Largest number in the Array having frequency same as value

Given an array arr containing N integers, the task is to find the largest number in the array whose frequency is equal to its value. If no such number exists, then print -1.
Examples:

Input: arr = [3, 2, 5, 2, 4, 5] 
Output: 2 
Explanation:
In this given array frequency of 2 is 2, whereas the frequency of the remaining numbers doesn’t match with itself. So the answer is 2.
Input: arr = [3, 3, 3, 4, 4, 4, 4] 
Output: 4 
Explanation:
In this given array frequency of 3 is 3 and 4 is 4 but largest number is 4. So the answer is 4.
Input: arr = [1, 1, 1, 2, 3, 3] 
Output: -1 
Explanation:
There is no such number in the given array whose frequency is equal to itself. Thus the output is -1.

Simple Approach:

1. Create a new array to keep the count of the occurrences in the given array.
2. Traverse the new array in reverse order.
3. Return the first number whose count is equal to itself.

Below is the implementation of the above approach:

C++

// C++ solution to the above problem

#include <bits/stdc++.h>
using namespace std;

// Function to find the largest number
// whose frequency is equal to itself.
int findLargestNumber(vector<int>& arr)
{

    // Find the maximum element in the array
    int k = *max_element(arr.begin(),
                         arr.end());
    int m[k] = {};

    for (auto n : arr)
        ++m[n];

    for (auto n = arr.size(); n > 0; --n) {
        if (n == m[n])
            return n;
    }
    return -1;
}

// Driver code
int main()
{
    vector<int> arr = { 3, 2, 5, 2, 4, 5 };

    cout << findLargestNumber(arr) << endl;
    return 0;
}

Java

// Java solution to the above problem
import java.util.*;

class GFG{

// Function to find the largest number
// whose frequency is equal to itself.
static int findLargestNumber(int[] arr)
{

    // Find the maximum element in the array
    int k = Arrays.stream(arr).max().getAsInt();
    int []m = new int[k + 1];

    for(int n : arr)
       ++m[n];

    for(int n = arr.length - 1; n > 0; --n)
    {
       if (n == m[n])
           return n;
    }
    return -1;
}

// Driver code
public static void main(String[] args)
{
    int[] arr = { 3, 2, 5, 2, 4, 5 };

    System.out.print(findLargestNumber(arr) + "\n");
}
}

// This code is contributed by amal kumar choubey

Python3

# Python3 solution to the above problem

# Function to find the largest number
# whose frequency is equal to itself.
def findLargestNumber(arr):

    # Find the maximum element in the array
    k = max(arr);
    m = [0] * (k + 1);

    for n in arr:
        m[n] += 1;

    for n in range(len(arr) - 1, 0, -1):
        if (n == m[n]):
            return n;

    return -1;

# Driver code
if __name__ == '__main__':

    arr = [ 3, 2, 5, 2, 4, 5 ];

    print(findLargestNumber(arr));

# This code is contributed by amal kumar choubey

C#

// C# solution to the above problem
using System;
using System.Linq;

class GFG{

// Function to find the largest number
// whose frequency is equal to itself.
static int findLargestNumber(int[] arr)
{

    // Find the maximum element in the array
    int k = arr.Max();
    int []m = new int[k + 1];

    foreach(int n in arr)
        ++m[n];

    for(int n = arr.Length - 1; n > 0; --n)
    {
       if (n == m[n])
           return n;
    }
    return -1;
}

// Driver code
public static void Main(String[] args)
{
    int[] arr = { 3, 2, 5, 2, 4, 5 };

    Console.Write(findLargestNumber(arr) + "\n");
}
}

// This code is contributed by amal kumar choubey

Javascript

<script>

// Javascript solution to the above problem

// Function to find the largest number
// whose frequency is equal to itself.
function findLargestNumber(arr)
{

    // Find the maximum element in the array
    var k = arr.reduce((a,b)=> Math.max(a,b));
    var m = Array(k).fill(0);

    arr.forEach(n => {
        ++m[n];
    });

    for (var n = arr.length; n > 0; --n) {
        if (n == m[n])
            return n;
    }
    return -1;
}

// Driver code
var arr = [3, 2, 5, 2, 4, 5];
document.write( findLargestNumber(arr));


</script>

Output:

2

Time Complexity: O(N) 
Auxiliary Space Complexity: O( N)
Note: This approach is valid only when the numbers in the given array are less than 65536 i.e. 2¹⁶.

