Count of subarrays with X as the most frequent element, for each value of X from 1 to N

Given an array arr[] of size N, (where 0<A[i]<=N, for all 0<=i<N), the task is to calculate for each number X from 1 to N, the number of subarrays in which X is the most frequent element. In subarrays, where more than one element has the maximum frequency, the smallest element should be considered as the most frequent.

Examples:

Input: arr[]={2, 1, 2, 3}, N=4
Output:
4 5 1 0
Explanation:

1. For X=1, the subarrays where X is the most frequent element, are {2, 1}, {1}, {1, 2}, {1, 2, 3}
2. For X=2, the subarrays where X is the most frequent element, are {2}, {2, 1, 2}, {2, 1, 2, 3}, {2}, {2, 3}
3. For X=3, the subarray where X is the most frequent element, is {3}
4. For X=4, there are no subarrays containing 4.

Input: arr[]={3, 1, 5, 1, 3}, N=5
Output:
12 0 2 0 1

Approach: The approach is to keep track of the most frequent element in each subarray using two loops and keep them stored in a separate array. Follow the steps below to solve the problem:

1. Initialize an array ans of size N to 0, to store the final answers.
2. Iterate from 0 to N-1, and for each current index i, do the following:
   1. Initialize a frequency array count of size N to 0, to store the current frequencies of each element from 1 to N.
   2. Initialize a variable best to 0, to store the most frequent element in the current subarray.
   3. Iterate from i to N-1, and for each current index j, do the following:
      1. Increment the count of current element i.e count[arr[j]-1]=count[arr[j]-1]+1
      2. Check if the frequency of the current element i.e arr[j] is greater than the frequency of best.
      3. Check if the frequency of the current element i.e arr[j] is equal to the frequency of best and the current element is less than best.
      4. If either of them is true, update best to the current element i.e best=arr[j]
      5. Increment the best index of the ans array i.e ans[best-1]=ans[best-1]+1.
3. Print the array ans.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to calculate the number of subarrays where
// X(1<=X<=N) is the most frequent element
int mostFrequent(int arr[], int N)
{
    // array to store the final answers
    int ans[N] = { 0 };

    for (int i = 0; i < N; i++) {

        // Array to store current frequencies
        int count[N];

        // Initialise count
        memset(count, 0, sizeof(count));

        // Variable to store the
        // current most frequent element
        int best = 0;
        for (int j = i; j < N; j++) {

            // Update frequency array
            count[arr[j] - 1]++;
            if (count[arr[j] - 1] > count[best - 1]
                || (count[arr[j] - 1] == count[best - 1]
                    && arr[j] < best)) {
                best = arr[j];
            }

            // Update answer
            ans[best - 1]++;
        }
    }

    // Print answer
    for (int i = 0; i < N; i++)
        cout << ans[i] << " ";
}
// Driver code
int main()
{
    // Input
    int arr[] = { 2, 1, 2, 3 };
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    mostFrequent(arr, N);
    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG {

    // Function to calculate the number of subarrays where
    // X(1<=X<=N) is the most frequent element
    public static void mostFrequent(int[] arr, int N)
    {
        // array to store the final answers
        int[] ans = new int[N];

        for (int i = 0; i < N; i++) {

            // Array to store current frequencies
            int[] count = new int[N];

            // Variable to store the
            // current most frequent element
            int best = 1;
            for (int j = i; j < N; j++) {

                // Update frequency array
                count[arr[j] - 1]++;
                if (best > 0) {
                    if ((count[arr[j] - 1]
                         > count[best - 1])
                        || (count[arr[j] - 1]
                                == count[best - 1]
                            && arr[j] < best)) {
                        best = arr[j];
                    }

                    // Update answer
                    ans[best - 1]++;
                }
            }
        }

        // Print answer
        for (int i = 0; i < N; i++)
        System.out.print(ans[i] + " ");
    }

    // Driver Code
    public static void main(String[] args)
    {

     // Input
        int[] arr = { 2, 1, 2, 3 };
        int N = arr.length;

        // Function call
        mostFrequent(arr, N);
    }
}

// This code is contributed by sanjoy_62.

Python3

# Python program for the above approach

# Function to calculate the number of subarrays where
# X(1<=X<=N) is the most frequent element
def mostFrequent(arr, N):
    # array to store the final answers
    ans = [0]*N

    for i in range(N):
        # Array to store current frequencies
        count = [0]*N

        # Initialise count
        # memset(count, 0, sizeof(count))

        # Variable to store the
        # current most frequent element
        best = 0
        for j in range(i,N):
            # Update frequency array
            count[arr[j] - 1]+=1
            if (count[arr[j] - 1] > count[best - 1]
                or (count[arr[j] - 1] == count[best - 1]
                    and arr[j] < best)):
                best = arr[j]

            # Update answer
            ans[best - 1] += 1

    # Print answer
    print(*ans)

# Driver code
if __name__ == '__main__':
    # Input
    arr= [2, 1, 2, 3]
    N = len(arr)

    # Function call
    mostFrequent(arr, N)

# This code is contributed by mohit kumar 29.

C#

// C# program for the above approach
using System;
class GFG {

    // Function to calculate the number of subarrays where
    // X(1<=X<=N) is the most frequent element
    public static void mostFrequent(int[] arr, int N)
    {
        // array to store the final answers
        int[] ans = new int[N];

        for (int i = 0; i < N; i++) {

            // Array to store current frequencies
            int[] count = new int[N];

            // Variable to store the
            // current most frequent element
            int best = 1;
            for (int j = i; j < N; j++) {

                // Update frequency array
                count[arr[j] - 1]++;
                if (best > 0) {
                    if ((count[arr[j] - 1]
                         > count[best - 1])
                        || (count[arr[j] - 1]
                                == count[best - 1]
                            && arr[j] < best)) {
                        best = arr[j];
                    }

                    // Update answer
                    ans[best - 1]++;
                }
            }
        }

        // Print answer
        for (int i = 0; i < N; i++)
            Console.Write(ans[i] + " ");
    }

    // Driver code
    public static void Main()
    {

        // Input
        int[] arr = { 2, 1, 2, 3 };
        int N = arr.Length;

        // Function call
        mostFrequent(arr, N);
    }
}

// This code is contributed by subham348.

Javascript

<script>
// Javascript program for the above approach

// Function to calculate the number of subarrays where
// X(1<=X<=N) is the most frequent element
function mostFrequent(arr, N) {
    // array to store the final answers
    let ans = new Array(N).fill(0)

    for (let i = 0; i < N; i++) {

        // Array to store current frequencies
        let count = new Array(N);

        // Initialise count
        count.fill(0)

        // Variable to store the
        // current most frequent element
        let best = 1;
        for (let j = i; j < N; j++) {

            // Update frequency array
            count[arr[j] - 1]++;
            if (count[arr[j] - 1] > count[best - 1]
                || (count[arr[j] - 1] == count[best - 1]
                    && arr[j] < best)) {
                best = arr[j];
            }

            // Update answer
            ans[best - 1]++;
        }
    }

    // Print answer
    console.log(ans)
    for (let i = 0; i < N; i++)
        document.write(ans[i] + " ");
}


// Driver code
// Input
let arr = [2, 1, 2, 3];
let N = arr.length

// Function call
mostFrequent(arr, N);
</script>

Output:

4 5 1 0

Time Complexity: O(N²)
Auxiliary Space: O(N)