Introduction to Greedy Algorithms
Learn the Greedy technique: Making locally optimal choices to solve global problems efficiently.
What is a Greedy Algorithm?
A Greedy Algorithm builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit.
It follows the problem-solving heuristic of making the locally optimal choice at each stage with the hope of finding a global optimum.
The Motivation: Coin Change
Imagine you are a cashier. You need to give change for $18 using the fewest number of coins.
Available Coins: $10, $5, $1.
How do you decide which coins to give?
Attempt 1: Brute Force
One way is to try every possible combination of coins that sum to 18 and pick the one with the fewest coins.
- 1+1+1... (18 coins)
- 5+5+5+1+1+1 (6 coins)
- 10+1+1... (9 coins)
This is exhaustive and extremely slow ($O(N^K)$).
Visualizing Brute Force Inefficiency
Initializing...
See the Logic in Motion
Stop memorizing code. Unlock the full interactive visualizer to master the logic step-by-step.When to use Greedy?
Pattern Recognition Triggers:
- Greedy Choice Property: You can choose the best option right NOW and it never negatively impacts future choices.
- Optimal Substructure: The optimal solution to the problem contains optimal solutions to sub-problems.
The Intuition: Pick the Biggest Coin!
Instead of guessing, let's use common sense:
- We want to reduce the remaining amount as much as possible.
- The
$10coin reduces the amount the fastest. - So, take as many
$10coins as fit. Then$5, then$1.
This is Greedy because at each step, we greedily grab the biggest value available.
Interactive Walkthrough (Optimal)
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See the Logic in Motion
Stop memorizing code. Unlock the full interactive visualizer to master the logic step-by-step.Stop Guessing, Start Mastering.
Build the FAANG intuition. Master this pattern with optimized implementations, visual dry runs, and our curated collection of high-yield problems.