# Problem Definition

## Description

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:**

```plaintext
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.
```

## Notes

1. [LeetCode discussion - Simple java DP solution](https://leetcode.com/problems/paint-house/discuss/68211/Simple-java-DP-solution)