Greedy Strategy
Learn to solve optimization problems by making the locally optimal choice at each step.
Learn to solve optimization problems by making the locally optimal choice at each step. This hands-on tutorial focuses on practical implementation of greedy strategy concepts.
Greedy Strategy
A Greedy Algorithm builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit.
[!IMPORTANT] A greedy choice works only if:
- Greedy Choice Property: A global optimum can be reached by choosing local optima.
- Optimal Substructure: An optimal solution to the problem contains optimal solutions to its subproblems.
1. Activity Selection Problem
Given a set of activities with start and end times, select the maximum number of activities that don't overlap. Strategy: Always pick the activity that finishes earliest.
Selected: A1, A4, A5
2. Fractional Knapsack
You have a knapsack with a weight limit. You want to maximize the total value by taking fractions of items. Strategy: Sort items by value per unit weight.
3. When Greedy Fails: Coin Change
Imagine coins of denominations 4. To make 6 cents:
- Greedy: 4 + 1 + 1 (3 coins)
- Optimal (DP): 3 + 3 (2 coins) This is why we need Dynamic Programming for certain optimization problems.
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Quiz
Quiz
Question 1 of 2What is the key criteria for a greedy algorithm to yield an optimal solution?