House Robber

Choose non-adjacent houses to maximize stolen money.

Pattern fit

This is the cleanest take-or-skip DP because each position only has two meaningful choices: rob it and skip the previous, or skip it and keep the previous best.

Key observation

The state only needs the best answer up to the previous position and the position before that.

Target complexity

O(n) / O(1)

How to break down the solution cleanly

This is the cleanest take-or-skip DP because each position only has two meaningful choices: rob it and skip the previous, or skip it and keep the previous best.

The state only needs the best answer up to the previous position and the position before that.

Name the state in plain language.

List the decisions that can transition into the state.

Reference implementation

Python

# Generic pattern template
# 1D DP
dp = [0] * (n + 1)
dp[0] = base
for i in range(1, n + 1):
    dp[i] = transition(dp, i)

# 2D DP
dp = [[0] * (m + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
    for j in range(1, m + 1):
        dp[i][j] = transition(dp, i, j)