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 x 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.
Solution. This problem is pretty similar to Lowest cost to adjust integer array, adjacencies differ less than k. dp[i][j] is calculated by each value in dp[i – 1] level.
We define dp[][]. Considering we already painted house [0,…,i], dp[i][j] means the minimum price when house i paints with color j.
Let minPos[i] is the color of the lowest price when we paint till house i
min1[i] is the lowest price when we paint till house i.
min2[i] is the second lowest price when we paint till house.
Then we have dp[i][j] = cost[i][j] + {
min1, when j != minPos[i – 1]
min2, when j == minPos[i – 1] }
dp[1][0] = cost[1][0] + min2[0] = 3 + 2
dp[1][1] = cost[1][1] + min1[0] = 2 + 1
No code for this problem because I don’t have premium access to leetcode or test cases.