# Leetcode Largest-Perimeter-Triangle

#### 2022-07-26 08:39

> ##### Algorithms:
>
> #algorithm #greedy #math
>
> ##### Difficulty:
>
> #coding_problem #difficulty-easy
>
> ##### Additional tags:
>
> #leetcode
>
> ##### Revisions:
>
> N/A

##### Related topics:

##### Links:

- [Link to problem](https://leetcode.com/problems/largest-perimeter-triangle/)

---

### Problem

Given an integer array `nums`, return _the largest perimeter of a triangle with a non-zero area, formed from three of these lengths_. If it is impossible to form any triangle of a non-zero area, return `0`.

#### Examples

**Example 1:**

**Input:** nums = [2,1,2]
**Output:** 5

**Example 2:**

**Input:** nums = [1,2,1]
**Output:** 0

#### Constraints

- `3 <= nums.length <= 104`
- `1 <= nums[i] <= 106`

### Thoughts

> [!summary]
> This is a #math problem.

After sorting, the answer must be consecutive 3 elements.

#### Why?

assume l, m , r.

if nums[l] + nums[m] < nums[r], because after sorting,
the order is ascending, anything before l and m will not suffice.

### Solution

```cpp
class Solution {
public:
  int largestPerimeter(vector<int> &nums) {
    sort(nums.begin(), nums.end());
    int r = nums.size() - 1;

    // change l first until its boundary

    for (int i = r; i > 1; i--) {
      if (nums[i] < nums[i - 1] + nums[i - 2]) {
        return nums[i] + nums[i - 1] + nums[i - 2];
      }
    }

    return 0;
  }
};
```