# Triangle

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

Notice

Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle

## Example

Given the following triangle:

```
[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]
```

## Solution

坐标型动态规划，i, j坐标。

```
class Solution:
    """
    @param triangle: a list of lists of integers.
    @return: An integer, minimum path sum.
    """
    def minimumTotal(self, triangle):
        # write your code here
        n = len(triangle)
        F = [[0 for x in range(n)] for y in range(n)]
        F[0][0] = triangle[0][0]
        if triangle is None or n == 0:
            return -1
        if triangle[0] is None or n == 0:
            return -1
        for i in range(1,n):
            F[i][0] = F[i-1][0] + triangle[i][0]
            F[i][i] = F[i-1][i-1] + triangle[i][i]
        for i in range(1,n):
            for j in range(1,i):
                F[i][j] = min(F[i-1][j],F[i-1][j-1]) + triangle[i][j]
        return min(F[- 1])
```


---

# 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://liuxue2010.gitbook.io/data-structure-and-algorithms/dynamic-programming-i/triangle.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.