. In Dijkstra's algorithm, what data structure is primarily used to keep track of the minimum distance from the source vertex?

A. Array
B. Stack
C. Queue
D. Priority Queue

Solution

A priority queue is used in Dijkstra's algorithm to efficiently retrieve the vertex with the smallest distance from the source.

Correct Answer: D — Priority Queue

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Q. In Dijkstra's algorithm, what data structure is typically used to keep track of the shortest path estimates?

A. Array
B. Linked List
C. Stack
D. Priority Queue

Solution

A priority queue is used to keep track of the shortest path estimates in Dijkstra's algorithm, allowing efficient retrieval of the next vertex with the smallest distance.

Correct Answer: D — Priority Queue

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Q. In Dijkstra's algorithm, what does the 'tentative distance' represent?

A. The actual shortest distance found
B. The estimated distance to the destination
C. The distance from the source to the current node
D. The maximum distance in the graph

Solution

The 'tentative distance' represents the current best-known distance from the source node to the current node being processed.

Correct Answer: C — The distance from the source to the current node

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Q. In Dijkstra's algorithm, what does the priority queue store?

A. All vertices
B. Only visited vertices
C. Only unvisited vertices
D. Only the shortest path vertices

Solution

The priority queue in Dijkstra's algorithm stores only the unvisited vertices, allowing the algorithm to efficiently select the next vertex with the smallest tentative distance.

Correct Answer: C — Only unvisited vertices

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Q. In Dijkstra's algorithm, what is the purpose of the 'visited' set?

A. To store all vertices
B. To keep track of the shortest path
C. To avoid processing the same vertex multiple times
D. To store the distances from the source

Solution

The 'visited' set is used to keep track of the vertices that have already been processed to avoid processing the same vertex multiple times, ensuring efficiency.

Correct Answer: C — To avoid processing the same vertex multiple times

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Q. In dynamic programming, what does the term 'overlapping subproblems' mean?

A. Subproblems that can be solved independently
B. Subproblems that share sub-subproblems
C. Subproblems that are never reused
D. Subproblems that require sorting

Solution

Overlapping subproblems refer to subproblems that share sub-subproblems, allowing for reuse of results.

Correct Answer: B — Subproblems that share sub-subproblems

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Q. In dynamic programming, what does the term 'overlapping subproblems' refer to?

A. Problems that can be solved in parallel
B. Subproblems that are solved multiple times
C. Subproblems that are independent
D. Problems that require sorting

Solution

Overlapping subproblems refer to subproblems that are solved multiple times in the process of solving a larger problem.

Correct Answer: B — Subproblems that are solved multiple times

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Q. In dynamic programming, what does the term 'state' refer to?

A. The current value of a variable
B. A specific subproblem
C. The final solution
D. The input size

Solution

In dynamic programming, a 'state' refers to a specific subproblem that is being solved.

Correct Answer: B — A specific subproblem

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Q. In dynamic programming, what is memoization?

A. A technique to store results of expensive function calls
B. A method to sort data efficiently
C. A way to represent data in a tree structure
D. A technique to optimize space complexity

Solution

Memoization is a 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 — A technique to store results of expensive function calls

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Q. In dynamic programming, what is the 'optimal substructure' property?

A. The optimal solution can be constructed from optimal solutions of its subproblems
B. The problem can be solved in linear time
C. The solution requires sorting the input data
D. The problem can be solved using a greedy approach

Solution

The optimal substructure property means that the optimal solution to a problem can be constructed from the optimal solutions of its subproblems.

Correct Answer: A — The optimal solution can be constructed from optimal solutions of its subproblems

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Q. In dynamic programming, what is the main advantage of using memoization?

A. Reduces space complexity
B. Avoids redundant calculations
C. Improves sorting speed
D. Simplifies code structure

Solution

Memoization helps avoid redundant calculations by storing the results of expensive function calls.

Correct Answer: B — Avoids redundant calculations

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Q. In dynamic programming, what is the primary advantage of using a bottom-up approach over a top-down approach?

A. Easier to implement
B. Less memory usage
C. Faster execution time
D. More intuitive

Solution

The bottom-up approach typically uses less memory than the top-down approach because it avoids the overhead of recursive calls.

Correct Answer: B — Less memory usage

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Q. In dynamic programming, what is the primary purpose of the 'table' or 'array' used?

A. To store intermediate results
B. To sort data
C. To track function calls
D. To manage memory allocation

Solution

The primary purpose of the table or array in dynamic programming is to store intermediate results to avoid redundant calculations.

Correct Answer: A — To store intermediate results

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Q. In dynamic programming, what is the purpose of a state transition equation?

A. To define the base case
B. To describe how to move from one state to another
C. To optimize the algorithm
D. To sort the data

Solution

A state transition equation describes how to move from one state to another in the dynamic programming solution, defining the relationship between subproblems.

Correct Answer: B — To describe how to move from one state to another

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Q. In dynamic programming, what is the purpose of memoization?

A. To sort data
B. To store intermediate results
C. To optimize space complexity
D. To reduce time complexity

Solution

Memoization is used to store intermediate results of subproblems to avoid redundant calculations and improve efficiency.

Correct Answer: B — To store intermediate results

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Q. In dynamic programming, what is the purpose of the 'base case'?

A. To initialize the DP table
B. To define the recursive function
C. To handle edge cases
D. To optimize the algorithm

Solution

The base case is used to initialize the DP table and provide starting values for the recursive relations.

Correct Answer: A — To initialize the DP table

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Q. In dynamic programming, what is the purpose of the 'state'?

A. To represent the final solution
B. To store the results of subproblems
C. To define the problem constraints
D. To track the number of iterations

Solution

In dynamic programming, the 'state' represents the results of subproblems, which are used to build up the solution to the overall problem.

Correct Answer: B — To store the results of subproblems

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Data Structures & Algorithms

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