Given an integer array nums, return the number of triplets chosen from the array that can make triangles if we take them as side lengths of a triangle.

triangleNumber.js

/**
 * @param {number[]} nums
 * @return {number}
 */
var triangleNumber = function(nums) {
    // Step 1: Sort the array to simplify triangle inequality checks
    nums.sort((a, b) => a - b);

    let count = 0;
    let n = nums.length;

    // Step 2: Fix the largest side of the triangle at index k
    for (let k = n - 1; k >= 2; k--) {
        let i = 0;      // Start pointer
        let j = k - 1;  // End pointer before k

        // Step 3: Use two pointers to find valid pairs (i, j) such that nums[i] + nums[j] > nums[k]
        while (i < j) {
            if (nums[i] + nums[j] > nums[k]) {
                // All elements between i and j are valid with j and k
                count += (j - i);
                j--;    // Try a smaller j to find more combinations
            } else {
                i++;    // Increase i to make the sum larger
            }
        }
    }

    return count;
};