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LC 322 Coin Change finds the minimum number of coins to make a target amount using unlimited coin supply. The recurrence dp[i] = min(dp[i - coin] + 1) over all coins is the canonical unbounded knapsack minimization problem, asked at Amazon, Google, and Microsoft as a core DP interview question.
LC 518 Coin Change II counts the number of combinations (not permutations) of coins that sum to a target amount. The key insight is the loop order: coins outer, amounts inner. This unbounded knapsack counting pattern is tested at Amazon and Google to distinguish candidates who understand loop-order reasoning from those who memorize templates.
LC 279 Perfect Squares finds the minimum number of perfect square integers that sum to n. It is isomorphic to Coin Change (LC 322) where the "coins" are all perfect squares up to n. The DP recurrence dp[i] = min(dp[i - j*j] + 1) runs in O(n * sqrt(n)) time and is asked at Google and Amazon.
LC 55 Jump Game asks if you can reach the last index given maximum jump lengths. The DP approach is O(n^2) but the greedy insight — tracking the farthest reachable index — reduces it to O(n) O(1). Asked at Amazon and Google as a test of recognizing when greedy is provably optimal over DP.
LC 45 Jump Game II finds the minimum number of jumps to reach the last index. The DP solution is O(n^2), but the greedy window technique — extending the current reachable window whenever a boundary is crossed — achieves O(n) O(1). Asked at Amazon and Google as a harder follow-up to Jump Game.