Topic Lesson
Learn Greedy from scratch
A complete 4-step path: handwritten notebook primer, animated visualizer, speed check quiz, and compiler practice.
What is Greedy
notebook noteA greedy algorithm makes the best-looking choice available right now, at every step, without ever looking back or second-guessing its decision. Think of a cashier making change by handing over the largest possible coin first, repeatedly, until the total is reached. Unlike dynamic programming, which saves and compares answers to multiple overlapping paths, a greedy strategy commits to one immediate option and keeps moving forward.
When to reach for it
Reach for greedy when problems ask for minimum jumps, interval scheduling, assigning resources to maximize satisfaction, or finding fractional values. Key signals include sorted orders where greedily taking the next item never hurts future options, or gas station round trips where running balances prove reachability. If you can prove that taking the immediate best choice never leaves you worse off than any alternative, greedy gives the fastest answer.
How to think about it
Start by sorting the input to bring the most promising candidates to the front. At each position, evaluate your local rule, take the best available piece, and update your running state. The crucial mental step is proving the greedy choice property: demonstrate that picking this immediate winner cannot block a better global solution down the road. If choosing an item now forces you to reconsider past decisions when conditions change later, greedy fails and you must switch to dynamic programming instead.
Operation costs
measured big-O| Operation | Time |
|---|---|
| sort elements to enable greedy selection | O(n log n) |
| greedy single-pass scan through sorted input | O(n) |
| greedy choice using a priority queue | O(n log n) |
Common mistakes to avoid
- Applying a greedy choice without proving it yields the global optimum, such as picking the largest coin first for arbitrary denominations where dynamic programming was required.
- Forgetting to sort the input before running the greedy loop, making local decisions on unordered elements that produce invalid answers.
- Picking items based on only one attribute when the optimal decision depends on a ratio or combination of multiple attributes.