Make change for cents using US coins (, , , ). Minimize the number of coins. Greedy approach: always pick the largest coin that fits. cents: take ( left)
cents: take ( left)
cents: take ( left)
cents: take ( left)
cents: take , take ( left) Total: coins. That's optimal for US coins. Why does greedy work here? Because US coins form a canonical system: each coin divides evenly into larger ones. This structure guarantees greedy works.