Greedy Algorithms

Learning Objectives Define a greedy algorithm and its core properties. Identify the greedy-choice property and optimal substructure in a problem. Differentiate between a greedy approach and a dynamic programming approach. Implement a greedy algorithm for the Activity Selection Problem. Solve the Fractional Knapsack problem using a greedy strategy. Analyze the time complexity of common greedy algorithms. Identify scenarios where a greedy algorithm fails to produce a globally optimal solution. Ever tried to give someone change using the fewest coins possible? 🪙 You've already used a greedy algorithm without even realizing it! This lesson introduces Greedy Algorithms, an intuitive and powerful algorithmic paradigm. You will learn how to make the best 'local'...

TermDefinitionExample Greedy AlgorithmAn algorithmic strategy that builds a solution piece by piece, always choosing the option that looks best at the moment without considering future consequences.In the change-making problem for USD, to make change for 48 cents, you greedily take the largest coin first (a quarter), then the next largest (a dime), then another (a dime), then three pennies. Total: 25+10+10+1+1+1. Greedy Choice PropertyA key property of problems where a globally optimal solution can be achieved by repeatedly making a locally optimal choice. The choice made at one step does not prevent you from reaching the overall best solution.In the Activity Selection Problem, greedily choosing the activity that finishes earliest is a 'safe' choice that always leads to an optim...

The Greedy Strategy Pattern 1. Identify the optimal substructure. 2. Develop a recursive solution. 3. Prove that a greedy choice at each step will lead to a global optimum. 4. Show that making a greedy choice leaves one subproblem to solve. 5. Develop an iterative algorithm that implements the greedy strategy. This is a general framework for designing and verifying a greedy algorithm. The most critical step is proving that the greedy choice is 'safe'—that it's always part of some optimal solution. Selection Function ChooseTheBest(CandidateSet) At the heart of any greedy algorithm is the selection function. This function defines the criterion for being 'greedy'. It evaluates all available candidates at the current step and picks the one that is locall...