Loop Order

When you compute $dp[i][j]$, you need $dp[i][k]$ and $dp[k+1][j]$ for various k. Both of those are shorter ranges than $[i,j]$.

So you must solve shorter ranges first. The outer loop iterates over length (from $1$), and the inner loop iterates over starting positions. This is different from most DP where you iterate over indices directly. Getting the loop order wrong means you'll access uncomputed values.