Number of Pairs Satisfying Inequality

arraybinary searchdivide and conquer

Problem Statement

You are given two 0-indexed integer arrays nums1 and nums2 , each of size n , and an integer diff . Find the number of pairs (i, j) such that:

0 <= i < j <= n - 1 and

nums1[i] - nums1[j] <= nums2[i] - nums2[j] + diff .

Return the number of pairs that satisfy the conditions.

Examples

Example 1

Input: nums1 = [3,2,5], nums2 = [2,2,1], diff = 1
Output: 3
There are 3 pairs that satisfy the conditions:
1. i = 0, j = 1: 3 - 2 <= 2 - 2 + 1. Since i < j and 1 <= 1, this pair satisfies the conditions.
2. i = 0, j = 2: 3 - 5 <= 2 - 1 + 1. Since i < j and -2 <= 2, this pair satisfies the conditions.
3. i = 1, j = 2: 2 - 5 <= 2 - 1 + 1. Since i < j and -3 <= 2, this pair satisfies the conditions.
Therefore, we return 3.

Example 2

Input: nums1 = [3,-1], nums2 = [-2,2], diff = -1
Output: 0
Since there does not exist any pair that satisfies the conditions, we return 0.

Constraints

n == nums1.length == nums2.length

2 <= n <= 10 ^5

-10 ^4 <= nums1[i], nums2[i] <= 10 ^4

-10 ^4 <= diff <= 10 ^4

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search