256_Paint House

256. Paint House

Level: easy

Tag: dynamic programming

Question

There are a row of n houses, each house can be painted with one of the three colors: red, blue or green. 
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 3 cost matrix. 
For example, costs[0][0] is the cost of painting house 0 with color red; 
costs[1][2] is the cost of painting house 1 with color green, and so on... 
Find the minimum cost to paint all houses.

Note:
All costs are positive integers.

Idea: dynamic programming, bottom-up

Start from the first house, there are three possibilities:

• paint in first color, then the previous house must be paint in one of the other two colors which gives smallest cost.

• paint in second color, then the previous house must be paint in one of the other two colors which gives smallest cost.

• paint in third color, then the previous house must be paint in one of the other two colors which gives smallest cost.

Solution: can be easily generated to more than 3 colors

Time: $O(n)$

Space: $O(1)$

class Solution(object):
    def minCost(self, costs):
        """
        :type costs: List[List[int]]
        :rtype: int
        """

        # dynamic programming, bottom-up
        prev = [0] * 3
        for now in costs:
            prev = [now[i] + min(prev[:i] + prev[i+1:]) for i in range(3)]
        return min(prev)