# 256\_Paint House

## 256. Paint House

Level: easy

Tag: dynamic programming

## Question

```
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.
```

### Idea: dynamic programming, bottom-up

Start from the first house, there are three possibilities:

* paint in first color, then the previous house must be paint in one of the other two colors which gives smallest cost.
* paint in second color, then the previous house must be paint in one of the other two colors which gives smallest cost.
* paint in third color, then the previous house must be paint in one of the other two colors which gives smallest cost.

### Solution: can be easily generated to more than 3 colors

Time: $$O(n)$$

Space: $$O(1)$$

```python
class Solution(object):
    def minCost(self, costs):
        """
        :type costs: List[List[int]]
        :rtype: int
        """

        # dynamic programming, bottom-up
        prev = [0] * 3
        for now in costs:
            prev = [now[i] + min(prev[:i] + prev[i+1:]) for i in range(3)]
        return min(prev)
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://lei-d.gitbook.io/leetcode/dynamic-programming/256paint-house.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.