# 120. Triangle

### Description

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

**Note:**

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.

### Constraints

### Approach

### Links

* GeeksforGeeks
* [Leetcode](https://leetcode.com/problems/triangle/)
* [ProgramCreek](https://www.programcreek.com/2013/01/leetcode-triangle-java/)
* [YouTube](https://youtu.be/hM4mHTi4AnA)

### **Examples**

{% tabs %}
{% tab title="Example 1" %}
**Input:**

\[

\[2],

\[3, 4],

\[6, 5, 7],

\[4, 1, 8, 3]

]

**Output:** 11

**Explanation:**

<div align="left"><img src="https://1091135627-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MEmU-aGQcUvtjjAH8_3%2F-MG7Xg92p_MgEvYBG0YG%2F-MG7_2ISVWKwpI403ehz%2Fimage.png?alt=media&#x26;token=247a0c1c-f690-4d22-b3a6-cb5f5ed836a1" alt=""></div>

&#x20;The minimum path sum from top to bottom is `11` (i.e., **2** + **3** + **5** + **1** = 11).
{% endtab %}
{% endtabs %}

### **Solutions**

{% tabs %}
{% tab title="Solution 1" %}

```java
/**
 * Time complexity : 
 * Space complexity : O(N) where N is the number of rows.
 */

class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        if(triangle == null || triangle.size() == 0) return 0;
        int n = triangle.size();
        int[] dp = new int[n+1];
        
        for(int i = n-1; i >= 0; i--) {
            List<Integer> row = triangle.get(i);
            for(int j = 0; j < row.size(); j++) {
                dp[j] = row.get(j) + Math.min(dp[j], dp[j+1]);
            }
        }
        
        return dp[0];
    }
}
```

{% endtab %}
{% endtabs %}

### **Follow up**

*