Minimize count of divisions by 2 required to make all array elements equal

Given an array arr[] consisting of N positive integers, the task is to find the minimum count of divisions(integer division) of array elements by 2 to make all array elements the same.

Examples:

Input: arr[] = {3, 1, 1, 3}
Output: 2
Explanation:
Operation 1: Divide arr[0] ( = 3) by 2. The array arr[] modifies to {1, 1, 1, 3}.
Operation 2: Divide arr[3] ( = 3) by 2. The array arr[] modifies to {1, 1, 1, 1}.
Therefore, the count of division operations required is 2.

Input: arr[] = {2, 2, 2}
Output: 0

Approach: The idea to solve the given problem is to find the maximum number to which all the elements in the array can be reduced. Follow the steps below to solve the problem:

• Initialize a variable, say ans, to store the minimum count of division operations required.
• Initialize a HashMap, say M, to store the frequencies of array elements.
• Traverse the array arr[] until any array element arr[i] is found to be greater than 0. Keep dividing arr[i] by 2 and simultaneously update the frequency of the element obtained in the Map M.
• Traverse the HashMap and find the maximum element with frequency N. Store it in maxNumber.
• Again, traverse the array arr[] and find the number of operations required to reduce arr[i] to maxNumber by dividing arr[i] by 2 and add the count of operations to the variable ans.
• After completing the above steps, print the value of ans as the result.

Below is the implementation of the above approach:

C++

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

// Function to count minimum number of
// division by 2 operations required to
// make all array elements equal
void makeArrayEqual(int A[], int n)
{
    // Stores the frequencies of elements
    map<int, int> mp;

    // Stores the maximum number to
    // which every array element
    // can be reduced to
    int max_number = 0;

    // Stores the minimum number
    // of operations required
    int ans = 0;

    // Traverse the array and store
    // the frequencies in the map
    for (int i = 0; i < n; i++) {

        int b = A[i];

        // Iterate while b > 0
        while (b) {
            mp[b]++;

            // Keep dividing b by 2
            b /= 2;
        }
    }

    // Iterate over the map to find
    // the required maximum number
    for (auto x : mp) {

        // Check if the frequency
        // is equal to n
        if (x.second == n) {

            // If true, store it in
            // max_number
            max_number = x.first;
        }
    }

    // Iterate over the array, A[]
    for (int i = 0; i < n; i++) {
        int b = A[i];

        // Find the number of operations
        // required to reduce A[i] to
        // max_number
        while (b != max_number) {

            // Increment the number of
            // operations by 1
            ans++;
            b /= 2;
        }
    }

    // Print the answer
    cout << ans;
}

// Driver Code
int main()
{
    int arr[] = { 3, 1, 1, 3 };
    int N = sizeof(arr) / sizeof(arr[0]);
    makeArrayEqual(arr, N);

    return 0;
}

Java

/*package whatever //do not write package name here */

import java.io.*;
import java.util.Map;
import java.util.HashMap;

class GFG
{

  // Function to count minimum number of
  // division by 2 operations required to
  // make all array elements equal
  public static void makeArrayEqual(int A[], int n)
  {

    // Stores the frequencies of elements
    HashMap<Integer, Integer> map = new HashMap<>();

    // Stores the maximum number to
    // which every array element
    // can be reduced to
    int max_number = 0;

    // Stores the minimum number
    // of operations required
    int ans = 0;

    // Traverse the array and store
    // the frequencies in the map
    for (int i = 0; i < n; i++) {

      int b = A[i];

      // Iterate while b > 0
      while (b>0) {
        Integer k = map.get(b);
        map.put(b, (k == null) ? 1 : k + 1);

        // Keep dividing b by 2
        b /= 2;
      }
    }

    // Iterate over the map to find
    // the required maximum number
    for (Map.Entry<Integer, Integer> e :
         map.entrySet()) {

      // Check if the frequency
      // is equal to n
      if (e.getValue() == n) {

        // If true, store it in
        // max_number
        max_number = e.getKey();
      }
    }

    // Iterate over the array, A[]
    for (int i = 0; i < n; i++) {
      int b = A[i];

      // Find the number of operations
      // required to reduce A[i] to
      // max_number
      while (b != max_number) {

        // Increment the number of
        // operations by 1
        ans++;
        b /= 2;
      }
    }

    // Print the answer
    System.out.println(ans + " ");
  }

  // Driver Code
  public static void main(String[] args)
  {
    int arr[] = { 3, 1, 1, 3 };
    int N = arr.length;
    makeArrayEqual(arr, N);
  }
}

// This code is contributed by aditya7409.

