Buttercola: Leetcode: Paint House II

Buttercola: Leetcode: Paint House II

Leetcode: Paint House II

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.

Note:
All costs are positive integers.

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

Understand the problem:
This is a classic back pack problem. 
 -- Define dp[n][k], where dp[i][j] means for house i with color j the minimum cost. 
 -- Initial value: dp[0][j] = costs[0][j]. For others, dp[i][j] = Integer.MAX_VALUE;, i >= 1
 -- Transit function: dp[i][j] = Math.min(dp[i][j], dp[i - 1][k] + cost[i][j]), where k != j.
 -- Final state: Min(dp[n - 1][k]).

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