# 265. 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?

# Solution

Approach 1: DP. For an O(nk) solution, record the minimum cost, second to minimum cost and the index of the minimum cost for each house.

# Code (Python) (not yet verified on leetcode)

Approach 1:

def min_cost_paint(costs): # n * k cost matrix, where n is the number of houses, and k is the number of colors
    # costs[h][c] -- total costs up to house h if h is colored with c. Need costs[houses-1] across all c's.
    houses, colors = len(costs), len(costs[0])
    minimum, second_minimum, minimum_index = 0, 0, -1
    for h in range(houses):
        new_minimum, new_second_minimum, new_minimum_index = float('inf'), float('inf'), -1
        for c in range(colors):
            # add the minimum cost if painting a different color, otherwise add the second minimum cost
            total_cost = costs[h][c] + (minimum if c != minimum_index else second_minimum)
            if total_cost <= new_minimum:
                new_minimum, new_second_minimum, new_minimum_index = total_cost, new_minimum, c
            elif total_cost <= new_second_minimum:
                new_second_minimum = total_cost
        minimum, second_minimum, minimum_index = new_minimum, new_second_minimum, new_minimum_index
    return minimum

# Code (C++)

Approach 1:

Approach 2: