# Question

Formatted question description: https://leetcode.ca/all/256.html

 256	Paint House

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 is the cost of painting house 0 with color red;
costs is the cost of painting house 1 with color green, and so on...

Find the minimum cost to paint all houses.

Example:

Given costs = [[14,2,11],[11,14,5],[14,3,10]]
return 10

house 0 is blue, house 1 is green, house 2 is blue, 2 + 5 + 3 = 10

Note:
All costs are positive integers.



# Algorithm

Two-dimensional dynamic array dp, where dp[i][j] represents the minimum cost of brushing to the i+1th house with color j, and the state transition equation is:

dp[i][j] = cost[i][j] + min(dp[i-1][(j + 1)% 3], dp[i-1][(j + 2)% 3])

Java