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Minimize steps to change N to power of 2 by deleting or appending any digit

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  • Difficulty Level : Medium
  • Last Updated : 25 May, 2022
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Given an integer N, the task is to find the minimum number of steps required to change the number N to a perfect power of 2 using the following steps:

  • Delete any one digit d from the number.
  • Add any digit d at the end of the number N.

Examples:

Input: N = 1092
Output: 2
Explanation:
Following are the steps followed:

  1. Removing digit 9 from the number N(= 1092) modifies it to 102.
  2. Adding digit 4 to the end of number N(= 102) modifies it to 1024.

After the above operations, the number N is converted into perfect power of 2 and the number of moves required is 2, which is the minimum. Therefore, print 2.

Input: N = 4444
Output: 3

Approach: The given problem can be solved using the Greedy Approach, the idea is to store all the numbers that are the power of 2 and are less than 1020 and check with each number the minimum steps to convert the given number into a power of 2. Follow the steps below to solve the problem:

  • Initialize an array and store all the numbers that are the power of 2 and less than 1020.
  • Initialize the answer variable best as length + 1 as the maximum number of steps needed.
  • Iterate over the range [0, len) where len is the length of the array using the variable x and perform the following steps:
    • Initialize the variable, say position as 0.
    • Iterate over the range [0, len) where len is the length of the number using the variable i and if the position is less than len(x) and x[position] is equal to num[i], then increase the value of a position by 1.
    • Update the value of best as the minimum of best or len(x) + len(num) – 2*position.
  • After performing the above steps, print the value of best 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 find the minimum number of
// steps required to reduce N to perfect
// power of 2 by performing given steps
void findMinimumSteps(int N){
 
    string num = to_string(N);
    long long c = 1;
    stack<string>a;
 
    // Stores all the perfect power of 2
    while(true){
        if (c > pow(10,20) || c>10)
            break;
        a.push(to_string(c));
        c = c * 2;
    }
 
    // Maximum number of steps required
    long long best = num.length() + 1;
     
    // Iterate for each perfect power of 2
    while(a.empty() == false){
        string x = a.top();
        a.pop();
        long long position = 0;
         
        // Comparing with all numbers
        for(int i=0;i<num.length();i++){
         
            if(position < x.length() && x[position] == num[i])
                position += 1;
 
        }
                 
        // Update the minimum number of
        // steps required
        best = min(best, (int)x.length() + (int)num.length() - 2 * position);
 
    }
         
    // Print the result
    cout<<(best-1)<<endl;
}
 
// Driver Code
int main()
{
    int N = 1092;
 
    // Function Call
    findMinimumSteps(N);
}
 
// code is contributed by shinjanpatra

Java




// Java Program to implement
// the above approach
import java.util.*;
 
class GFG {
 
  // Function to find the minimum number of
  // steps required to reduce N to perfect
  // power of 2 by performing given steps
  static void findMinimumSteps(int N) {
    String num = String.valueOf(N);
    int c = 1;
 
    Stack<String> a = new Stack<>();
 
    // Stores all the perfect power of 2
    while (true) {
      if (c > (int)Math.pow(10, 20)|| c>10 ) {
        break;
      }
      a.add(String.valueOf(c));
      c = c * 2;
    }
 
    // Maximum number of steps required
    int best = num.length()+1;
 
    // Iterate for each perfect power of 2
    String x;
    int i = 0;
    while (!a.isEmpty()) {
      x = a.pop();
      int position = 0;
 
      // Comparing with all numbers
      for (i = 0; i < num.length(); i++) {
 
        if (position < x.length() && x.charAt(position) == num.charAt(i))
          position += 1;
      }
 
      // Update the minimum number of
      // steps required
      best = (int) (Math.min(best, x.length() + num.length() - 2 * position));
 
    }
 
    // Print the result
    System.out.print(best-1);
 
  }
 
  // Driver Code
  public static void main(String[] args) {
    int N = 1092;
 
    // Function Call
    findMinimumSteps(N);
  }
}
 
// This code is contributed by Rajput-Ji

Python3




# Python program for the above approach
 
# Function to find the minimum number of
# steps required to reduce N to perfect
# power of 2 by performing given steps
def findMinimumSteps(N):
 
    num = str(N)
    c = 1
    a = []
 
    # Stores all the perfect power of 2
    while True:
        if (c > 10 ** 20):
            break
        a.append(str(c))
        c = c * 2
 
    # Maximum number of steps required
    best = len(num) + 1
     
    # Iterate for each perfect power of 2
    for x in a:
        position = 0
         
        # Comparing with all numbers
        for i in range(len(num)):
           
            if position < len(x) and x[position] == num[i]:
                position += 1
                 
        # Update the minimum number of
        # steps required
        best = min(best, len(x) + len(num) - 2 * position)
         
    # Print the result
    print(best)
 
# Driver Code
N = 1092
 
# Function Call
findMinimumSteps(N)

Javascript




<script>
 
        // JavaScript Program to implement
        // the above approach
 
        // Function to find the minimum number of
        // steps required to reduce N to perfect
        // power of 2 by performing given steps
        function findMinimumSteps(N)
        {
            num = N.toString()
            c = 1
            a = []
 
            // Stores all the perfect power of 2
            while (1) {
                if (c > Math.pow(10, 20)) {
                    break;
                }
                a.push(c.toString())
                c = c * 2
            }
             
            // Maximum number of steps required
            best = num.length + 1
 
            // Iterate for each perfect power of 2
            for (x of a) {
                position = 0
 
                // Comparing with all numbers
                for (let i = 0; i < num.length; i++) {
 
                    if (position < x.length && x[position] == num[i])
                        position += 1
                }
                 
                // Update the minimum number of
                // steps required
                best = Math.min(best, x.length + num.length - 2 * position)
            }
             
            // Print the result
            document.write(best)
        }
         
        // Driver Code
        let N = 1092
 
        // Function Call
        findMinimumSteps(N)
 
    // This code is contributed by Potta Lokesh
    </script>

Output: 

2

 

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


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