Greedy Algorithms Last Updated : 28 Mar, 2024 Improve Improve Like Article Like Save Share Report Greedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. In these algorithms, decisions are made based on the information available at the current moment without considering the consequences of these decisions in the future. The key idea is to select the best possible choice at each step, leading to a solution that may not always be the most optimal but is often good enough for many problems. Greedy Algorithms Table of Content What is a Greedy Algorithm? Steps for Creating a Greedy Algorithm Greedy Algorithm Examples Applications of Greedy Algorithm Disadvantages/Limitations of Using a Greedy Algorithm Basics of Greedy Algorithm Standard Greedy Algorithms Greedy Problems on Array Greedy Problems on Operating System Greedy Problems on Graph Approximate Greedy Algorithm for NP Complete Greedy for Special cases of DP Easy Problems on Greedy Algorithm Medium Problems on Greedy Algorithm Hard Problems on Greedy Algorithm What is a Greedy Algorithm? A greedy algorithm is a type of optimization algorithm that makes locally optimal choices at each step with the goal of finding a globally optimal solution. It operates on the principle of “taking the best option now” without considering the long-term consequences. Steps for Creating a Greedy Algorithm: Define the problem: Clearly state the problem to be solved and the objective to be optimized. Identify the greedy choice: Determine the locally optimal choice at each step based on the current state. Make the greedy choice: Select the greedy choice and update the current state. Repeat: Continue making greedy choices until a solution is reached. Greedy Algorithm Examples: Below are some example of Greedy Algorithm: Fractional Knapsack: Optimizes the value of items that can be fractionally included in a knapsack with limited capacity. Dijkstra’s algorithm: Finds the shortest path from a source vertex to all other vertices in a weighted graph. Kruskal’s algorithm: Finds the minimum spanning tree of a weighted graph. Huffman coding: Compresses data by assigning shorter codes to more frequent symbols. Applications of Greedy Algorithm: Below are some applications of Greedy Algorithm: Assigning tasks to resources to minimize waiting time or maximize efficiency. Selecting the most valuable items to fit into a knapsack with limited capacity. Dividing an image into regions with similar characteristics. Reducing the size of data by removing redundant information. Disadvantages/Limitations of Using a Greedy Algorithm: Below are some disadvantages of Greedy Algorithm: Greedy algorithms may not always find the best possible solution. The order in which the elements are considered can significantly impact the outcome. Greedy algorithms focus on local optimizations and may miss better solutions that require considering a broader context. Greedy algorithms are not applicable to problems where the greedy choice does not lead to an optimal solution. Basics of Greedy Algorithm: Introduction to Greedy Algorithm – Data Structures and Algorithm Tutorials Greedy Algorithms (General Structure and Applications) Difference between Greedy Algorithm and Divide and Conquer Algorithm Greedy approach vs Dynamic programming Comparison among Greedy, Divide and Conquer and Dynamic Programming algorithm Standard Greedy Algorithms: Activity Selection Problem Job Sequencing Problem Huffman Coding Huffman Decoding Water Connection Problem Minimum Swaps for Bracket Balancing Egyptian Fraction Policemen catch thieves Fitting Shelves Problem Assign Mice to Holes Greedy Problems on Array: Minimum product subset of an array Maximize array sum after K negations using Sorting Minimum sum of product of two arrays Minimum sum of absolute difference of pairs of two arrays Minimum increment/decrement to make array non-Increasing Sorting array with reverse around middle Sum of Areas of Rectangles possible for an array Largest lexicographic array with at-most K consecutive swaps Partition into two subarrays of lengths k and (N – k) such that the difference of sums is maximum Greedy Problems on Operating System: First Fit algorithm in Memory Management Best Fit algorithm in Memory Management Worst Fit algorithm in Memory Management Shortest Job First Scheduling Job Scheduling with two jobs allowed at a time Program for Optimal Page Replacement Algorithm Greedy Problems on Graph: Kruskal’s Minimum Spanning Tree Prim’s Minimum Spanning Tree Boruvka’s Minimum Spanning Tree Dijkastra’s Shortest Path Algorithm Dial’s Algorithm Minimum cost to connect all cities Max Flow Problem Introduction Number of single cycle components in an undirected graph Approximate Greedy Algorithm for NP Complete: Set cover problem Bin Packing Problem Graph Coloring K-centers problem Shortest superstring problem Approximate solution for Travelling Salesman Problem using MST Greedy for Special cases of DP: Fractional Knapsack Problem Minimum number of coins required Easy Problems on Greedy Algorithm: Split n into maximum composite numbers Buy Maximum Stocks if i stocks can be bought on i-th day Find the minimum and maximum amount to buy all N candies Maximum sum possible equal to sum of three stacks Divide cuboid into cubes such that sum of volumes is maximum Maximum number of customers that can be satisfied with given quantity Minimum rotations to unlock a circular lock Minimum rooms for m events of n batches with given schedule Minimum cost to make array size 1 by removing larger of pairs Minimum cost for acquiring all coins with k extra coins allowed with every coin Minimum increment by k operations to make all elements equal Find minimum number of currency notes and values that sum to given amount Smallest subset with sum greater than all other elements Medium Problems on Greedy Algorithm: Maximum trains for which stoppage can be provided Minimum Fibonacci terms with sum equal to K Divide 1 to n into two groups with minimum sum difference Paper cut into minimum number of squares Minimum difference between groups of size two Connect n ropes with minimum cost Minimum number of Platforms required for a railway/bus station Minimum initial vertices to traverse whole matrix with given conditions Largest palindromic number by permuting digits Find Smallest number with given number of digits and digits sum Lexicographically largest subsequence such that every character occurs at least k times Hard Problems on Greedy Algorithm: Maximum elements that can be made equal with k updates Minimize cash flow among friends Minimum Cost to cut a board into squares Minimum cost to process m tasks where switching costs Minimum time to finish all jobs with given constraints Minimize the maximum difference between the heights of towers Minimum edges to reverse to make path from a source to a destination Find the Largest Cube formed by Deleting minimum Digits from a number Rearrange characters in a string such that no two adjacent are same Rearrange a string so that all same characters become d distance away Quick Links: Learn Data Structure and Algorithms | DSA Tutorial Top 20 Greedy Algorithms Interview Questions ‘Practice Problems’ on Greedy Algorithms ‘Quiz’ on Greedy Algorithms Like Article Suggest improvement Previous Backtracking Algorithm Next Dynamic Programming or DP Share your thoughts in the comments Add Your Comment Please Login to comment...