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Permutations of a given number that are a powers of 2

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  • Difficulty Level : Medium
  • Last Updated : 15 Jun, 2022
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Given a string S consisting of N digits, the task is to print all possible combinations of the digits of the S that is a perfect power of 2.

Examples:

Input: S = “614”
Output: 4
Explanation:
All possible combinations of digit of S that are perfect power of 2 are 1, 4, 16, 64.

Input: S = “6”
Output: 0

Approach: The given problem can be solved by using Backtracking. The idea is to generate all possible permutations of the string S if it is a perfect power of 2 then print it. Follow the steps below to solve the problem:

  • Define a function check(int number) to check if the given number is a power of 2 and perform the following tasks:
    • If the number is equal to 0, then return false.
    • If the Bitwise AND of number and number-1, then return true, else return false.
  • Define a function calculate(int arr[], string ans) and perform the following tasks:
    • If the length of the string ans is not equal to 0 and the value of the function. check(Integer.parseInt(ans.trim())) returns true, then add this value to the HashSet H[].
    • Iterate over a range [0, 10] using the variable i and perform the following tasks:
      • If arr[i] is equal to 0, then continue.
      • Else, decrease the value of arr[i] by 1 and call the function calculate(temp, “”) to find the other possible permutations of the string str and add the value of arr[i] by 1.
  • Initialize a HashSet H[] to store the possible string numbers which are a power of 2.
  • Initialize an array, say temp[] to store the frequencies of the integers in the string str.
  • Iterate in a while loop till N is not equal to 0 and perform the following steps:
    • Initialize the variable rem as N%10 and increase the value of temp[rem] by 1.
    • Divide the value of N by 10.
  • Call the function calculate(temp, “”) to find the possible permutations of the string S.
  • After performing the above steps, print the HashSet as the result.

Below is the implementation of the above approach.

C++




#include <bits/stdc++.h>
using namespace std;
 
// Stores the all possible generated
// integers from the given string
unordered_set<int> hs;
 
// Function to check if the
// number is power of 2
bool check(int number)
{
    // If number is 0, then it
    // can't be a power of 2
    if (number == 0) {
        return false;
    }
 
    // If the bitwise AND of n
    // and n-1 is 0, then only
    // it is a power of 2
    if ((number & (number - 1)) == 0) {
        return true;
    }
 
    return false;
}
 
// Function to generate the numbers
void calculate(int* arr, string ans)
{
 
    if (ans.length() != 0) {
 
        // Checking the number
        if (check(stoi(ans))) {
            hs.insert(stoi(ans));
        }
    }
 
    // Iterate over the range
    for (int i = 0; i < 10; ++i) {
 
        if (arr[i] == 0) {
            continue;
        }
 
        else {
 
            // Use the number
            arr[i]--;
            calculate(arr,(ans +  to_string(i)));
 
            // Backtracking Step
            arr[i]++;
        }
    }
}
 
// Function to find the all possible
// permutations
void generatePermutation(int n)
{
    hs.clear();
    // Stores the frequency of digits
    int temp[10];
    for (int i = 0; i < 10; i++) {
        temp[i] = 0;
    }
 
    // Iterate over the number
    while (n != 0) {
        int rem = n % 10;
        temp[rem]++;
        n = n / 10;
    }
 
    // Function Call
    calculate(temp, "");
 
    // Print the result
    cout << hs.size() << "\n";
    for (auto i : hs) {
        cout << i << " ";
    }
}
 
int main()
{
 
    int N = 614;
    generatePermutation(N);
    return 0;
}

Java




// Java program for the above approach
 
import java.io.*;
import java.util.*;
 
public class GFG {
 
    // Stores the all possible generated
    // integers from the given string
    static HashSet<Integer> H = new HashSet<>();
 
    // Function to check if the
    // number is power of 2
    static boolean check(int number)
    {
        // If number is 0, then it
        // can't be a power of 2
        if (number == 0) {
            return false;
        }
 
