LeetCode 312 Burst Balloons - State Definition

Define $dp[i][j]$ = max coins from bursting all balloons strictly between i and j (exclusive). We add virtual balloons with value $1$ at positions $0$ and n+$1$.

Base case: $dp[i][i+1]$ = $0$. No balloons between adjacent positions. Goal: $dp[0][n+1]$, the max coins from bursting all balloons between the virtual boundaries. Choosing what dp[i][j] represents is often the hardest part. It must capture everything needed to solve that range on its own.