State
dp[i][c] = min cost to paint first i houses, house i is color c.
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Transition
dp[i][R] = cost[i][R] + min(dp[i-1][G], dp[i-1][B]);
dp[i][G] = cost[i][G] + min(dp[i-1][R], dp[i-1][B]);
dp[i][B] = cost[i][B] + min(dp[i-1][R], dp[i-1][G]);Advertisement
Answer
min(dp[n-1][R], dp[n-1][G], dp[n-1][B]). Whichever color the last house ends up as.