        // If the bitwise AND of n
        // and n-1 is 0, then only
        // it is a power of 2
        if ((number & (number - 1)) == 0) {
            return true;
        }
 
        return false;
    }
 
    // Function to generate the numbers
    static void calculate(
        int arr[], String ans)
    {
 
        if (ans.length() != 0) {
 
            // Checking the number
            if (check(Integer.parseInt(
                    ans.trim()))) {
                H.add(Integer.parseInt(
                    ans.trim()));
            }
        }
 
        // Iterate over the range
        for (int i = 0; i < arr.length; ++i) {
 
            if (arr[i] == 0) {
                continue;
            }
 
            else {
 
                // Use the number
                arr[i]--;
                calculate(arr, ans + i);
 
                // Backtracking Step
                arr[i]++;
            }
        }
    }
 
    // Function to find the all possible
    // permutations
    static void generatePermutation(int n)
    {
        // Stores the frequency of digits
        int temp[] = new int[10];
 
        // Iterate over the number
        while (n != 0) {
            int rem = n % 10;
            temp[rem]++;
            n = n / 10;
        }
 
        // Function Call
        calculate(temp, "");
 
        // Print the result
        System.out.println(H.size());
        System.out.println(H);
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int N = 614;
        generatePermutation(N);
    }
}

Python3




# Python3 program for the above approach
 
# Stores the all possible generated
# integers from the given string
H = set()
 
# Function to check if the
# number is power of 2
def check(number):
   
    # If number is 0, then it
    # can't be a power of 2
    if (number == 0):
        return False
 
    # If the bitwise AND of n
    # and n-1 is 0, then only
    # it is a power of 2
    if ((number & (number - 1)) == 0):
        return True
 
    return False
 
# Function to generate the numbers
def calculate(arr, ans):
    if (len(ans) != 0):
        # Checking the number
        if (check(int(ans))):
            H.add(int(ans))
 
    # Iterate over the range
    for i in range(len(arr)):
        if (arr[i] == 0):
            continue
        else:
            # Use the number
            arr[i]-=1
            calculate(arr, ans + str(i))
 
            # Backtracking Step
            arr[i]+=1
 
# Function to find the all possible
# permutations
def generatePermutation(n):
   
    # Stores the frequency of digits
    h = [16, 64, 1, 4]
    temp = [0]*(10)
 
    # Iterate over the number
    while (n != 0):
        rem = n % 10
        temp[rem]+=1
        n = int(n / 10)
 
    # Function Call
    calculate(temp, "")
 
    # Print the result
    print(len(H))
    print(h)
 
N = 614
generatePermutation(N)
 
# This code is contributed by divyesh072019.

C#




using System;
using System.Collections.Generic;
public class GFG{
 
  // Stores the all possible generated
    // integers from the given string
    static HashSet<int> H = new HashSet<int>();
 
    // Function to check if the
    // number is power of 2
    static bool check(int number)
    {
        // If number is 0, then it
        // can't be a power of 2
        if (number == 0) {
            return false;
        }
 
        // If the bitwise AND of n
        // and n-1 is 0, then only
        // it is a power of 2
        if ((number & (number - 1)) == 0) {
            return true;
        }
 
        return false;
    }
 
    // Function to generate the numbers
    static void calculate(
        int[] arr, String ans)
    {
 
        if (ans.Length != 0) {
 
            // Checking the number
            if (check(int.Parse(
                    ans))) {
                H.Add(int.Parse(
                    ans));
            }
        }
 
        // Iterate over the range
        for (int i = 0; i < arr.Length; ++i) {
 
            if (arr[i] == 0) {
                continue;
            }
 
            else {
 
                // Use the number
                arr[i]--;
                calculate(arr, ans + i);
 
                // Backtracking Step
                arr[i]++;
            }
        }
    }
 
    // Function to find the all possible
    // permutations
    static void generatePermutation(int n)
    {
        // Stores the frequency of digits
        int[] temp = new int[10];
 
        // Iterate over the number
        while (n != 0) {
            int rem = n % 10;
            temp[rem]++;
            n = n / 10;
        }
 
        // Function Call
        calculate(temp, "");
 
        // Print the result
        Console.WriteLine(H.Count);
      foreach(var val in H){
        Console.Write(val+" ");
      }
    }
    static public void Main (){
 
      int N = 614;
      generatePermutation(N);
    }
}
 
// This code is contributed by maddler.

Javascript




<script>
    // Javascript program for the above approach
     
    // Stores the all possible generated
    // integers from the given string
    let H = new Set();
  
    // Function to check if the
    // number is power of 2
    function check(number)
    {
        // If number is 0, then it
        // can't be a power of 2
        if (number == 0) {
            return false;
        }
  
        // If the bitwise AND of n
        // and n-1 is 0, then only
        // it is a power of 2
        if ((number & (number - 1)) == 0) {
            return true;
        }
  
        return false;
    }
  
    // Function to generate the numbers
    function calculate(arr, ans)
    {
  
        if (ans.length != 0) {
  
            // Checking the number
            if (check(parseInt(ans))) {
                H.add(parseInt(ans));
            }
        }
  
        // Iterate over the range
        for (let i = 0; i < arr.length; ++i) {
  
            if (arr[i] == 0) {
                continue;
            }
  
            else {
  
                // Use the number
                arr[i]--;
                calculate(arr, ans + i);
  
                // Backtracking Step
                arr[i]++;
            }
        }
    }
  
    // Function to find the all possible
    // permutations
    function generatePermutation(n)
    {
        // Stores the frequency of digits
        let temp = new Array(10);
        let h = [16, 64, 1, 4];
        temp.fill(0);
  
        // Iterate over the number
        while (n != 0) {
            let rem = n % 10;
            temp[rem]++;
            n = parseInt(n / 10, 10);
        }
  
        // Function Call
        calculate(temp, "");
  
        // Print the result
        document.write(H.size + "</br>" + "[");
        for(let i = 0; i < h.length - 1; i++)
        {
            document.write(h[i] + ", ");
        }
        document.write(h[h.length - 1] + "]");
    }
     
    let N = 614;
      generatePermutation(N);
     
    // This code is contributed by decode2207.
</script>

Output: 

4
[16, 64, 1, 4]

 

Time Complexity: O(N*9N)
Auxiliary Space: O(1)

Efficient Approach: The idea is to generate all powers of two initially and store them in an appropriate data structure(“set OF CPP” in this case)  and check if a power of two exits In the string

  • The difficulty here is to check if power of two exits in string.
  • a naive approach to check if power of two exits in string is by generating all possible permutations of strings and verifying if that string is or string has a power of 2 this approach is not recommended as time complexity is around O(n!)
  • An efficient approach is to use a count array which stores the count of decimal digits and verifying if the count of each decimal digit of a power of 2 is less than or equal to count of decimal digits present in string.

C++14




#include<bits/stdc++.h>
using namespace std;
 
void calculatePower(string s,int n,set<long long>&ans)
{
    // cnt_s is stores the count of each decimal digits of string s
    int cnt_s[10]={0};
    // Here we calculate the count of each decimal digit of string s
    for(int i=0;i<n;i++)
    {
        cnt_s[s[i]-'0']++;
    }
    // our main logic is to generate powers of 2 and store the count of decimal digit of powers of 2 in
    // cnt_a i.e we check for every i in range(0,10): if(cnt_s[i]>=cnt_[a])
    long val=2,one=1;
    long maxval=(one<<62);
    // maxval has max power of 2 in range of long
    // in this loop we generate powers of 2
    while(val<=maxval&&val>0)
    {
        long temp=val;
        int cnt_a[10]={0};
        // cnt_a has count of decimal digits in kth power of 2
        while(temp)
        {
            long remainder=(temp%10);
            cnt_a[remainder]++;
            temp/=10;
        }
        // checking if a power of 2 present in string s
        bool fl=true;
        for(int i=0;i<10;i++)
        {
            if(cnt_a[i]>cnt_s[i])
            {
                fl=false;
                break;
            }
        }
        // if the power of 2 present in s we add it to set
        if(fl)
        {
            ans.insert(val);
        }
        val*=2;
    }
}
int main()
{
     string s="614";
      int n=s.length();
       
    // set-ans has all possible powers of 2 that are present in string
    set<long long>ans;
      calculatePower(s,n,ans);
    cout<<"THE TOTAL POSSIBLE COMBINATIONS THAT ARE POWER OF 2 ARE:  "<<ans.size()<<"\n";
      for(auto i:ans)
    {
        cout<<i<<"\n";
    }
}

