LeetCode 518 Coin Change II - Walkthrough

Trace Coin Change II with coins $[1, 2, 5]$ and amount $5$. The key is loop order: coins in outer loop to count combinations (not permutations). Let $dp[a]$ = number of ways to make amount $a$. After coin $1$: $dp[1..5] = 1$ (only one way using just 1s). After coin $2$: $dp[2]=2$, $dp[3]=2$, $dp[4]=3$, $dp[5]=3$. After coin $5$: $dp[5]=4$.

Answer: $4$ ways. They are: $[1,1,1,1,1]$, $[1,1,1,2]$, $[1,2,2]$, $[5]$.