Valid Triangle Number
<p>Given an integer array <code>nums</code>, return <em>the number of triplets chosen from the array that can make triangles if we take them as side lengths of a triangle</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,2,3,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Valid combinations are: 
2,3,4 (using the first 2)
2,3,4 (using the second 2)
2,2,3
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [4,2,3,4]
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
</ul>
Greedy; Array; Two Pointers; Binary Search; Sorting
impl Solution {
    pub fn triangle_number(mut nums: Vec<i32>) -> i32 {
        nums.sort();
        let n = nums.len();
        let mut res = 0;
        for i in (2..n).rev() {
            let mut left = 0;
            let mut right = i - 1;
            while left < right {
                if nums[left] + nums[right] > nums[i] {
                    res += right - left;
                    right -= 1;
                } else {
                    left += 1;
                }
            }
        }
        res as i32
    }
}
