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Leetcode
Medium
Arrays
Sorting
Two Pointers
Amazon
Count The Number Of Fair Pairs

Count the number of index pairs whose sum lies within an inclusive range.

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Problem Statement

Problem

Given an integer array nums and two integers lower and upper, count the number of fair pairs of indices (i, j) such that:

  • 0 <= i < j < nums.length
  • lower <= nums[i] + nums[j] <= upper

Return the total number of such pairs.

A pair is considered fair if its sum falls within the inclusive range [lower, upper].

Notes

  • Each index may be used in at most one pair occurrence, but the same value can appear multiple times at different indices.
  • Count pairs by index, not by value.
  • The answer may be large, so use an integer type that can hold the full count.

Input Format

  • An integer array nums
  • Two integers lower and upper

Output Format

  • Return one integer: the number of pairs (i, j) with i < j and lower <= nums[i] + nums[j] <= upper.

Constraints

  • 1 <= nums.length
  • Pair counting is based on indices, not distinct values
  • lower <= upper
  • Values may be negative, zero, or positive
  • The result may exceed 32-bit integer range
Examples
Sample cases returned by the problem API.

Example 1

Input

nums = [0,1,7,4,4,5], lower = 3, upper = 6

Output

6

Explanation

The fair pairs are the index pairs whose sums are 3, 4, 5, or 6. There are 6 such pairs in total.

Example 2

Input

nums = [1,7,9,2,5], lower = 11, upper = 11

Output

1

Explanation

Only one pair sums to exactly 11: (2, 9).

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