Introduction
Learn the origin of the word algorithm, its definition, characteristics and design strategies.
📚 Programming Tutorial
Design and Analysis of Algorithms
The word algorithm comes from the name of a Persian, Abu Ja'far Muhammad ibn Musa al-Khwarizmi, dubbed the father of algebra (al-jabr). An algorithm is a series of step-by-step instructions that aim to solve a particular problem.
DAA Tutorial Index
37 Topics📘 Basics
What is an Algorithm
Understand what an algorithm is and how step-by-step instructions solve a problem.
📊 Performance Analysis
Space Complexity
Learn instruction space, data space and how the space requirement of an algorithm is calculated.
Time Complexity
Learn how the running time of an algorithm is estimated.
📈 Asymptotic Notations
Big 'oh'(O)
Learn the upper bound (worst case) notation used to describe growth of an algorithm.
Big Omega(Ω)
Learn the lower bound (best case) notation.
Big Theta(Θ)
Learn the tight bound notation that bounds a function from above and below.
✂️ Divide-and-Conquer
Introduction
Learn the divide-and-conquer strategy of splitting a problem into smaller subproblems.
Binary Search
Search for an element efficiently in a sorted array by repeatedly dividing the search interval into two halves.
Quick Sort
Learn how Quick Sort uses a pivot element to partition an array and recursively sort smaller subarrays.
Merge Sort
Learn how Merge Sort divides an array into smaller subarrays, sorts them recursively, and merges them into a sorted array.
Strassen’s Matrix Multiplication
Learn how Strassen’s algorithm multiplies two matrices efficiently by reducing the number of recursive multiplications.
🔗 Disjoint Sets
Disjoint Set Operations
Understand the basic operations performed on disjoint sets, including creating sets, finding representatives, and combining sets.
Union and Find Algorithms
Learn how the Union and Find algorithms identify set representatives and merge two disjoint sets efficiently.
Priority Queue
Understand how a priority queue stores elements based on priority and supports efficient insertion and deletion operations.
Heaps
Learn the structure of binary heaps, including min-heaps, max-heaps, heap properties, insertion, and deletion operations.
Heapsort
Learn how the Heapsort algorithm uses a binary heap to sort elements efficiently in ascending or descending order.
↩️ Backtracking
General Method of Backtracking
Learn the general backtracking approach using state-space trees, promising functions, and systematic solution exploration.
N-Queens Problem
Learn how to place N queens on an N × N chessboard so that no two queens attack each other using backtracking.
Sum of Subsets Problem
Learn how to find subsets of a given set whose elements add up to a specified target sum using backtracking.
Graph Coloring
Understand how to assign colors to the vertices of a graph so that no two adjacent vertices have the same color.
Hamiltonian Cycles
Learn how to find a cycle in a graph that visits every vertex exactly once and returns to the starting vertex using backtracking.
🧠 Dynamic Programming
General Method of Dynamic Programming
Understand the general approach of dynamic programming using optimal substructure, overlapping subproblems, recurrence relations, and tabulation.
Optimal Binary Search Tree
Learn how to construct a binary search tree with minimum expected search cost using the probabilities of successful and unsuccessful searches.
0/1 Knapsack Problem
Learn how to select items with given weights and profits to maximize total profit without exceeding the knapsack capacity using dynamic programming.
All Pairs Shortest Path Problem
Learn how to find the shortest paths between every pair of vertices in a weighted graph using the Floyd-Warshall algorithm.
Traveling Salesperson Problem
Learn how to find the minimum-cost tour that visits every city exactly once and returns to the starting city using dynamic programming.
Reliability Design
Understand how dynamic programming helps design highly reliable systems by selecting components and configurations to maximize overall system reliability within a given budget.
⚙️ Greedy Method
General Method of Greedy Method
Understand the general approach of greedy algorithms, including candidate selection, feasibility checking, objective functions, and solution construction.
Job Sequencing with Deadlines
Learn how to schedule jobs with deadlines and profits to maximize the total profit by selecting and arranging jobs efficiently.
Knapsack Problem
Learn how to maximize the total profit by selecting items with given weights and values without exceeding the knapsack capacity using the greedy approach.
Minimum Cost Spanning Trees
Learn how to construct a spanning tree with minimum total edge weight using Prim’s and Kruskal’s algorithms.
Single Source Shortest Path Problem
Learn how to find the shortest paths from a single source vertex to all other vertices in a weighted graph using Dijkstra’s algorithm.
🔍 Basic Traversal and Search Techniques
Techniques for Binary Trees
Learn binary tree traversal techniques including preorder, inorder, postorder, and level order traversal with suitable examples.
Techniques for Graphs
Understand graph traversal techniques including Breadth First Search (BFS) and Depth First Search (DFS) to explore vertices and edges.
Connected Components
Learn how to identify maximal connected subgraphs in an undirected graph using graph traversal techniques.
Biconnected Components
Understand biconnected components in an undirected graph and identify subgraphs that remain connected even after removing any single vertex.
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