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
class Solution:
    def triangleNumber(self, nums: List[int]) -> int:
        nums.sort()
        ans, n = 0, len(nums)
        for i in range(n - 2):
            for j in range(i + 1, n - 1):
                k = bisect_left(nums, nums[i] + nums[j], lo=j + 1) - 1
                ans += k - j
        return ans
