# 256. Paint House

Reference: LeetCode
Difficulty: Easy

Twitter OA 2019 | Coloring the blocks

## Problem

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:

## Analysis

### DP

• Define: dp[i][j] is the minimum cost of painting i-th house with color j.
• Recurrence: (3 states)
• dp[i][0] = min(dp[i-1][1], dp[i-1][2]) + costs[i][0]
• dp[i][1] = min(dp[i-1][0], dp[i-1][2]) + costs[i][1]
• dp[i][2] = min(dp[i-1][0], dp[i-1][1]) + costs[i][2]
• Init:
• dp[0][0] = cost[i][0]
• dp[0][1] = cost[i][1]
• dp[0][2] = cost[i][2]

Time: $O(N)$
Space: $O(N)$

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Junhao Wang
a software engineering cat