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Formatted question description: https://leetcode.ca/all/1885.html

# 1885. Count Pairs in Two Arrays

Medium

## Description

Given two integer arrays nums1 and nums2 of length n, count the pairs of indices (i, j) such that i < j and nums1[i] + nums1[j] > nums2[i] + nums2[j].

Return the number of pairs satisfying the condition.

Example 1:

Input: nums1 = [2,1,2,1], nums2 = [1,2,1,2]

Output: 1

Explanation: The pairs satisfying the condition are:

• (0, 2) where 2 + 2 > 1 + 1.

Example 2:

Input: nums1 = [1,10,6,2], nums2 = [1,4,1,5]

Output: 5

Explanation: The pairs satisfying the condition are:

• (0, 1) where 1 + 10 > 1 + 4.
• (0, 2) where 1 + 6 > 1 + 1.
• (1, 2) where 10 + 6 > 4 + 1.
• (1, 3) where 10 + 2 > 4 + 5.
• (2, 3) where 6 + 2 > 1 + 5.

Constraints:

• n == nums1.length == nums2.length
• 1 <= n <= 10^5
• 1 <= nums1[i], nums2[i] <= 10^5

## Solution

Create an array differences with length n such that differences[i] = nums1[i] - nums2[i] for all 0 <= i < n. Sort differences. For each 0 <= i < n - 1, find the minimum index such that differences[index] + differences[i] > 0, or index = n if differences[n - 1] + differences[i] <= 0, and the number of j’s for the current i is n - index. In this way, the number of pairs of indices (i, j) can be calculated.

• class Solution {
public long countPairs(int[] nums1, int[] nums2) {
long count = 0;
int n = nums1.length;
int[] differences = new int[n];
for (int i = 0; i < n; i++)
differences[i] = nums1[i] - nums2[i];
Arrays.sort(differences);
for (int i = 0; i < n - 1; i++) {
int target = -differences[i] + 1;
int index = binarySearch(differences, n, target, i + 1);
count += n - index;
}
return count;
}

public int binarySearch(int[] differences, int n, int target, int startIndex) {
int low = startIndex, high = n - 1;
if (differences[high] < target)
return n;
while (low < high) {
int mid = (high - low) / 2 + low;
if (differences[mid] < target)
low = mid + 1;
else
high = mid;
}
return low;
}
}

############

class Solution {
public long countPairs(int[] nums1, int[] nums2) {
int n = nums1.length;
int[] d = new int[n];
for (int i = 0; i < n; ++i) {
d[i] = nums1[i] - nums2[i];
}
Arrays.sort(d);
long ans = 0;
for (int i = 0; i < n; ++i) {
int left = i + 1, right = n;
while (left < right) {
int mid = (left + right) >> 1;
if (d[mid] > -d[i]) {
right = mid;
} else {
left = mid + 1;
}
}
ans += n - left;
}
return ans;
}
}

• class Solution:
def countPairs(self, nums1: List[int], nums2: List[int]) -> int:
n = len(nums1)
d = [nums1[i] - nums2[i] for i in range(n)]
d.sort()
return sum(n - bisect_right(d, -v, lo=i + 1) for i, v in enumerate(d))


• class Solution {
public:
long long countPairs(vector<int>& nums1, vector<int>& nums2) {
int n = nums1.size();
vector<int> d(n);
for (int i = 0; i < n; ++i) d[i] = nums1[i] - nums2[i];
sort(d.begin(), d.end());
long long ans = 0;
for (int i = 0; i < n; ++i) {
int j = upper_bound(d.begin() + i + 1, d.end(), -d[i]) - d.begin();
ans += n - j;
}
return ans;
}
};

• func countPairs(nums1 []int, nums2 []int) int64 {
n := len(nums1)
d := make([]int, n)
for i, v := range nums1 {
d[i] = v - nums2[i]
}
sort.Ints(d)
var ans int64
for i, v := range d {
left, right := i+1, n
for left < right {
mid := (left + right) >> 1
if d[mid] > -v {
right = mid
} else {
left = mid + 1
}
}
ans += int64(n - left)
}
return ans
}