259. 3Sum Smaller

Given an array of n integers nums and a target, find the number of index triplets i, j, k with 0 <= i < j < k < n that satisfy the condition nums[i] + nums[j] + nums[k] < target.

For example, given nums = [-2, 0, 1, 3], and target = 2.

Return 2. Because there are two triplets which sums are less than 2:

[-2, 0, 1]
[-2, 0, 3]
Follow up:
Could you solve it in O(n2) runtime?

**解题思路 **
Binary Search Using n O(n2) runtime
注意： all hi in (lo, hi] will also satisfy the condition , 所以是 count += hi - lo 而不是count++;

    public int threeSumSmaller(int[] nums, int target) {
        int count = 0;
        Arrays.sort(nums);
        int len = nums.length;
        
        for (int i = 0; i < len - 2; i++) {
            int lo = i + 1, hi = len - 1;
            while (lo < hi) {
                if (nums[i] + nums[lo] + nums[hi] >= target) {
                    hi--;
                } else {
                    count += hi - lo;  // all hi in (lo, hi] will also satisfy the condition
                    lo++;
                }
            }
        }
        return count;
    }