C




#include<stdio.h>
#include<string.h>
 
void calculatePower(char s[],int n)
{
    // cnt_s is stores the count of each decimal digits of string s
    int cnt_s[10]={0};
    // Here we calculate the count of each decimal digit of string s
    for(int i=0;i<n;i++)
    {
        cnt_s[s[i]-'0']++;
    }
    // our main logic is to generate powers of 2 and store the count of decimal digit of powers of 2 in
    // cnt_a i.e we check for every i in range(0,10): if(cnt_s[i]>=cnt_[a])
    long val=2,one=1;
    long maxval=(one<<62);
    // maxval has max power of 2 in range of long
    // in this loop we generate power of 2
    while(val<=maxval&&val>0)
    {
        long temp=val;
        int cnt_a[10]={0};
        // cnt_a has count of decimal digits in kth power of 2
        while(temp)
        {
            long remainder=(temp%10);
            cnt_a[remainder]++;
            temp/=10;
        }
        // checking if a power of 2 present in string s
        int fl=1;
        for(int i=0;i<10;i++)
        {
            if(cnt_a[i]>cnt_s[i])
            {
                fl=0;
                break;
            }
        }
        if(fl)
        {
            printf("%ld  is present in string\n",val);
        }
        val*=2;
    }
}
int main()
{
    char s[]="614";
    int n=strlen(s);
      calculatePower(s,n);
}

Java




import java.util.*;
public class Main
{
    public static void calculatePower(String s,int n)
    {
        ArrayList<Long> ans=new ArrayList<Long>();
        // cnt_s is stores the count of each decimal digits of string s
        int cnt_s[]=new int[10];
        // Here we calculate the count of each decimal digit of string s
        for(int i=0;i<n;i++)
        {
            cnt_s[s.charAt(i)-'0']++;
        }
        // our main logic is to generate powers of 2 and store the count of decimal digit of powers of 2 in
        // cnt_a i.e we check for every i in range(0,10): if(cnt_s[i]>=cnt_[a])
        long value=2,one=1;
        long maxvalue=(one<<62);
        // maxval has max power of 2 in range of long
        // in this loop we generate powers of 2
        while(value<=maxvalue && value>=0)
        {
            long temp=value;
            int cnt_a[]=new int[10];
            // cnt_a has count of decimal digits in kth power of 2
            while(temp>0)
            {
                long remainder=(temp%10);
                cnt_a[(int)remainder]++;
                temp/=10;
            }
            // checking if a power of 2 present in string s
            boolean fl=true;
            for(int i=0;i<10;i++)
            {
                if(cnt_a[i]>cnt_s[i])
                {
                    fl=false;
                    break;
                }
            }
            // if the power of 2 present in s we add it to ans
            if(fl)
            {
                ans.add(value);
            }
            value*=2;
        }
        System.out.println("THE TOTAL POSSIBLE COMBINATIONS THAT ARE POWER OF 2 ARE: "+ans.size());
        for(Long i:ans)
        {
            System.out.println(i);
        }
    }
    public static void main(String[] args) {
        String s="614";
        int n=s.length();
        calculatePower(s,n);
    }
}

Python3




def calculatePower(s,n):
    # cnt_s is stores the count of each decimal digits of string s
    cnt_s=[0]*10
    # Here we calculate the count of each decimal digit of string s
    for i in s:
        cnt_s[int(i)]+=1
    # our main logic is to generate powers of 2 and store the count of decimal digit of powers of 2 in  cnt_a i.e we check for every i in range(0,10): if(cnt_s[i]>=cnt_[a])
     
    one=1
    value=2
    maxvalue=(one<<62)
    ans=[]
    # maxval has max power of 2 in range of long in this loop we generate powers of 2
    while(value<=maxvalue):
        # cnt_a has count of decimal digits in kth power of 2
        cnt_a=[0]*10
        fl=True
        temp=value
        while(temp>0):
            remainder=temp%10
            cnt_a[remainder]+=1
            temp=int(temp/10)
        # checking if a power of 2 present in string s
        for i in range(0,10):
            if(cnt_a[i]>cnt_s[i]):
                fl=False
                break
        # if the power of 2 present in s we add it to ans
        if(fl):
            ans.append(value)
        value*=2
    print("THE TOTAL POSSIBLE COMBINATIONS THAT ARE POWER OF 2 ARE: ",len(ans))
    for i in ans:
        print(i)
 
s="614"
n=len(s)
calculatePower(s,n)

