# 0256. Paint House

<https://leetcode.com/problems/paint-house>

## Description

There is a row of `n` houses, where each house can be painted one of 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 an `n x 3` cost matrix `costs`.

* For example, `costs[0][0]` is the cost of painting house `0` with the color red; `costs[1][2]` is the cost of painting house 1 with color green, and so on...

Return *the minimum cost to paint all houses*.

**Example 1:**

```
**Input:** costs = [[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.
```

**Example 2:**

```
**Input:** costs = [[7,6,2]]
**Output:** 2
```

**Constraints:**

* `costs.length == n`
* `costs[i].length == 3`
* `1 <= n <= 100`
* `1 <= costs[i][j] <= 20`

## ac

override original value in the cell

```java
class Solution {
    public int minCost(int[][] costs) {
        // edge case
        if (costs == null || costs.length == 0 || costs[0].length == 0)
            return 0;

        int row = costs.length, col = costs[0].length;

        for (int r = 1; r < row; r++) { // each house
            for (int c = 0; c < col; c++) {  // update this row

                // find minimum cost in previous house
                int min = Integer.MAX_VALUE;
                for (int cc = 0; cc < col; cc++) {
                    if (cc == c) continue;  // skip same color
                    min = Math.min(min, costs[r-1][cc]);
                }

                costs[r][c] += min;
            }
        }

        int res = Integer.MAX_VALUE;
        for (int c = 0; c < col; c++) {
            res = Math.min(res, costs[row-1][c]);
        }

        return res;
    }
}

/*
1 2 3
4 5 6
7 8 9

*/
```


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