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Find an index of maximum occurring element with equal probability

Given an array of integers, find the most occurring element of the array and return any one of its indexes randomly with equal probability.

Examples:

Input: 
arr[] = [-1, 4, 9, 7, 7, 2, 7, 3, 0, 9, 6, 5, 7, 8, 9]

Output:  
Element with maximum frequency present at index 6
OR
Element with maximum frequency present at Index 3
OR
Element with maximum frequency present at index 4
OR
Element with maximum frequency present at index 12

All outputs above have equal probability.



The idea is to iterate through the array once and find out the maximum occurring element and its frequency n. Then we generate a random number r between 1 and n and finally return the r’th occurrence of maximum occurring element in the array.

Below is C++ implementation of above idea –

// C++ program to return index of most occurring element
// of the array randomly with equal probability
#include <iostream>
#include <unordered_map>
#include <climits>
using namespace std;
  
// Function to return index of most occurring element
// of the array randomly with equal probability
void findRandomIndexOfMax(int arr[], int n)
{
    // freq store frequency of each element in the array
    unordered_map<int, int> freq;
    for (int i = 0; i < n; i++)
        freq[arr[i]] += 1;
  
    int max_element; // stores max occurring element
  
    // stores count of max occurring element
    int max_so_far = INT_MIN;
  
    // traverse each pair in map and find maximum
    // occurring element and its frequency
    for (pair<int, int> p : freq)
    {
        if (p.second > max_so_far)
        {
            max_so_far = p.second;
            max_element = p.first;
        }
    }
  
    // generate a random number between [1, max_so_far]
    int r = (rand() % max_so_far) + 1;
  
    // traverse array again and return index of rth
    // occurrence of max element
    for (int i = 0, count = 0; i < n; i++)
    {
        if (arr[i] == max_element)
            count++;
  
        // print index of rth occurence of max element
        if (count == r)
        {
            cout << "Element with maximum frequency present "
                 "at index " << i << endl;
            break;
        }
    }
}
  
// Driver code
int main()
{
    // input array
    int arr[] = { -1, 4, 9, 7, 7, 2, 7, 3, 0, 9, 6, 5,
                  7, 8, 9 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    // randomize seed
    srand(time(NULL));
  
    findRandomIndexOfMax(arr, n);
  
    return 0;
}

Output:

Element with maximum frequency present at index 12

Time complexity of above solution is O(n).
Auxiliary space used by the program is O(n).

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

tags:

Randomized

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