¶ Greedy Algorithms
¶ Competitive programming
¶ Introduction to Greedy Algorithms: Building the Mindset Behind One of Competitive Programming’s Smartest Strategies
Greedy algorithms have a unique place in competitive programming. They are simple, elegant, surprisingly powerful, and yet—paradoxically—often misunderstood. Many beginners assume greedy solutions are nothing more than picking the “best possible option at each step,” but those who’ve been around long enough know the truth: if you can train your mind to recognize when a greedy choice is safe, you unlock one of the most efficient and satisfying ways to solve problems.
This course of 100 articles is meant to take you far beyond the simplistic description of greediness. We’ll explore the intuition, the pitfalls, the proofs, the patterns, and all the subtle hints that most people overlook. By the end of this journey, greedy thinking won’t feel like guesswork—it will feel like a reliable tool that clicks naturally the moment you see the right kind of structure in a problem.
Before diving into the details in later articles, let’s take a step back and understand what greedy algorithms really are, why they work so beautifully in some cases, and why they fall apart in others.
¶ Why Greedy Algorithms Even Exist
At the heart of every greedy solution is a philosophy:
“If you can make a locally optimal choice that guarantees a globally optimal solution, then you should do it.”
Life itself gives us so many situations where we behave greedily without even thinking:
- You choose the shortest queue at the supermarket to get out faster.
- You pick the closest parking spot to save time.
- You fill your backpack with the lightest items to carry more things.
Sometimes this intuition works perfectly, and sometimes it backfires. Competitive programming is no different. Greedy strategies aren’t random impulses—they’re guided by a deeper logical structure. But when that structure exists, greediness becomes not just correct, but incredibly efficient.
The real art lies in identifying when a problem fits that structure.
¶ The Magic Behind a Greedy Solution
A greedy algorithm succeeds only when a problem has certain hidden properties—properties like optimal substructure, exchangeability, or monotonicity. These terms may sound theoretical at first, but their intuition is very natural.
For example, consider scheduling jobs with deadlines. Intuition says: complete the job with the earliest deadline first. And it turns out this is exactly the right greedy choice. Why? Because missing an early deadline closes more future possibilities than missing a later one.
Or think about building a minimal spanning tree with Kruskal’s algorithm: always pick the smallest remaining edge that doesn’t form a cycle. It feels like a simple rule, but it works because the graph’s structure ensures that choosing the smallest edge available at that moment can never ruin the optimality of the final tree.
The beauty of greedy algorithms lies in these small, trustworthy choices. When you find them, the solution becomes blazingly fast—often linear or O(n log n)—while alternatives like dynamic programming may be far heavier.
¶ Why Greedy Thinking is So Valuable in Competitive Programming
Greedy solutions have two powerful advantages:
-
They are fast—both to write and to run.
A good greedy solution often needs only sorting, scanning, or simple math. -
They are intuitive once you get used to them.
You start seeing patterns: “pick the smallest,” “pick the earliest,” “remove the worst,” “merge the closest,” and so on.
But many people misuse greedy logic because they mistake intuition for correctness. A greedy algorithm is valuable only when supported by reasoning. Part of mastering greedy techniques is learning how to justify why the greedy choice doesn’t harm the global solution.
This course will help you sharpen that sense until you can see greedy structures instantly.
¶ Where Greedy Algorithms Shine
Greedy techniques dominate some of the most common competitive programming themes:
- minimizing or maximizing something using step-by-step optimization,
- interval scheduling and resource allocation,
- choosing edges or weights in graph problems,
- compressing or merging data in optimal ways,
- priority-based selections (huffman coding, Dijkstra’s algorithm),
- problems involving lexicographical decisions,
- distributing tasks under constraints,
- minimizing costs or maximizing efficiency,
- making irreversible decisions while maintaining optimal choices.
You’ll start seeing categories of problems where greedy is not just one solution—it’s the solution.
Some iconic examples include:
- Activity selection
- Fractional knapsack
- Huffman coding
- Minimum spanning trees (Kruskal & Prim)
- Interval merging problems
- Choosing optimal meeting rooms
- Scheduling machines or tasks
- Dijkstra’s algorithm using priority queues
The patterns will become clearer as you progress: sometimes the key lies in sorting, other times in a priority-based selection, and sometimes in always picking the “most extreme” option—smallest, largest, nearest, earliest, and so on.
¶ The Tricky Side of Greedy Solutions
Greedy algorithms can be deceptive. They often produce answers that “seem” right at first glance. Many problems have multiple plausible greedy approaches, and only one of them leads to the correct global optimum.
This is where so many beginners stumble.
Think of the classic 0/1 knapsack problem: the fractional version is perfectly solved by greed—choose the item with the highest value-to-weight ratio. But in the 0/1 variant, the same tactic sometimes fails spectacularly.