1. Here, use the input array to store the count.
2. Since the values are limited, simply use the first half(first 16 bits) of the integer for keeping the count by adding 65536.
3. Use the right shift operator(right shift by 16 bits) while traversing the array in reverse order and return the first number whose count is equal to itself.

Below is the implementation of the above approach:

C++

// C++ code for the above problem

#include <bits/stdc++.h>
using namespace std;

// Function to find the largest number
// whose frequency is equal to itself.
int findLargestNumber(vector<int>& arr)
{
    for (auto n : arr) {
        n &= 0xFFFF;
        if (n <= arr.size()) {
            // Adding 65536 to keep the
            // count of the current number
            arr[n - 1] += 0x10000;
        }
    }

    for (auto i = arr.size(); i > 0; --i) {
        // right shifting by 16 bits
        // to find the count of the
        // number i
        if ((arr[i - 1] >> 16) == i)
            return i;
    }
    return -1;
}

// Driver code
int main()
{
    vector<int> arr
        = { 3, 2, 5, 5, 2, 4, 5 };

    cout << findLargestNumber(arr)
         << endl;
    return 0;
}

Java

// Java code for the above problem
class GFG{

// Function to find the largest number
// whose frequency is equal to itself.
static int findLargestNumber(int[] arr, int n)
{
    for(int i = 0; i < n; i++)
    {
        arr[i] &= 0xFFFF;
        if (arr[i] <= n)
        {

            // Adding 65536 to keep the
            // count of the current number
            arr[i] += 0x10000;
        }
    }

    for(int i = n - 1; i > 0; --i)
    {

        // Right shifting by 16 bits
        // to find the count of the
        // number i
        if ((arr[i] >> 16) == i)
            return i + 1;
    }
    return -1;
}

// Driver code
public static void main(String[] args)
{
    int []arr = { 3, 2, 5, 5, 2, 4, 5 };
    int n = arr.length;

    System.out.print(findLargestNumber(arr, n) + "\n");
}
}

// This code is contributed by gauravrajput1

Python3

# Python3 code for the above problem

# Function to find the largest number
# whose frequency is equal to itself.
def findLargestNumber(arr, n):
    for i in range(n):
        arr[i] &= 0xFFFF;
        if (arr[i] <= n):

            # Adding 65536 to keep the
            # count of the current number
            arr[i] += 0x10000;

    for i in range(n - 1, 0, -1):

        # Right shifting by 16 bits
        # to find the count of the
        # number i
        if ((arr[i] >> 16) == i):
            return i + 1;

    return -1;

# Driver code
if __name__ == '__main__':
    arr = [ 3, 2, 5, 5, 2, 4, 5 ];
    n = len(arr);

    print(findLargestNumber(arr, n));

# This code is contributed by Rohit_ranjan

C#

// C# code for the above problem
using System;

class GFG{

// Function to find the largest number
// whose frequency is equal to itself.
static int findLargestNumber(int[] arr, int n)
{
    for(int i = 0; i < n; i++)
    {
        arr[i] &= 0xFFFF;
        if (arr[i] <= n)
        {

            // Adding 65536 to keep the
            // count of the current number
            arr[i] += 0x10000;
        }
    }

    for(int i = n - 1; i > 0; --i)
    {

        // Right shifting by 16 bits
        // to find the count of the
        // number i
        if ((arr[i] >> 16) == i)
            return i + 1;
    }
    return -1;
}

// Driver code
public static void Main(String[] args)
{
    int []arr = { 3, 2, 5, 5, 2, 4, 5 };
    int n = arr.Length;

    Console.Write(findLargestNumber(arr, n) + "\n");
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript code for the above problem

// Function to find the largest number
// whose frequency is equal to itself.
function findLargestNumber(arr)
{
    arr.forEach(n => {

        n &= 0xFFFF;
        if (n <= arr.length) {
            // Adding 65536 to keep the
            // count of the current number
            arr[n - 1] += 0x10000;
        }
    });

    for(var i = arr.length; i > 0; --i) {
        // right shifting by 16 bits
        // to find the count of the
        // number i
        if ((arr[i - 1] >> 16) == i)
            return i;
    }
    return -1;
}

// Driver code
var arr
    = [3, 2, 5, 5, 2, 4, 5];
document.write( findLargestNumber(arr))

// This code is contributed by rrrtnx.
</script>

Output:

2

Time Complexity: O(N) 
Auxiliary Space Complexity: O(1)