> For the complete documentation index, see [llms.txt](https://jenhsuan.gitbook.io/algorithm/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jenhsuan.gitbook.io/algorithm/leetcode/120.-triangle.md).

# 120. Triangle

## 1.問題 

## 2.想法 <a href="#id-2-xiang-fa" id="id-2-xiang-fa"></a>

* 提問
  * 確認題意:  binary tree的類型, 若非perfect tree, 則無法確定left或right一定存在
* function header, parameter
* test input
* 觀察
  * 第一個邊有一個成員, 第二個邊有兩個成員, 第三個邊有三個成員, 這是一個正三角形
* 說明想法
  * 動態規劃, 跟機器人的路線可能性很像, 不同的只是改成了三角形, 左右兩邊  (正確來說是對角線與row 0)的規則是matrix\[j]\[i] += matrix\[j - 1]\[i], 而中心部分的來源有兩個, 取最小值
  * 切記matrix的縱座標為row (y), 橫坐標為column(x), 表示法為matrix\[r]\[c]&#x20;
* 測試計算複雜度

## **3.程式碼** <a href="#id-3-cheng-shi" id="id-3-cheng-shi"></a>

```
class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        if (triangle.size() == 0) {
            return 0;
        }
        
        int n = triangle.size();
        for (int r = 1; r < n; r++) {
            //對角線
            triangle[r][0] += triangle[r - 1][0]; 
            triangle[r][r] += triangle[r - 1][r - 1];
            
            //中間
            for (int c = 1; c < triangle[r].size() - 1; c++) {
                triangle[r][c] = triangle[r][c] + min(triangle[r - 1][c - 1], triangle[r - 1][c]);
            }
        }
        
        int minVal = INT_MAX;
        
        for (int c = 0; c < triangle[n - 1].size(); c++) {
            minVal = min(minVal, triangle[n - 1][c]);
        }
        
        return minVal;
    }
};
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## 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://jenhsuan.gitbook.io/algorithm/leetcode/120.-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.