Why? Because greedy choices in 0/1 knapsack can block you from choosing a combination that would have given a higher total value. This simple example teaches a crucial lesson:
Greedy is not about choosing the “nicest-looking” option—it’s about choosing the option that never ruins future optimality.
Understanding this difference will change how you approach problems.
As the course progresses, we’ll dissect common greedy traps, learn how to test choices, and develop methods to prove or disprove greedy correctness.
¶ Building the Greedy Mindset
Greedy thinking is like developing a mathematical instinct. It isn’t about memorizing templates; it's about recognizing structures.
Here are some common mindsets you’ll develop through the course:
-
“What is the bottleneck?”
Greedy decisions often revolve around the most restrictive factor. -
“Which choice gives me the most flexibility?”
Greedy correctness often depends on preserving future freedom. -
“Can every non-greedy solution be converted into a greedy one?”
This is part of the “exchange argument,” a powerful conceptual tool. -
“Does the problem guarantee that an optimal solution will use decisions of a specific kind?”
This is where proofs of correctness come from. -
“Is the problem monotonic?”
Many greedy strategies depend on something increasing or decreasing predictably.
As we explore each greedy idea in later articles, these questions—and many more—will start becoming instinctive.
¶ Greedy Algorithms in Real Life
Competitive programming problems often come from real-world systems: scheduling flights, routing deliveries, compressing data, minimizing costs, organizing events, or optimizing resources. Behind many of these are greedy concepts.
You’ll find greedy thinking embedded in:
- CPU scheduling in operating systems
- Network routing
- Data compression formats like JPEG or MP3
- Traffic signal optimization
- Financial planning and investment allocation
- File merging and log consolidation
- Load balancing across servers
- Real-time decision systems
- Priority-based event handling
Learning greedy algorithms isn’t just about contest problems—it’s about learning how to think in situations where decisions are permanent, the pace is fast, and resources are limited.
¶ Why Greedy Algorithms Help You Grow as a Problem Solver
One of the most interesting aspects of greedy algorithms is the mental discipline they teach.
They make you think about:
- global vs. local optimality,
- committing to decisions without backtracking,
- simplicity versus correctness,
- the hidden structure of problems,
- reducing complexity through clever choices,
- the consequences of irreversible steps.
In competitive programming, time matters. You want solutions that run quickly for large constraints. Greedy algorithms often deliver linear or log-linear performance, making them ideal for problems with massive input sizes.
By mastering greedy strategies, you gain not just speed but clarity of thought.
¶ What This 100-Article Course Will Help You Achieve
This introductory article sets the stage. The real journey unfolds across 100 carefully crafted articles that dive into:
- intuitive greedy foundations,
- classical problems and their modern extensions,
- the art of proving greedy correctness,
- exchange argument, matroid theory, and structural guarantees,
- priority-based greedy strategies,
- sorting-driven greedy solutions,
- greedy algorithms for graphs, strings, intervals, and arrays,
- complexity considerations and optimization tricks,
- tricky edge cases that break common intuition,
- comparing greedy vs. dynamic programming,
- hybrid approaches that mix greedy with other paradigms,
- and dozens of fully explored competitive-programming problems.
By the end of the course, greedy algorithms won’t feel like lucky guesses or risky assumptions. They’ll feel like logical, reliable, powerful tools you can confidently apply under pressure.
You’ll develop the ability to look at a problem and instantly recognize patterns like:
- “This smells like an interval scheduling problem.”
- “This wants a sorting-based greedy solution.”
- “This structure guarantees exchangeability.”
- “This monotonic behavior supports a greedy choice.”
- “A priority queue will guide the decisions here.”
- “This can’t be solved greedily because the choices block future solutions.”
That intuition is exactly what separates top competitive programmers from the rest.
¶ The Journey Ahead
Greedy algorithms offer something rare: the combination of intuition and precision. When they work, they work beautifully—giving solutions that are fast, elegant, and easy to implement under timed conditions. When they fail, they teach valuable lessons about the structure of problems and the importance of reasoning.
This course is designed to help you master not just the standard greedy tricks, but the deeper thought processes that define them. Step by step, with each article, you’ll sharpen your understanding until greedy strategies feel as natural as breathing.
Whether you're preparing for major contests, strengthening your algorithmic mindset, or simply exploring the art of efficient problem-solving, this journey into greedy algorithms will become one of the most rewarding parts of your learning experience.