Python3

# Python 3 program for the above approach

# Function to count minimum number of
# division by 2 operations required to
# make all array elements equal
def makeArrayEqual(A, n):

  # Stores the frequencies of elements
  mp = dict()

  # Stores the maximum number to
  # which every array element
  # can be reduced to
  max_number = 0

  # Stores the minimum number
  # of operations required
  ans = 0

  # Traverse the array and store
  # the frequencies in the map
  for i in range(n):
    b = A[i]

      # Iterate while b > 0
    while (b>0):
      if (b in mp):
        mp[b] += 1
      else:
        mp[b] = mp.get(b,0)+1

      # Keep dividing b by 2
      b //= 2

  # Iterate over the map to find
  # the required maximum number
  for key,value in mp.items():

    # Check if the frequency
    # is equal to n
    if (value == n):

      # If true, store it in
      # max_number
      max_number = key

  # Iterate over the array, A[]
  for i in range(n):
    b = A[i]

      # Find the number of operations
      # required to reduce A[i] to
      # max_number
    while (b != max_number):

      # Increment the number of
      # operations by 1
      ans += 1
      b //= 2

  # Print the answer
  print(ans)

# Driver Code
if __name__ == '__main__':
  arr = [3, 1, 1, 3]
  N = len(arr)
  makeArrayEqual(arr, N)

  # This code is contributed by bgangwar59.

C#

using System;
using System.Collections.Generic;

class GFG
{

  // Function to count minimum number of
  // division by 2 operations required to
  // make all array elements equal
  public static void makeArrayEqual(int[] A, int n)
  {

    // Stores the frequencies of elements
    Dictionary<int, int> map = new Dictionary<int, int>();

    // Stores the maximum number to
    // which every array element
    // can be reduced to
    int max_number = 0;

    // Stores the minimum number
    // of operations required
    int ans = 0;

    // Traverse the array and store
    // the frequencies in the map
    for (int i = 0; i < n; i++) {

      int b = A[i];

      // Iterate while b > 0
      while (b > 0)
      {
        if (map.ContainsKey(b))
            map[b] ++;
        else
            map[b]=  1;

        // Keep dividing b by 2
        b /= 2;
      }
    }

    // Iterate over the map to find
    // the required maximum number
    foreach(KeyValuePair<int, int> e in map)
    {

      // Check if the frequency
      // is equal to n
      if (e.Value == n) {

        // If true, store it in
        // max_number
        max_number = e.Key;
      }
    }

    // Iterate over the array, A[]
    for (int i = 0; i < n; i++) {
      int b = A[i];

      // Find the number of operations
      // required to reduce A[i] to
      // max_number
      while (b != max_number) {

        // Increment the number of
        // operations by 1
        ans++;
        b /= 2;
      }
    }

    // Print the answer
    Console.Write(ans + " ");
  }

  // Driver Code
  public static void Main(String[] args)
  {
    int[] arr = { 3, 1, 1, 3 };
    int N = arr.Length;
    makeArrayEqual(arr, N);
  }
}

// This code is contributed by shubhamsingh10.

Javascript

<script>

// Javascript program for the above approach

// Function to count minimum number of
// division by 2 operations required to
// make all array elements equal
function makeArrayEqual(A, n)
{

    // Stores the frequencies of elements
    let mp = new Map();

    // Stores the maximum number to
    // which every array element
    // can be reduced to
    let max_number = 0;

    // Stores the minimum number
    // of operations required
    let ans = 0;

    // Traverse the array and store
    // the frequencies in the map
    for(let i = 0; i < n; i++)
    {
        let b = A[i];

        // Iterate while b > 0
        while (b)
        {
            if (mp.has(b))
            {
                mp.set(b, mp.get(b) + 1)
            }
            else
            {
                mp.set(b, 1)
            }

            // Keep dividing b by 2
            b = Math.floor(b / 2);
        }
    }

    // Iterate over the map to find
    // the required maximum number
    for(let x of mp)
    {

        // Check if the frequency
        // is equal to n
        if (x[1] == n)
        {

            // If true, store it in
            // max_number
            max_number = x[0];
        }
    }

    // Iterate over the array, A[]
    for(let i = 0; i < n; i++)
    {
        let b = A[i];

        // Find the number of operations
        // required to reduce A[i] to
        // max_number
        while (b != max_number)
        {

            // Increment the number of
            // operations by 1
            ans++;
            b = Math.floor(b / 2);
        }
    }

    // Print the answer
    document.write(ans);
}

// Driver Code
let arr = [ 3, 1, 1, 3 ];
let N = arr.length

makeArrayEqual(arr, N);

// This code is contributed by gfgking

</script>

Output:

2

Time Complexity: O(N*log N)
Auxiliary Space: O(N)