paint_house_ii

Problem

There are a row of n houses, each house can be painted with one of the k colors. The cost of painting each house with a certain color is different. You have to paint all the houses such that no two adjacent houses have the same color.

The cost of painting each house with a certain color is represented by a n * k cost matrix.

For example, costs[0][0] is the cost of painting house 0 with color 0; costs[1][2] is the cost of painting house 1 with color 2, and so on...

Find the minimum cost to paint all houses.

Note: All costs are positive integers.

Follow up: Could you solve it in O(nk) runtime?

Solution

DP with state savings, dont need all n * k states

For each iteration over 'house', get the max and min for previous houses:

dp[i][j]= (dp[i-1][j] == preMin ? preSecondMin : preMin) + costs[i][j]