从两个数组中计算差异超过 K 的对 |设置 2

给定两个整数数组arr[]和brr[] 分别由大小为N和M的不同元素和一个整数K 组成，任务是找到对(arr[i] , brr[j])的计数，使得(brr [j] – arr[i]) > K。

例子：

Input: arr[] = {5, 9, 1, 8}, brr[] = {10, 12, 7, 4, 2, 3}, K = 3
Output: 6
Explanation:
Possible pairs that satisfy the given conditions are: {(5, 10), (5, 12), (1, 10), (1, 12), (1, 7), (8, 12)}.
Therefore, the required output is 6.

Input: arr[] = {2, 10}, brr[] = {5, 7}, K = 2
Output: 2
Explanation:
Possible pairs that satisfy the given conditions are: {(2, 5), (2, 7)}.
Therefore, the required output is 2.

朴素的方法：请参阅本文的前一篇文章，了解解决此问题的最简单方法。
时间复杂度： O(N * M)
辅助空间： O(1)

双指针方法：参考本文前一篇文章，关于此问题的双指针解决方案。
时间复杂度： O(N * log(N) + M * log(M))
辅助空间： O(1)

高效的方法：想法是对较小的数组进行排序，并为每个元素遍历较大的数组，在较小的数组中找到合适的元素进行配对，使用二分搜索。请按照以下步骤解决问题：

• 初始化一个变量count来存储对的计数。
• 如果arr[]大小小于brr[] ，则执行以下操作。
  • 对数组arr[] 进行排序并遍历数组brr[]。
  • 在arr[] 中找到(brr[j] – k)的下界，因为在arr[]中小于brr[j] – k的数字将与brr[j]完美配对。
  • 将下限索引与计数相加。
• 如果brr[]大小小于arr[] ，则执行以下操作。
  • 对数组brr[] 进行排序并遍历arr[] 。
  • 在brr[] 中找到(arr[i] + k)的上限，因为在brr[]中大于arr[i]+k的数字将与arr[i]完美配对。
  • 将(brr[] 的大小 – 上限索引)与计数相加。
• 完成以上步骤后，打印count的值作为结果。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to count pairs that satisfy
// the given conditions
int countPairs(int v1[], int v2[],
               int n, int m, int k)
{
    // Stores the count of pairs
    int count = 0;
 
    // If v1[] is smaller than v2[]
    if (n <= m) {
 
        // Sort the array v1[]
        sort(v1, v1 + n);
 
        // Traverse the array v2[]
        for (int j = 0; j < m; j++) {
 
            // Returns the address of
            // the first number which
            // is >= v2[j] - k
            int index
                = lower_bound(v1, v1 + n,
                              v2[j] - k)
                  - v1;
 
            // Increase the count by all
            // numbers less than v2[j] - k
            count += index;
        }
    }
 
    // Otherwise
    else {
 
        // Sort the array v2[]
        sort(v2, v2 + m);
 
        // Traverse the array v1[]
        for (int i = 0; i < n; i++) {
 
            // Returns the address of
            // the first number which
            // is > v1[i] + k
            int index
                = upper_bound(v2, v2 + m,
                              v1[i] + k)
                  - v2;
 
            // Increase the count by all
            // numbers greater than v1[i] + k
            count += m - index;
        }
    }
 
    // Return the total count of pairs
    return count;
}
 
// Driver Code
int main()
{
    int arr[] = { 5, 9, 1, 8 };
    int brr[] = { 10, 12, 7, 4, 2, 3 };
 
    int K = 3;
 
    int N = sizeof(arr)
            / sizeof(arr[0]);
 
    int M = sizeof(brr)
            / sizeof(brr[0]);
 
    cout << countPairs(arr, brr,
                       N, M, K);
    return 0;
}

Java

// Java program for the
// above approach
import java.util.*;
class GFG{
 
// Function to count pairs
// that satisfy the given
// conditions
static int countPairs(int v1[], int v2[],
                      int n, int m, int k)
{
  // Stores the count of pairs
  int count = 0;
 
  // If v1[] is smaller than v2[]
  if (n <= m)
  {
    // Sort the array v1[]
    Arrays.sort(v1);
 
    // Traverse the array v2[]
    for (int j = 0; j < m; j++)
    {
      // Returns the address of
      // the first number which
      // is >= v2[j] - k
      int index = lowerBound(v1, 0, n,
                             v2[j] - k);
 
      // Increase the count by all
      // numbers less than v2[j] - k
      count += index;
    }
  }
 
  // Otherwise
  else
  {
    // Sort the array v2[]
    Arrays.sort(v2);
 
    // Traverse the array v1[]
    for (int i = 0; i < n; i++)
    {
      // Returns the address of
      // the first number which
      // is > v1[i] + k
      int index = upperBound(v2, 0, m,
                             v1[i] + k);
 
      // Increase the count by all
      // numbers greater than v1[i] + k
      count += m - index;
    }
  }
 
  // Return the total count of pairs
  return count;
}
 
static int lowerBound(int[] a, int low,
                      int high, int element)
{
  while(low < high)
  {
    int middle = low +
                 (high - low) / 2;
     
    if(element > a[middle])
      low = middle + 1;
    else
      high = middle;
  }
  return low;
}
 
static int upperBound(int[] a, int low,
                      int high, int element)
{
  while(low < high)
  {
    int middle = low +
                 (high - low) / 2;
     
    if(a[middle] > element)
      high = middle;
    else
      low = middle + 1;
  }
  return low;
}
   
// Driver Code
public static void main(String[] args)
{
  int arr[] = {5, 9, 1, 8};
  int brr[] = {10, 12, 7,
               4, 2, 3};
  int K = 3;
  int N = arr.length;
  int M = brr.length;
  System.out.print(countPairs(arr, brr,
                              N, M, K));
}
}
 