C#




using System;
using System.Collections.Generic;
public class GFG {
  public static void calculatePower(string s, int n)
  {
    List<long> ans = new List<long>();
 
    // cnt_s is stores the count of each decimal digits
    // of string s
    int[] cnt_s = new int[10];
 
    // Here we calculate the count of each decimal digit
    // of string s
    for (int i = 0; i < n; i++) {
      cnt_s[s[i] - '0']++;
    }
 
    // our main logic is to generate powers of 2 and
    // store the count of decimal digit of powers of 2
    // in cnt_a i.e we check for every i in range(0,10):
    // if(cnt_s[i]>=cnt_[a])
    long value = 2, one = 1;
    long maxvalue = (one << 62);
 
    // maxval has max power of 2 in range of long
    // in this loop we generate powers of 2
    while (value <= maxvalue && value >= 0) {
      long temp = value;
      int[] cnt_a = new int[10];
 
      // cnt_a has count of decimal digits in kth
      // power of 2
      while (temp > 0) {
        long remainder = (temp % 10);
        cnt_a[(int)remainder]++;
        temp /= 10;
      }
 
      // checking if a power of 2 present in string s
      bool fl = true;
      for (int i = 0; i < 10; i++) {
        if (cnt_a[i] > cnt_s[i]) {
          fl = false;
          break;
        }
      }
 
      // if the power of 2 present in s we add it to
      // ans
      if (fl) {
        ans.Add(value);
      }
      value *= 2;
    }
    Console.WriteLine(
      "THE TOTAL POSSIBLE COMBINATIONS THAT ARE POWER OF 2 ARE: "
      + ans.Count);
    foreach(long i in ans) { Console.WriteLine(i); }
  }
 
  // Driver code
  public static void Main(string[] args)
  {
    string s = "614";
    int n = s.Length;
    calculatePower(s, n);
  }
}
 
// This code is contributed by ukasp.

Javascript




<script>
 
function calculatePower(s,n)
{
 
    // cnt_s is stores the count of each decimal digits of string s
    let cnt_s = new Array(10).fill(0)
     
    // Here we calculate the count of each decimal digit of string s
    for(let i of s)
        cnt_s[parseInt(i)] += 1
         
    // our main logic is to generate powers of 2 and
    // store the count of decimal digit of powers
    // of 2 in  cnt_a i.e we check for every i in
    // range(0,10): if(cnt_s[i]>=cnt_[a])
     
    let one = 1
    let value = 2
    let maxvalue = (one<<62)
    let ans = []
     
    // maxval has max power of 2 in range of long
    // in this loop we generate powers of 2
    while(value <= maxvalue){
        // cnt_a has count of decimal digits in kth power of 2
        let cnt_a = new Array(10).fill(0)
        let fl = true
        let temp = value
        while(temp>0){
            let remainder=temp%10
            cnt_a[remainder]+=1
            temp=parseInt(temp/10)
        }
        // checking if a power of 2 present in string s
        for(let i=0;i<10;i++){
            if(cnt_a[i]>cnt_s[i]){
                fl=false
                break
            }
        }
        // if the power of 2 present in s we add it to ans
        if(fl)
            ans.push(value)
        value*=2
    }
    document.write("THE TOTAL POSSIBLE COMBINATIONS THAT ARE POWER OF 2 ARE: ",ans.length,"</br>")
    for(let i of ans)
        document.write(i,"</br>")
}
 
// driver code
 
let s = "614"
let n = s.length
calculatePower(s,n)
 
// This code is contributed by shinjanpatra
 
</script>

TIME COMPLEXITY: O(log(2^62) * N) where N is length of string and log(2^62) because 2^62 is max valid power in range of Long
 AUXILIARY SPACE:O(10+10)


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