C++ Exercises: Count the Amicable pairs in an array

Last update on April 12 2025 12:59:54 (UTC/GMT +8 hours)

29. Count Amicable Pairs in an Array

Write a C++ program to count the amicable pairs in an array.

Sample Solution:

C++ Code :

#include <bits/stdc++.h> // Include all standard C++ libraries

using namespace std; // Using the standard namespace

int ProDivSum(int n)
{
    int sum = 1; // Initializing sum with 1
    for (int i = 2; i <= sqrt(n); i++) // Loop through numbers from 2 to square root of 'n'
    {
        if (n % i == 0) // Check if 'i' is a divisor of 'n'
        {
            sum += i; // Add 'i' to the sum

            // To handle perfect squares, if 'n' is divisible by 'i' but not equal to 'i', add the corresponding divisor to the sum
            if (n / i != i)
                sum += n / i;
        }
    }
    return sum; // Return the sum of proper divisors
}

bool chkAmicable(int a, int b)
{
    return (ProDivSum(a) == b && ProDivSum(b) == a); // Return true if the sum of proper divisors of 'a' equals 'b' and vice versa
}

int ChkPairs(int arr[], int num1)
{
    int ctr = 0; // Counter for amicable pairs
    for (int i = 0; i < num1; i++) // Iterate through the array
    {
        for (int j = i + 1; j < num1; j++)
        {
            if (chkAmicable(arr[i], arr[j])) // Check if elements at index i and j form an amicable pair
                ctr++; // Increment the counter if they are an amicable pair
        }
    }
    return ctr; // Return the count of amicable pairs
}

int main()
{
    int nn; // Declare variables
    int n, i, j, ctr;
    cout << "\n\n Count the Amicable pairs in a specific array: \n"; // Display a message
    cout << " Sample pairs : (220, 284)(1184,1210) (2620,2924) (5020,5564) (6232,6368)... \n"; // Display sample pairs
    cout << " ------------------------------------------------------------------------------\n";

    cout << "\n Input the number of elements to be stored in the array: ";
    cin >> nn; // Input the number of elements in the array
    int arr1[nn]; // Declare an array of size nn

    for (i = 0; i < nn; i++) // Input the elements of the array
    {
        cout << "element - " << i << ": ";
        cin >> arr1[i];
    }

    int n1 = sizeof(arr1) / sizeof(arr1[0]); // Calculate the number of elements in the array
    cout << " Number of Amicable pairs present in the array: " << ChkPairs(arr1, n1) << endl; // Count and display the number of amicable pairs in the array
    return 0; // Exit the program
}

Sample Output:

Count the Amicable pairs in a specific array:                         
 Sample pairs : (220, 284)(1184,1210) (2620,2924) (5020,5564) (6232,6368)...                                                                  
 ------------------------------------------------------------------------------                                                               
                                                                       
 Input the number of elements to be stored in the array: 2             
element - 0: 220                                                       
element - 1: 284                                                       
 Number of Amicable pairs presents in the array: 1

Flowchart:

For more Practice: Solve these Related Problems:

Write a C++ program to count amicable pairs within an array by checking every possible pair with nested loops.
Write a C++ program to identify and count amicable pairs in an array using STL algorithms and custom predicates.
Write a C++ program to compute amicable pairs in an array by mapping each number to its divisor sum and comparing.
Write a C++ program to count amicable pairs from an array with error checking for duplicate pairings.

C++ Code Editor:

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