# leetcode\_976

Given an array A of positive lengths, return the largest perimeter of a triangle with non-zero area, formed from 3 of these lengths.

If it is impossible to form any triangle of non-zero area, return 0.

Example 1:

Input: \[2,1,2] Output: 5 Example 2:

Input: \[1,2,1] Output: 0 Example 3:

Input: \[3,2,3,4] Output: 10 Example 4:

Input: \[3,6,2,3] Output: 8

Note:

3 <= A.length <= 10000 1 <= A\[i] <= 10^6

## Solutions

1. **math**
2. for `a <= b <= c`, a + b > c is the sufficient requirement for them to make up a valid triangle

```cpp
class Solution {
public:
    int largestPerimeter(vector<int>& A) {
        if (A.size() <= 2) return 0;
        sort(A.begin(), A.end());

        for (int i = A.size() - 3; i >= 0; i--)
            if (A[i] + A[i + 1] > A[i + 2])
                return A[i] + A[i + 1] + A[i + 2];

        return 0;
    }
};
```