Minimize operations of removing 2i -1 array elements to empty given array

Given an array arr[] of size N, the task is to empty given array by removing 2ⁱ – 1 array elements in each operation (i is any positive integer). Find the minimum number of operations required.

Examples:

Input: arr[] = { 2, 3, 4 } 
Output: 1 
Explanation:
Removing (2² – 1) elements i.e { arr[0], arr[1], arr[2] } modifies arr[] to { } 
Since no elements left in the array therefore, the required output is 1.

Input: arr[] = { 1, 2, 3, 4 } 
Output: 2 
Explanation:
Removing (2¹ – 1) element i.e, { arr[0] } modifies arr[] to { 2, 3, 4 } 
Removing (2² – 1) elements i.e, { arr[0], arr[1], arr[2] } modifies arr[] to { } 
Since no elements left in the array therefore, the required output is 2.

Approach: The problem can be solved using Greedy technique. The idea is to always remove the maximum possible count(2ⁱ – 1) of elements from the array. Follow the steps below to solve the problem:

• Initialize a variable, say cntSteps, to store the minimum count of operations required to empty given array.
• Removing N array elements modifies arr[] to 0 length array. Therefore, increment the value of N by 1.
• Traverse each bit of N using variable i and for every i^th bit, check if the bit is set or not. If found to be true, then update cntSteps += 1
• Finally, print the value of cntSteps.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach

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

// Function to find minimum count of steps
// required to remove all the array elements
int minimumStepReqArr(int arr[], int N)
{

    // Stores minimum count of steps required
    // to remove all the array elements
    int cntStep = 0;

    // Update N
    N += 1;

    // Traverse each bit of N
    for (int i = 31; i >= 0; i--) {

        // If current bit is set
        if (N & (1 << i)) {

            // Update cntStep
            cntStep += 1;
        }
    }

    return cntStep;
}

// Driver Code
int main()
{
    int arr[] = { 1, 2, 3 };

    int N = sizeof(arr) / sizeof(arr[0]);
    cout << minimumStepReqArr(arr, N);

    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;
class GFG
{

  // Function to find minimum count of steps
  // required to remove all the array elements
  static int minimumStepReqArr(int[] arr, int N)
  {

    // Stores minimum count of steps required
    // to remove all the array elements
    int cntStep = 0;

    // Update N
    N += 1;

    // Traverse each bit of N
    for (int i = 31; i >= 0; i--)
    {

      // If current bit is set
      if ((N & (1 << i)) != 0)
      {

        // Update cntStep
        cntStep += 1;
      }
    }
    return cntStep;
  }

  // Driver code
  public static void main(String[] args)
  {
    int[] arr = { 1, 2, 3 };

    int N = arr.length;
    System.out.println(minimumStepReqArr(arr, N));
  }
}

// This code is contributed by susmitakundugoaldanga

Python3

# Python3 program to implement
# the above approach

# Function to find minimum count of steps
# required to remove all the array elements
def minimumStepReqArr(arr, N):

    # Stores minimum count of steps required
    # to remove all the array elements
    cntStep = 0

    # Update N
    N += 1

    i = 31

    while(i >= 0):

        # If current bit is set
        if (N & (1 << i)):

            # Update cntStep
            cntStep += 1

        i -= 1

    return cntStep

# Driver Code
if __name__ == '__main__':

    arr = [ 1, 2, 3 ]
    N = len(arr)

    print(minimumStepReqArr(arr, N))

# This code is contributed by SURENDRA_GANGWAR

C#

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

  // Function to find minimum count of steps
  // required to remove all the array elements
  static int minimumStepReqArr(int[] arr, int N)
  {

    // Stores minimum count of steps required
    // to remove all the array elements
    int cntStep = 0;

    // Update N
    N += 1;

    // Traverse each bit of N
    for (int i = 31; i >= 0; i--)
    {

      // If current bit is set
      if ((N & (1 << i)) != 0)
      {

        // Update cntStep
        cntStep += 1;
      }
    }
    return cntStep;
  }

  // Driver code
  static void Main()
  {
    int[] arr = { 1, 2, 3 };

    int N = arr.Length;
    Console.WriteLine(minimumStepReqArr(arr, N));
  }
}

// This code is contributed by divyesh072019

Javascript

<script>
    // Javascript program to implement the above approach

    // Function to find minimum count of steps
    // required to remove all the array elements
    function minimumStepReqArr(arr, N)
    {

      // Stores minimum count of steps required
      // to remove all the array elements
      let cntStep = 0;

      // Update N
      N += 1;

      // Traverse each bit of N
      for (let i = 31; i >= 0; i--)
      {

        // If current bit is set
        if ((N & (1 << i)) != 0)
        {

          // Update cntStep
          cntStep += 1;
        }
      }
      return cntStep;
    }

    let arr = [ 1, 2, 3 ];

    let N = arr.length;
    document.write(minimumStepReqArr(arr, N));

// This code is contributed by suresh07.
</script>

Output:

1

Time Complexity: O(31)
Auxiliary Space: O(1)