2-D DP

Grid and interval dynamic programming.

2-D DP

A grid of subproblems — two indices, often strings or coordinates.

Core syntax

Build the grid without aliasing rows:

dp = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(1, m + 1):
    for j in range(1, n + 1):
        if a[i-1] == b[j-1]:
            dp[i][j] = dp[i-1][j-1] + 1
        else:
            dp[i][j] = max(dp[i-1][j], dp[i][j-1])

Watch out

[[0]*n]*m shares one row object — always use the comprehension.

Full cheat sheet →