Algorithmic Problem Solving Essentials

What is the purpose of asymptotic notation in algorithm analysis?

• To provide a step-by-step guide for coding algorithms.

• To compare the aesthetics of different algorithms.

• To calculate the exact runtime of an algorithm.

• To describe the efficiency and scalability of algorithms.

Explain the brute force approach in problem solving.

• The brute force approach is a technique that focuses on theoretical analysis rather than practical application.

• The brute force approach involves using advanced algorithms to optimize problem-solving.

• The brute force approach is a method that relies on intuition and experience to find solutions.

• The brute force approach is a method of solving problems by trying all possible solutions until the correct one is found.

What is the time complexity of selection sort in the worst case?

• O(n log n)

• O(n)

• O(log n)

• O(n^2)

Describe the divide and conquer strategy in algorithm design.

• Divide and conquer requires solving all subproblems simultaneously.

• It is a method that combines all subproblems into one before solving them.

• Divide and conquer is an algorithm design strategy that divides a problem into smaller subproblems, solves them independently, and combines their solutions.

• Divide and conquer is a strategy that only focuses on the largest subproblem.

How does the master method help in solving recurrences?

• It provides a graphical representation of recurrences.

• It only applies to linear recurrences.

• It eliminates the need for any mathematical calculations.

• The master method helps in solving recurrences by providing a structured approach to analyze and determine their time complexity.

What is the main advantage of merge sort over bubble sort?

• Merge sort is easier to implement than bubble sort.

• Merge sort is more efficient with a better time complexity.

• Bubble sort is faster for large datasets than merge sort.

• Merge sort requires less memory than bubble sort.

In which scenario would you prefer using quick sort over merge sort?

• When the input is nearly sorted.

• When stability is required.

• When memory efficiency is a priority.

• When sorting small datasets.

What is the average time complexity of binary search?

• O(1)

• O(log n)

• O(n log n)

• O(n)

How does bucket sort differ from radix sort?

• Bucket sort sorts all elements in a single pass without using buckets.

• Radix sort distributes elements into groups based on their values before sorting.

• Bucket sort processes digits of numbers in order like radix sort.

• Bucket sort distributes elements into buckets and sorts each bucket, while radix sort processes digits of numbers in order.

What are the key differences between linear search and binary search?

• Linear search is faster than binary search for large datasets.

• Linear search is O(n) and unsorted; binary search is O(log n) and requires a sorted list.

• Linear search is O(log n) and requires a sorted list.

• Binary search is O(n) and can be used on unsorted lists.