Greedy algorithms build a solution incrementally, always taking the locally optimal option without revisiting previous choices. The decisive question is: does the greedy choice property hold? — meaning a globally optimal solution always includes the greedy first choice.

Activity Selection is the canonical greedy success. After sorting by end time, the algorithm scans left-to-right and selects each activity whose start time >= lastEnd. The proof is an exchange argument: suppose an optimal solution starts with activity B instead of the earliest-finishing A. Since end(A) <= end(B), replacing B with A produces a solution that is still valid and has the same count — so including A is never worse. By induction, the greedy solution is globally optimal.

The same "sort by end" key powers related problems: Interval Scheduling Maximization (maximize tasks on one machine), and LeetCode 435 Non-overlapping Intervals (minimum removals = total − greedy count). Interval Partitioning (minimize conference rooms) instead uses a min-heap keyed on room end times.

Other greedy classics include Fractional Knapsack (sort by value/weight ratio; indivisible items break this), Huffman Coding (always merge two lowest-frequency nodes), Dijkstra's shortest path (relax the closest unvisited vertex), and Kruskal's MST (add the cheapest edge that doesn't form a cycle).

Greedy fails when local choices foreclose globally better branches — 0/1 Knapsack and shortest path with negative edges need DP or more careful relaxation.