// This code is contributed by shikhasingrajput

Python3

# Python3 program for the above approach
from bisect import bisect_left, bisect_right
 
# Function to count pairs that satisfy
# the given conditions
def countPairs(v1, v2, n, m, k):
     
    # Stores the count of pairs
    count = 0
 
    # If v1[] is smaller than v2[]
    if (n <= m):
         
        # Sort the array v1[]
        v1 = sorted(v1)
 
        # Traverse the array v2[]
        for j in range(m):
             
            # Returns the address of
            # the first number which
            # is >= v2[j] - k
            index = bisect_left(v1, v2[j] - k)
             
            # Increase the count by all
            # numbers less than v2[j] - k
            count += index
 
    # Otherwise
    else:
         
        # Sort the array v2[]
        v2 = sorted(v2)
         
        # Traverse the array v1[]
        for i in range(n):
             
            # Returns the address of
            # the first number which
            # is > v1[i] + k
            index = bisect_right(v2, v1[i] + k)
 
            # Increase the count by all
            # numbers greater than v1[i] + k
            count += m - index
 
    # Return the total count of pairs
    return count
 
# Driver Code
if __name__ == '__main__':
     
    arr = [ 5, 9, 1, 8 ]
    brr = [ 10, 12, 7, 4, 2, 3]
 
    K = 3
 
    N = len(arr)
    M = len(brr)
 
    print(countPairs(arr, brr, N, M, K))
 
# This code is contributed by mohit kumar 29

C#

// C# program for the
// above approach
using System;
class GFG{
 
// Function to count pairs
// that satisfy the given
// conditions
static int countPairs(int []v1, int []v2,
                      int n, int m, int k)
{
  // Stores the count of pairs
  int count = 0;
 
  // If v1[] is smaller than v2[]
  if (n <= m)
  {
    // Sort the array v1[]
    Array.Sort(v1);
 
    // Traverse the array v2[]
    for (int j = 0; j < m; j++)
    {
      // Returns the address of
      // the first number which
      // is >= v2[j] - k
      int index = lowerBound(v1, 0, n,
                             v2[j] - k);
 
      // Increase the count by all
      // numbers less than v2[j] - k
      count += index;
    }
  }
 
  // Otherwise
  else
  {
    // Sort the array v2[]
    Array.Sort(v2);
 
    // Traverse the array v1[]
    for (int i = 0; i < n; i++)
    {
      // Returns the address of
      // the first number which
      // is > v1[i] + k
      int index = upperBound(v2, 0, m,
                             v1[i] + k);
 
      // Increase the count by all
      // numbers greater than v1[i] + k
      count += m - index;
    }
  }
 
  // Return the total count
  // of pairs
  return count;
}
 
static int lowerBound(int[] a, int low,
                      int high, int element)
{
  while(low < high)
  {
    int middle = low +
                 (high - low) / 2;
     
    if(element > a[middle])
      low = middle + 1;
    else
      high = middle;
  }
  return low;
}
 
static int upperBound(int[] a, int low,
                      int high, int element)
{
  while(low < high)
  {
    int middle = low +
                 (high - low) / 2;
     
    if(a[middle] > element)
      high = middle;
    else
      low = middle + 1;
  }
  return low;
}
   
// Driver Code
public static void Main(String[] args)
{
  int []arr = {5, 9, 1, 8};
  int []brr = {10, 12, 7,
               4, 2, 3};
  int K = 3;
  int N = arr.Length;
  int M = brr.Length;
  Console.Write(countPairs(arr, brr,
                              N, M, K));
}
}
 
// This code is contributed by 29AjayKumar

Javascript

 
// JavaScript program to implement
// the above approach
 
// Function to count pairs
// that satisfy the given
// conditions
function countPairs(v1, v2, n, m, k)
{
  // Stores the count of pairs
  let count = 0;
  
  // If v1[] is smaller than v2[]
  if (n <= m)
  {
    // Sort the array v1[]
    v1.sort();
  
    // Traverse the array v2[]
    for (let j = 0; j < m; j++)
    {
      // Returns the address of
      // the first number which
      // is >= v2[j] - k
      let index = lowerBound(v1, 0, n,
                             v2[j] - k);
  
      // Increase the count by all
      // numbers less than v2[j] - k
      count += index;
    }
  }
  
  // Otherwise
  else
  {
    // Sort the array v2[]
    v2.sort();
  
    // Traverse the array v1[]
    for (let i = 0; i < n; i++)
    {
      // Returns the address of
      // the first number which
      // is > v1[i] + k
      let index = upperBound(v2, 0, m,
                             v1[i] + k);
  
      // Increase the count by all
      // numbers greater than v1[i] + k
      count += m - index;
    }
  }
  
  // Return the total count of pairs
  return count;
}
  
function lowerBound(a, low,
                      high, element)
{
  while(low < high)
  {
    let middle = low +
                 (high - low) / 2;
      
    if(element > a[middle])
      low = middle + 1;
    else
      high = middle;
  }
  return low;
}
  
function upperBound(a, low,
                   high, element)
{
  while(low < high)
  {
    let middle = low +
                 (high - low) / 2;
      
    if(a[middle] > element)
      high = middle;
    else
      low = middle + 1;
  }
  return low;
}
 
// Driver Code
 
    let arr = [5, 9, 1, 8];
    let brr = [10, 12, 7,
               4, 2, 3];
  let K = 3;
  let N = arr.length;
  let M = brr.length;
  document.write(countPairs(arr, brr,
                              N, M, K));
           

输出：

6

时间复杂度： O((N+M) * min(log(N), log(M)))
辅助空间： O(1)

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