给定两个由N个整数组成的数组arr []和brr [] ,任务是计算两个数组中对(i,j)的对数,使得(arr [i] – brr [j])和(arr [ j] – brr [i])相等。
例子:
Input: A[] = {1, 2, 3, 2, 1}, B[] = {1, 2, 3, 2, 1}
Output: 2
Explanation: The pairs satisfying the condition are:
- (1, 5): arr[1] – brr[5] = 1 – 1 = 0, arr[5[ – brr[1] = 1 – 1 = 0
- (2, 4): arr[2] – brr[4] = 2 – 2 = 0, arr[4] – brr[2] = 2 – 2 = 0
Input: A[] = {1, 4, 20, 3, 10, 5}, B[] = {9, 6, 1, 7, 11, 6}
Output: 4
天真的方法:解决问题的最简单方法是从两个给定的数组中生成所有对,并检查所需条件。对于每一个的量,条件被发现是真对,增加这种对计数。最后,打印获得的计数。
时间复杂度: O(N 2 )
辅助空间: O(1)
高效方法:想法是将给定的表达式(a [i] – b [j] = a [j] – b [i])转换为形式(a [i] + b [i] = a [j]) + b [j]) ,然后计算满足条件的对。步骤如下:
- 转换表达式a [i] – b [j] = a [j] – b [i] ==> a [i] + b [i] = a [j] + b [j] 。表达式的一般形式变为对任何对(i,j)的两个数组的每个对应索引处的值之和进行计数。
- 初始化辅助数组c []以在每个索引i处存储对应的和c [i] = a [i] + b [i] 。
- 现在,问题减少了,以找到具有相同c [i]值的可能对的数量。
- 计算数组c []中每个元素的频率,如果任何c [i]频率值大于1,则可以成对。
- 使用公式计算以上步骤中的有效对数:
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
using namespace std;
// Function to count the pairs such that
// given condition is satisfied
int CountPairs(int* a, int* b, int n)
{
// Stores the sum of element at
// each corresponding index
int C[n];
// Find the sum of each index
// of both array
for (int i = 0; i < n; i++) {
C[i] = a[i] + b[i];
}
// Stores frequency of each element
// present in sumArr
map freqCount;
for (int i = 0; i < n; i++) {
freqCount[C[i]]++;
}
// Initialize number of pairs
int NoOfPairs = 0;
for (auto x : freqCount) {
int y = x.second;
// Add possible vaid pairs
NoOfPairs = NoOfPairs
+ y * (y - 1) / 2;
}
// Return Number of Pairs
cout << NoOfPairs;
}
// Driver Code
int main()
{
// Given array arr[] and brr[]
int arr[] = { 1, 4, 20, 3, 10, 5 };
int brr[] = { 9, 6, 1, 7, 11, 6 };
// Size of given array
int N = sizeof(arr) / sizeof(arr[0]);
// Function calling
CountPairs(arr, brr, N);
return 0;
}
Java
// Java program for the above approach
import java.util.*;
import java.io.*;
class GFG{
// Function to find the minimum number
// needed to be added so that the sum
// of the digits does not exceed K
static void CountPairs(int a[], int b[], int n)
{
// Stores the sum of element at
// each corresponding index
int C[] = new int[n];
// Find the sum of each index
// of both array
for(int i = 0; i < n; i++)
{
C[i] = a[i] + b[i];
}
// Stores frequency of each element
// present in sumArr
// map freqCount;
HashMap freqCount = new HashMap<>();
for(int i = 0; i < n; i++)
{
if (!freqCount.containsKey(C[i]))
freqCount.put(C[i], 1);
else
freqCount.put(C[i],
freqCount.get(C[i]) + 1);
}
// Initialize number of pairs
int NoOfPairs = 0;
for(Map.Entry x : freqCount.entrySet())
{
int y = x.getValue();
// Add possible vaid pairs
NoOfPairs = NoOfPairs +
y * (y - 1) / 2;
}
// Return Number of Pairs
System.out.println(NoOfPairs);
}
// Driver Code
public static void main(String args[])
{
// Given array arr[] and brr[]
int arr[] = { 1, 4, 20, 3, 10, 5 };
int brr[] = { 9, 6, 1, 7, 11, 6 };
// Size of given array
int N = arr.length;
// Function calling
CountPairs(arr, brr, N);
}
}
// This code is contributed by bikram2001jha
Python3
# Python3 program for the above approach
# Function to count the pairs such that
# given condition is satisfied
def CountPairs(a, b, n):
# Stores the sum of element at
# each corresponding index
C = [0] * n
# Find the sum of each index
# of both array
for i in range(n):
C[i] = a[i] + b[i]
# Stores frequency of each element
# present in sumArr
freqCount = dict()
for i in range(n):
if C[i] in freqCount.keys():
freqCount[C[i]] += 1
else:
freqCount[C[i]] = 1
# Initialize number of pairs
NoOfPairs = 0
for x in freqCount:
y = freqCount[x]
# Add possible vaid pairs
NoOfPairs = (NoOfPairs + y *
(y - 1) // 2)
# Return Number of Pairs
print(NoOfPairs)
# Driver Code
# Given array arr[] and brr[]
arr = [ 1, 4, 20, 3, 10, 5 ]
brr = [ 9, 6, 1, 7, 11, 6 ]
# Size of given array
N = len(arr)
# Function calling
CountPairs(arr, brr, N)
# This code is contributed by code_hunt
C#
// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG{
// Function to find the minimum number
// needed to be added so that the sum
// of the digits does not exceed K
static void CountPairs(int []a, int []b,
int n)
{
// Stores the sum of element at
// each corresponding index
int []C = new int[n];
// Find the sum of each index
// of both array
for(int i = 0; i < n; i++)
{
C[i] = a[i] + b[i];
}
// Stores frequency of each element
// present in sumArr
// map freqCount;
Dictionary freqCount = new Dictionary();
for(int i = 0; i < n; i++)
{
if (!freqCount.ContainsKey(C[i]))
freqCount.Add(C[i], 1);
else
freqCount[C[i]] = freqCount[C[i]] + 1;
}
// Initialize number of pairs
int NoOfPairs = 0;
foreach(KeyValuePair x in freqCount)
{
int y = x.Value;
// Add possible vaid pairs
NoOfPairs = NoOfPairs +
y * (y - 1) / 2;
}
// Return Number of Pairs
Console.WriteLine(NoOfPairs);
}
// Driver Code
public static void Main(String []args)
{
// Given array []arr and brr[]
int []arr = { 1, 4, 20, 3, 10, 5 };
int []brr = { 9, 6, 1, 7, 11, 6 };
// Size of given array
int N = arr.Length;
// Function calling
CountPairs(arr, brr, N);
}
}
// This code is contributed by Amit Katiyar
输出:
4
时间复杂度: O(N)
辅助空间: O(N)