Probability of a Random Pair Being the Maximum Weighted Pair in C++

Given with two different arrays and the task is to find the probability of the random pair chosen to be the maximum weighted pair.

A Pair will contain one element from let’s say array1 and another element form another array let’s say array2. So the program must find the probability of the pair that will contain first element to be the maximum element of array 1 and second element to be the maximum element of array 2 hence forming the maximum weighted pair.

Input 

arr1[] = { 2, 23 }
arr2[] = { 10, 3, 8 }

Output 

probability of maximum pair : 0.166667

Explanation 

set of pairs from both the arrays are -: {(2, 10), (2, 3), (2, 8), (23, 10), (23, 3), (23, 8)}
Maximum weighted pair from the given set is: (23, 8)
Probability is : 1 / 6 = 0.166667

Input −

arr1[] = { 4, 5, 6 }
arr2[] = { 6, 2, 6 }

Output −

probability of maximum pair : 0.222222

Explanation 

set of pairs from both the arrays are -: {(4, 6), (4, 2), (4, 6), (5, 6), (5, 2), (5, 6), (6, 6), (6, 2), (6, 6)}
Maximum weighted pair from the given set is (6, 6) which is occurring twice.
Probability is : 2 / 9 = 0.2222

Approach

• Input the array elements

• Find the maximum elements from both the arrays and calculate the total number of maximum weighted pairs so formed

• Calculate the probability by dividing the total number of maximum weighted pairs with the total number of pairs in the set

• Print the calculated probability

Algorithm

Start
Step1→ declare function to calculate maximum weighted pair
   double max_pair(int arr1[], int arr2[], int size_1, int size_2)
      declare int max_pair1 = INT_MIN, count_1 = 0
      Loop For int i = 0 and i < size_1 and i++
      IF arr1[i] > max_pair1
         Set max_pair1 = arr1[i]
         Set count_1 = 1
      End
      Else IF arr1[i] = max_pair1
         Set count_1++
      End
   End
   Declare int max_pair2 = INT_MIN, count_2 = 0
   Loop For int i = 0 and i < size_2 and i++
      IF arr2[i] > max_pair2
         Set max_pair2 = arr2[i]
         Set count_2 = 1
      End
      Else IFarr2[i] = max_pair2
         Set count_2++
      End
   End
   return (double)(count_1 * count_2) / (size_1 * size_2)
Step 2→ In main()
   Declare int arr1[] = { 2, 23 }
   Declare int arr2[] = { 10, 3, 8 }
   Calculate int size_1 = sizeof(arr1) / sizeof(arr1[0])
   Calculate int size_2 = sizeof(arr2) / sizeof(arr2[0])
   Call max_pair(arr1, arr2, size_1, size_2)
Stop

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
// Function to return probability
double max_pair(int arr1[], int arr2[], int size_1, int size_2){
   //pair from array 1
   int max_pair1 = INT_MIN, count_1 = 0;
   for (int i = 0; i < size_1; i++){
      if (arr1[i] > max_pair1){
         max_pair1 = arr1[i];
         count_1 = 1;
      }
      else if (arr1[i] == max_pair1){
         count_1++;
      }
   }
   //pair from array 2
   int max_pair2 = INT_MIN, count_2 = 0;
   for (int i = 0; i < size_2; i++){
      if (arr2[i] > max_pair2){
         max_pair2 = arr2[i];
         count_2 = 1;
      }
      else if (arr2[i] == max_pair2){
         count_2++;
      }
   }
   return (double)(count_1 * count_2) / (size_1 * size_2);
}
int main(){
   int arr1[] = { 2, 23 };
   int arr2[] = { 10, 3, 8 };
   int size_1 = sizeof(arr1) / sizeof(arr1[0]);
   int size_2 = sizeof(arr2) / sizeof(arr2[0]);
   cout <<"probability of maximum pair in both the arrays are "<<max_pair(arr1, arr2, size_1, size_2);
   return 0;
}

Output

If run the above code it will generate the following output −

probability of maximum pair in both the arrays are 0.166667