Radhika Nanda

Algorithm Viva Questions and Answers Algorithm Viva Questions and Detailed Answers 2. Divide and Conquer Approach Q1. What is the Divide and Conquer strategy? It is an algorithmic paradigm that breaks a problem into subproblems, solves them recursively, and then combines their results. Examples include Merge Sort, Quick Sort, and Binary Search. Q2. Explain Finding Minimum and Maximum using Divide and Conquer. The array is split into halves. Recursively, min and max of each half are found, and finally the overall min and max are determined using a comparison of results from the halves. Q3. Describe Merge Sort. Merge Sort divides the list into halves, recursively sorts them, and merges the sorted halves. It has a time complexity of O(n log n) and is stable but not in-place. Q4. Explain Quick Sort. Quick Sort selects a pivot, partitions the array such that elements lesser are on the left and greater on the right, then recursively sort...

Top 10 Questions on Sorting Algorithms and Divide and Conquer Approach Top 10 Questions on Sorting Algorithms and Divide and Conquer Approach Understanding basic sorting algorithms and the divide and conquer approach is crucial for every computer science student. Below are the most frequently asked questions with answers from Module 1: Introduction to Algorithms . 1. What is Selection Sort and how does it work? Selection Sort is a comparison-based algorithm that divides the array into a sorted and unsorted part. It repeatedly selects the minimum element from the unsorted section and moves it to the beginning. Time Complexity: O(n²) Stable: No In-place: Yes 2. What are the steps involved in Insertion Sort? Insertion Sort builds the sorted array one element at a time by inserting each new element into its correct position among the previously sorted elements. Best Case: O(n) Worst Case: O(n²) Stable: Ye...

Branch and Bound Algorithm: A Comprehensive Overview  Introduction to Branch and Bound Branch and Bound (B&B) is an algorithmic paradigm for solving combinatorial optimization problems. It systematically enumerates candidate solutions by searching through the solution space in a state space tree fashion, while using bounding functions to prune suboptimal branches.  Core Principles 1. Branching The algorithm divides the problem into smaller subproblems (branches), creating a tree structure of possible solutions. Each node represents a partial solution.  2. Bounding For each node, the algorithm computes: - A lower bound (for minimization problems) - An upper bound (for maximization problems) These bounds estimate the best possible solution in that subtree. 3. Pruning Nodes are eliminated when: - Their bound indicates they cannot contain the optimal solution (bound pruning) - They represent infeasible solutions (feasibility pruning) - They represent complete solutions wo...

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Prim's Algorithm: Building the Cheapest Network Purpose : Prim’s Algorithm is used to find the Minimum Spanning Tree (MST) of a connected, weighted, undirected graph. It connects all vertices with the minimum total edge weight and no cycles . Imagine you're designing a water pipeline to connect several houses. You want to use the least amount of pipe possible. Prim's Algorithm helps you find the shortest network to connect everything. What Is Prim's Algorithm? (The Definition) Prim's Algorithm is a way to find the shortest set of connections between points in a network. It starts with one point and adds the closest points until everything is connected, without creating any loops. Prims algorithm and Kruskal algorithm are based on Minimum Spanning Tree. So, we will see what is minimum spanning tree. What is MST (Minimum Spanning Tree)? An MST or Minimum Spanning Tree is a special kind of subgraph in a connected, weighted, undirected graph . It connects all the ...

Kruskal's Algorithm: Building a Minimum Spanning Tree the Easy Way Imagine you have a bunch of islands, and you want to build bridges to connect all of them so that you can travel between any two islands. Building bridges costs money, and you want to do it in the cheapest way possible. That's where Kruskal's algorithm comes in handy! It's a clever method to find the most cost-effective way to connect all the islands (or nodes in a network) using the fewest possible bridges (or edges). The resulting network is called a Minimum Spanning Tree (MST) . What Exactly is Kruskal's Algorithm? (The Definition) Kruskal's algorithm is a greedy algorithm used in graph theory to find a minimum spanning tree for a weighted, undirected graph. This means it finds a subset of the edges that connects all the vertices (nodes) together, without any cycles, and with the minimum possible total edge weight. Key Terms: Graph: A collection of vertices (nodes) connected by edges. Weig...

  Divide and Conquer Approach  This strategy works like a skilled general dividing an army - it breaks complex problems into smaller, more manageable sub-problems. Each sub-problem is solved independently, and their solutions are cleverly combined to solve the original problem. Think of it like solving a jigsaw puzzle: you separate edge pieces first, then work on different sections before assembling the complete picture. It's particularly effective for sorting algorithms (like merge sort) and mathematical computations (like fast Fourier transforms). The approach shines when sub-problems don't overlap, allowing for efficient parallel processing. However, the combination phase can sometimes become complex, adding overhead to the solution process.    Greedy Method Approach  The greedy approach is like a determined treasure hunter who always picks the shiniest gem at each step, hoping this leads to the richest haul. It makes locally optimal choices at each decision ...

    What is Dijkstra's Algorithm? (Simple Explanation)  Definition of Dijkstra’s Algorithm: Dijkstra’s Algorithm is a shortest path algorithm used to find the minimum distance from a starting node to all other nodes in a graph with non-negative edge weights.  It is single source shortest path algorithm. It is commonly used in routing and navigation systems to find the quickest path between locations. Dijkstra's Algorithm is a way to find the  shortest path  between one starting point and all other points in a network, like cities connected by roads or computers linked in a network. Imagine you’re trying to find the quickest way to travel from your home to all your friends’ houses. Dijkstra’s algorithm helps you figure that out. Here’s how it works: You start at the source point (like your home), and from there, you check all the nearby places you can go. You pick the one with the smallest travel time. Then from that place, you look at where else you ca...