Top 10 Greedy Algorithms for Competitive Programming
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Competitive programming is a thrilling arena where efficiency and speed are paramount. One of the most powerful strategies to solve problems quickly is using greedy algorithms. These algorithms make locally optimal choices at each step, aiming to find a global optimum. Whether you’re preparing for coding competitions or technical interviews, mastering greedy algorithms is essential. To help you get started, we’ve compiled a list of the Top 10 Greedy Algorithms every competitive programmer should know.
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What Are Greedy Algorithms?
Greedy algorithms are a class of algorithms that make the best possible choice at each step to solve a problem. They are widely used in optimization problems where the goal is to find the most efficient solution. Unlike dynamic programming, which considers all possible choices, greedy algorithms focus on immediate gains, often leading to simpler and faster solutions.
However, greedy algorithms don’t always guarantee the optimal solution. They work best when the problem exhibits the greedy choice property and optimal substructure. For example, problems like the Fractional Knapsack or Huffman Coding are classic examples where greedy algorithms shine.
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Top 10 Greedy Algorithms for Competitive Programming
1. Activity Selection Problem
The Activity Selection Problem is a classic example of a greedy algorithm. The goal is to select the maximum number of activities that don’t overlap, given their start and end times.
- Approach: Sort activities by their finish time and select the first activity. Then, iteratively choose the next activity that starts after the last selected activity ends.
- Time Complexity: O(n log n) due to sorting.
- Use Case: Scheduling tasks, resource allocation.
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2. Fractional Knapsack Problem
The Fractional Knapsack Problem involves selecting items with given weights and values to maximize the total value in a knapsack of limited capacity.
- Approach: Sort items by their value-to-weight ratio in descending order. Add items to the knapsack until it’s full, splitting the last item if necessary.
- Time Complexity: O(n log n) due to sorting.
- Use Case: Resource optimization, logistics.
Also Read: Top 10 Distributed System Design Challenges
3. Huffman Coding
Huffman Coding is a lossless data compression algorithm that uses a greedy approach to assign variable-length codes to characters based on their frequencies.
- Approach: Build a Huffman tree by repeatedly combining the two least frequent nodes. Assign shorter codes to more frequent characters.
- Time Complexity: O(n log n) using a priority queue.
- Use Case: Data compression, file storage.
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4. Dijkstra’s Algorithm
Dijkstra’s Algorithm is a greedy algorithm used to find the shortest path from a source node to all other nodes in a weighted graph.
- Approach: Use a priority queue to always select the node with the smallest tentative distance. Update distances for adjacent nodes.
- Time Complexity: O(V^2) for adjacency matrix, O(E + V log V) for adjacency list.
- Use Case: Network routing, GPS navigation.
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5. Prim’s Algorithm
Prim’s Algorithm is a greedy method to find the Minimum Spanning Tree (MST) of a connected, undirected graph.
- Approach: Start with an arbitrary node and iteratively add the shortest edge connecting the MST to a new node.
- Time Complexity: O(V^2) for adjacency matrix, O(E + V log V) for adjacency list.
- Use Case: Network design, clustering.
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6. Kruskal’s Algorithm
Kruskal’s Algorithm is another greedy algorithm for finding the MST, but it works differently from Prim’s.
- Approach: Sort all edges by weight and iteratively add the smallest edge that doesn’t form a cycle.
- Time Complexity: O(E log E) due to sorting and union-find operations.
- Use Case: Network design, circuit wiring.
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7. Coin Change Problem
The Coin Change Problem involves finding the minimum number of coins required to make a given amount.
- Approach: Use the largest denomination first and work downwards.
- Time Complexity: O(n) for the greedy approach (if denominations allow).
- Use Case: Vending machines, financial transactions.
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8. Job Sequencing Problem
The Job Sequencing Problem involves scheduling jobs with deadlines and profits to maximize total profit.
- Approach: Sort jobs by profit in descending order and schedule them as late as possible.
- Time Complexity: O(n log n) due to sorting.
- Use Case: Task scheduling, project management.
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9. Egyptian Fraction
The Egyptian Fraction problem involves representing a fraction as a sum of unique unit fractions.
- Approach: Use the largest possible unit fraction at each step.
- Time Complexity: O(log n) for each step.
- Use Case: Mathematical computations, number theory.
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10. Interval Graph Coloring
The Interval Graph Coloring problem involves coloring intervals such that no two overlapping intervals share the same color.
- Approach: Sort intervals by start time and assign colors greedily.
- Time Complexity: O(n log n) due to sorting.
- Use Case: Scheduling, resource allocation.
Also Read: Ultimate Guide to DSA & Design in 2025
FAQs
1. What is the main advantage of greedy algorithms?
Greedy algorithms are simple, efficient, and often provide quick solutions to optimization problems.
2. When do greedy algorithms fail?
Greedy algorithms fail when the problem requires considering future choices or when the greedy choice doesn’t lead to a global optimum.
3. How do greedy algorithms differ from dynamic programming?
Greedy algorithms make locally optimal choices, while dynamic programming considers all possible choices.
4. Can greedy algorithms be used in real-world applications?
Yes, greedy algorithms are widely used in applications like Huffman Coding, Dijkstra’s Algorithm, and Prim’s Algorithm.
5. How can I practice greedy algorithms effectively?
Practice problems from platforms like LeetCode, Codeforces, and HackerRank. Enroll in our DSA course: Join Now.
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