719. Find K-th Smallest Pair Distance

Given an integer array, return the k-th smallest distance among all the pairs. The distance of a pair (A, B) is defined as the absolute difference between A and B. 

Example 1:

Input:
nums = [1,3,1]
k = 1
Output: 0 
Explanation:
Here are all the pairs:
(1,3) -> 2
(1,1) -> 0
(3,1) -> 2
Then the 1st smallest distance pair is (1,1), and its distance is 0.

class Solution {
public:
    int smallestDistancePair(vector<int>& nums, int k) {
        sort(nums.begin(),nums.end());
        int lo = 0;
        int hi = nums[nums.size() - 1] - nums[0];
        while (lo < hi) {
            int mi = (lo + hi) / 2;
            int count = 0, left = 0;
            for (int right = 0; right < nums.size(); ++right) {
                while (nums[right] - nums[left] > mi) left++;
                count += right - left;
            }
            //count = number of pairs with distance <= mi
            if (count >= k) hi = mi;
            else lo = mi + 1;
        }
        return lo;
    }
};