2563 - Count the Number of Fair Pairs

Given a 0-indexed integer array nums of size n and two integers lower and upper, return the number of fair pairs.

A pair (i, j) is fair if:

• 0 <= i < j < n, and
• lower <= nums[i] + nums[j] <= upper

 Example 1:

Input: nums = [0,1,7,4,4,5], lower = 3, upper = 6
Output: 6
Explanation: There are 6 fair pairs: (0,3), (0,4), (0,5), (1,3), (1,4), and (1,5).

Example 2:

Input: nums = [1,7,9,2,5], lower = 11, upper = 11
Output: 1
Explanation: There is a single fair pair: (2,3).

 Constraints:

• 1 <= nums.length <= 105
• nums.length == n
• -109 <= nums[i] <= 109
• -109 <= lower <= upper <= 109

Solution 1: Sorting + Binary Search

C++

• class Solution {
  public:
      long long countFairPairs(vector<int>& nums, int lower, int upper) {
          long long ans = 0;
          sort(nums.begin(), nums.end());
          for (int i = 0; i < nums.size(); ++i) {
              auto j = lower_bound(nums.begin() + i + 1, nums.end(), lower - nums[i]);
              auto k = lower_bound(nums.begin() + i + 1, nums.end(), upper - nums[i] + 1);
              ans += k - j;
          }
          return ans;
      }
  };

JAVA

• class Solution {
      public long countFairPairs(int[] nums, int lower, int upper) {
          Arrays.sort(nums);
          long ans = 0;
          int n = nums.length;
          for (int i = 0; i < n; ++i) {
              int j = search(nums, lower - nums[i], i + 1);
              int k = search(nums, upper - nums[i] + 1, i + 1);
              ans += k - j;
          }
          return ans;
      }
  
      private int search(int[] nums, int x, int left) {
          int right = nums.length;
          while (left < right) {
              int mid = (left + right) >> 1;
              if (nums[mid] >= x) {
                  right = mid;
              } else {
                  left = mid + 1;
              }
          }
          return left;
      }
  }

PYTHON

• from typing import List
  from bisect import bisect_left
  
  class Solution:
      def countFairPairs(self, nums: List[int], lower: int, upper: int) -> int:
          nums.sort()
          ans = 0
          for i in range(len(nums)):
              j = bisect_left(nums, lower - nums[i], i + 1)
              k = bisect_left(nums, upper - nums[i] + 1, i + 1)
              ans += k - j
          return ans