How does dynamic programming optimize the Matrix Chain Multiplication algorithm?
- By applying the greedy algorithm.
- By employing a randomized algorithm.
- By reusing solutions to overlapping subproblems.
- By using a divide and conquer approach.
Dynamic programming optimizes the Matrix Chain Multiplication algorithm by reusing solutions to overlapping subproblems. It breaks down the problem into smaller subproblems and solves them only once, storing the solutions in a table to avoid redundant calculations.
How does Quick Sort handle duplicate elements during its sorting process?
- Duplicate elements are always placed at the beginning of the array
- Duplicate elements are handled through careful partitioning, ensuring equal distribution
- Duplicate elements are ignored and excluded from the sorting process
- Duplicate elements lead to an error in Quick Sort
Quick Sort handles duplicate elements by ensuring careful partitioning during the sorting process. The algorithm is designed to distribute equal elements on both sides of the pivot, maintaining efficiency and accuracy in sorting, even when duplicates are present.
Separate chaining resolves collisions by storing collided elements in _______ associated with each index of the hash table.
- Arrays
- Linked lists
- Queues
- Stacks
Separate chaining resolves collisions by using linked lists associated with each index of the hash table. When a collision occurs, the collided elements are stored in a linked list at the respective index, allowing multiple elements to coexist at the same position.
How does merge sort divide and conquer a given list/array?
- It multiplies each element by a random factor
- It randomly splits the list into parts
- It recursively divides the list into halves, sorts each half, and then merges them back together.
- It selects the smallest element and moves it to the beginning
Merge sort divides a given list or array by recursively breaking it into halves until individual elements. Then, it sorts each segment and merges them back together to construct a sorted array.
In a social network application, you need to find the shortest path between two users based on mutual friends. Would BFS be suitable for this task, or would another algorithm be more appropriate?
- A* Algorithm
- Breadth-First Search (BFS)
- Depth-First Search (DFS)
- Dijkstra's Algorithm
BFS would be suitable for finding the shortest path based on mutual friends in a social network. BFS explores neighbors first, making it effective for finding mutual connections. Other algorithms like DFS may not guarantee the shortest path and Dijkstra's Algorithm is more suitable for weighted graphs, which may not be relevant in a social network context.
In selection sort, what is the main operation performed in each iteration?
- Doubling the size of the sorted portion
- Finding the minimum element in the unsorted portion and swapping it with the first element of the unsorted part
- Multiplying elements in the unsorted portion
- Randomly rearranging elements in the unsorted portion
The main operation in each iteration of selection sort is finding the minimum element in the unsorted portion and swapping it with the first element of the unsorted part. This gradually builds the sorted portion.
What is the main disadvantage of the basic implementation of Quick Sort?
- Limited applicability
- Not in-place
- Poor performance on small datasets
- Unstable sorting
The main disadvantage of the basic implementation of Quick Sort is its poor performance on small datasets. While efficient for large datasets, it may not be the best choice for smaller ones due to overhead in the recursive calls and partitioning.
Quick Sort can handle duplicate elements efficiently due to its _______ step.
- Merging
- Partitioning
- Searching
- Sorting
Quick Sort handles duplicate elements efficiently due to its partitioning step, where elements are rearranged such that duplicates end up together, making the subsequent steps more efficient.
What is the time complexity of the dynamic programming approach for solving the longest common substring problem?
- O(n log n)
- O(n)
- O(n^2)
- O(n^3)
The time complexity of the dynamic programming approach for the longest common substring problem is O(n^2), where 'n' is the length of the input strings. This is achieved by using a 2D table to store intermediate results and avoiding redundant computations.
How does the A* search algorithm differ from other search algorithms like Depth-First Search and Breadth-First Search?
- A* combines both the depth-first and breadth-first approaches
- A* considers only the breadth-first approach
- A* considers only the depth-first approach
- A* has no similarities with Depth-First and Breadth-First Search
A* search algorithm differs from others by combining elements of both depth-first and breadth-first approaches. It uses a heuristic to guide the search, unlike the purely blind search of Depth-First and Breadth-First Search.