Mastering Algorithms and Data Structures

What is the time complexity of binary search?

• O(n)

• O(n log n)

• O(log n)

• O(1)

Explain the difference between quicksort and mergesort.

• Quicksort is always slower than Mergesort.

• Quicksort is stable and guarantees O(n) time complexity.

• Quicksort is faster on average and uses less memory, while Mergesort is stable and guarantees O(n log n) time complexity.

• Mergesort is faster on average and uses less memory.

How can Dijkstra's algorithm be applied to find the shortest path in a graph?

• Dijkstra's algorithm randomly selects nodes to explore without considering distance.

• Dijkstra's algorithm uses a depth-first search to find the shortest path.

• Dijkstra's algorithm finds the shortest path by using a priority queue to explore nodes based on the smallest cumulative distance.

• Dijkstra's algorithm requires all edge weights to be negative to function correctly.

What is the base case in a recursive function, and why is it important?

• The base case is the first function call in recursion.

• The base case is a random value chosen during recursion.

• The base case is a loop that runs until a certain condition is met.

• The base case is a condition that stops recursion, preventing infinite loops and allowing for a result.

Describe the concept of memoization in dynamic programming.

• Memoization is a method for storing data in a database.

• Memoization is a technique that stores previously computed results to optimize recursive algorithms in dynamic programming.

• Memoization is a way to visualize dynamic programming algorithms.

• Memoization is a technique used to compress data for faster access.