LeetCode 322 Coin Change - Walkthrough

Coin Change is Unbounded Knapsack in disguise. Given coins $[1, 3, 4]$ and amount $6$, find the minimum number of coins. Let $dp[a]$ = minimum coins for amount $a$.

Base case: $dp[0]=0$. Transition: $dp[a] = \min(dp[a - coin] + 1)$ for each coin. $dp[1]=1$, $dp[2]=2$, $dp[3]=1$, $dp[4]=1$, $dp[5]=2$, $dp[6]=2$ (using coins $3+3$). This is "minimum count" rather than "maximum value", but the structure is the same. Unbounded items, capacity constraint, optimal selection.