Greedy Algorithms

Hook

Finish an activity early to preserve future room; pack divisible items by value density.

Watch

Choose locally only when an exchange proof permits it. Change the input to test a base case, a repeated subproblem and an unreachable or constrained state where applicable.

How it works

1. For interval scheduling, sort by finish time.
2. Take each compatible activity.
3. For fractional knapsack, sort by value/weight and split the final item if needed.

Try it

Predict a recurrence choice, comparison or valid search branch. Explain which stored state or constraint makes the next decision correct.

Complexity

O(n log n) time and O(n) teaching copy. The player states the recurrence or greedy/search invariant and counts teaching operations rather than measuring animation time.

Code

The four reference languages show the core operations under the same bounded input assumptions. Full tables preserve predecessor information for reconstruction; a table-only reference returns those states for the caller to backtrack. Backtracking references include N-Queens, subsets, permutations and a budgeted 9×9 Sudoku solver.

When to use

Use when a valid exchange argument makes local optimal decisions globally safe.

Interview pitfalls

Fractional density greediness does not solve 0/1 knapsack. Weighted interval scheduling is also a different problem.

Quiz

Check the state definition, cost model and boundary conditions below.