Start by clarifying the problem constraints and edge cases, then explain a dynamic programming solution where dp[i][j] represents the minimum cost to paint the first i houses with house i painted color j. Optimize the transition by tracking the two smallest costs from the previous row, reducing time complexity from O(n*k^2) to O(n*k).
Pro tip: Mention that you can optimize space to O(k) by only keeping the previous row's costs, and highlight that this problem is a classic example of dynamic programming with optimization, often asked at top tech companies.
Confirm the problem details: n houses, k colors, costs matrix, and adjacency constraint. Ask about edge cases like n=0 or k=1.
Define dp[i][j] as the minimum cost to paint houses 0..i with house i painted color j. Base case: dp[0][j] = costs[0][j].
For each house i and color j, dp[i][j] = costs[i][j] + min(dp[i-1][c]) for all c != j. Naively this is O(n*k^2).
Track the smallest and second smallest values from the previous row along with their color indices. Then for each j, the min excluding j is either the smallest (if j != index of smallest) or the second smallest.
Time complexity: O(n*k), space: O(k) with rolling array. Handle n=0 (return 0), k=1 (if n>1, impossible).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.