Count Index Triples that Form Nondegenerate Triangles
Company: Bloomberg
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
Return how many ways to select three distinct indices from nums whose values form the side lengths of a triangle. Different index selections count separately, including when values repeat. A triangle must have positive area.
```cpp
class Solution {
public:
int triangleNumber(vector<int>& nums);
};
```
### Examples
**Example 1:**
```text
nums = [3,3,4,5]
Output: 4
Explanation: Every three-index selection satisfies the strict triangle inequality.
```
**Example 2:**
```text
nums = [0,2,2]
Output: 0
Explanation: A zero side gives a degenerate shape.
```
### Constraints
- There are 1..1000 candidate sides. Every side value is in 0..1000.
### Clarifying Questions
Count index multiplicities and enforce strict triangle inequalities despite repeated or zero values.
```hint Read the boundary condition
Once the largest side is fixed, when can several left endpoints be counted together?
```
### Contract considerations
Count index multiplicities and enforce strict triangle inequalities despite repeated or zero values.
Overview: Count Index Triples that Form Nondegenerate Triangles. Return how many ways to select three distinct indices from nums whose values form the side lengths of a triangle.