Paint House
Created: March 4, 2020 by [lek-tin]
Last updated: March 4, 2020
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.
Example
Input: [[17,2,17],[16,16,5],[14,3,19]]
Output: 10
Explanation: Paint house 0 into blue, paint house 1 into green, paint house 2 into blue.
Minimum cost: 2 + 5 + 3 = 10.
Solution (in-place top-down dp)
n: number of houses, k: number of colors
Time: O(nk)
Space: O(1)
class Solution:
def minCost(self, costs: List[List[int]]) -> int:
N = len(costs)
if not costs or N == 0:
return 0
for i in range(N-1, 0, -1):
costs[i-1][0] += min(costs[i][1], costs[i][2])
costs[i-1][1] += min(costs[i][0], costs[i][2])
costs[i-1][2] += min(costs[i][0], costs[i][1])
return min(min(costs[0][0], costs[0][1]), costs[0][2])