¶ Greedy Algorithms
¶ Beginner Level
1. Introduction to Greedy Algorithms
2. What Are Greedy Algorithms and Why Are They Useful?
3. Basic Terminology in Greedy Algorithms
4. Understanding the Greedy Choice Property
5. Understanding Optimal Substructure
6. Examples of Greedy Algorithms in Real Life
7. Introduction to the Activity Selection Problem
8. Solving the Activity Selection Problem
9. Introduction to the Fractional Knapsack Problem
10. Solving the Fractional Knapsack Problem
11. Introduction to the Coin Change Problem
12. Solving the Coin Change Problem
13. Introduction to the Huffman Coding Problem
14. Solving the Huffman Coding Problem
15. Introduction to the Job Sequencing Problem
16. Solving the Job Sequencing Problem
17. Introduction to the Minimum Spanning Tree Problem
18. Solving the Minimum Spanning Tree Problem
19. Introduction to the Shortest Path Problem
20. Solving the Shortest Path Problem
¶ Intermediate Level
21. Advanced Greedy Techniques
22. Solving Problems with Multiple Constraints
23. Solving Problems with Weighted Constraints
24. Solving Problems with Unweighted Constraints
25. Solving Problems with Time Constraints
26. Solving Problems with Space Constraints
27. Solving Problems with Resource Constraints
28. Solving Problems with Capacity Constraints
29. Solving Problems with Precedence Constraints
30. Solving Problems with Dependency Constraints
31. Solving Problems with Overlapping Constraints
32. Solving Problems with Non-Overlapping Constraints
33. Solving Problems with Interval Constraints
34. Solving Problems with Range Constraints
35. Solving Problems with Boundary Constraints
36. Solving Problems with Edge Cases
37. Solving Problems with Large Inputs
38. Solving Problems with Small Inputs
39. Solving Problems with Dynamic Inputs
40. Solving Competitive Programming Problems with Greedy Algorithms
¶ Advanced Level
41. Advanced Greedy Algorithms
42. Solving Problems with Multiple Objectives
43. Solving Problems with Conflicting Objectives
44. Solving Problems with Complementary Objectives
45. Solving Problems with Mutually Exclusive Objectives
46. Solving Problems with Dependent Objectives
47. Solving Problems with Independent Objectives
48. Solving Problems with Sequential Objectives
49. Solving Problems with Parallel Objectives
50. Solving Problems with Hierarchical Objectives
51. Solving Problems with Nested Objectives
52. Solving Problems with Recursive Objectives
53. Solving Problems with Iterative Objectives
54. Solving Problems with Backtracking Objectives
55. Solving Problems with Branch and Bound Objectives
56. Solving Problems with Divide and Conquer Objectives
57. Solving Problems with Dynamic Programming Objectives
58. Solving Problems with Greedy and Dynamic Programming Combined
59. Solving Problems with Greedy and Divide and Conquer Combined
60. Solving Competitive Programming Problems with Advanced Greedy Algorithms
¶ Expert Level
61. Greedy Algorithms in Real-Time Applications
62. Greedy Algorithms for Streaming Data
63. Greedy Algorithms in Distributed Systems
64. Greedy Algorithms for Solving Graph Problems
65. Greedy Algorithms in Network Flow Problems
66. Greedy Algorithms for Solving Matrix-Based Problems
67. Greedy Algorithms in Machine Learning Applications
68. Greedy Algorithms for Natural Language Processing (NLP)
69. Greedy Algorithms in Data Compression
70. Greedy Algorithms for Solving Cryptography Problems
71. Greedy Algorithms in Game Theory Problems
72. Greedy Algorithms for Solving Geometry Problems
73. Greedy Algorithms in Computational Geometry
74. Greedy Algorithms for Solving Optimization Problems
75. Greedy Algorithms in Quantum Computing
76. Greedy Algorithms for Solving Parallel Computing Problems
77. Greedy Algorithms in Randomized Algorithms
78. Greedy Algorithms for Solving Approximation Algorithms
79. Greedy Algorithms in Online Algorithms
80. Greedy Algorithms for Solving Dynamic Programming Problems
¶ Mastery Level
81. Advanced Problem-Solving Techniques with Greedy Algorithms
82. Combining Greedy Algorithms with Other Data Structures
83. Greedy Algorithms in Multi-Dimensional Problems
84. Greedy Algorithms for Solving NP-Hard Problems
85. Greedy Algorithms in Approximation Algorithms
86. Greedy Algorithms for Solving Interactive Problems
87. Greedy Algorithms in Adversarial Problem Solving
88. Greedy Algorithms for Solving Probabilistic Problems
89. Greedy Algorithms in Randomized Competitive Programming
90. Greedy Algorithms for Solving Interactive Problems
91. Greedy Algorithms in Real-World Competitive Programming Contests
92. Greedy Algorithms in ACM-ICPC Problems
93. Greedy Algorithms in Google Code Jam Problems
94. Greedy Algorithms in Codeforces and Topcoder Problems
95. Greedy Algorithms in AtCoder Problems
96. Greedy Algorithms in LeetCode Hard Problems
97. Greedy Algorithms in Advanced Interview Problems
98. Greedy Algorithms in Research-Level Problems
99. Open Problems and Future Directions with Greedy Algorithms
100. Mastering Greedy Algorithms: A Comprehensive Review