Smallest number by rearranging digits of a given number

Find the Smallest number (Not leading Zeros) which can be obtained by rearranging the digits of a given number. 

Examples:

Input: n = 846903
Output: 304689

Input: n = 55010
Output: 10055

Input: n = -40505
Output: -55400

Steps to find the smallest number.  

1. Count the frequency of each digit in the number.
2. If it is a non-negative number then
   1. Place the smallest digit (except 0) at the left most of the required number. 
      and decrement the frequency of that digit by 1.
   2. Place all remaining digits in ascending order from left to right.
3. Else if it is a negative number then
   1. Place the largest digit at the left most of the required number. and decrement the frequency of that digit by 1.
   2. Place all remaining digits in descending order from right to left.

This solution is based on counting sort. 

C++

// C++ program for finding smallest number
// from digits of given number
#include<iostream>
using namespace std;

// function to find the smallest number
int smallest(int num)
{
    // initialize frequency of each digit to Zero
    int freq[10] = {0};

      // Checking Number is positive or Negative
    bool is_pos = (num>0);

      // Getting the absolute value of num
    num = abs(num);

    // count frequency of each digit in the number
    while (num)
    {
        int d = num % 10; // extract last digit
        freq[d]++; // increment counting
        num = num / 10; //remove last digit
    }

    int result = 0;

      // If it is positive Number then it should be smallest
      if(is_pos)
    {
      // Set the Leftmost digit to minimum except 0
      for (int i = 1 ; i <= 9 ; i++)
      {
          if (freq[i])
          {
              result = i;
              freq[i]--;
              break;
          }
      }

      // arrange all remaining digits
      // in ascending order
      for (int i = 0 ; i <= 9 ; i++)
          while (freq[i]--)
              result = result * 10 + i;
    }
    else  // If negative then number should be Largest
    {
      // Set the Leftmost digit to maximum
      for (int i = 9 ; i >= 1 ; i--)
      {
         if (freq[i])
         {
            result = i;
            freq[i]--;
            break;
         }
      }

      // arrange all remaining digits
      // in descending order
      for (int i = 9 ; i >=0 ; i--)
         while (freq[i]--)
            result = result * 10 + i;

      // Negative number should be returned here
      result = -result;
    }
    return result;
}

// Driver Program
int main()
{
    int num = 570107;
    cout << smallest(num) << endl;

    int num2 = -691005;
    cout << smallest(num2);
    return 0;
}

Java

import java.lang.Math;

// Java program for finding smallest number
// from digits of given number
public class GFG {

    // function to find the smallest number
    static int smallest(int num)
    {
        // initialize frequency of each digit to Zero
        int[] freq = new int[10];

           // Checking Number is positive or Negative
        boolean is_pos = (num>0);

          // Getting the absolute value of num
        num = Math.abs(num);

        // count frequency of each digit in the number
        while (num > 0)
        {
            int d = num % 10; // extract last digit
            freq[d]++; // increment counting
            num = num / 10; //remove last digit
        }

       int result = 0;

          // If it is positive Number then it should be smallest
          if(is_pos)
        {
            // Set the LEFTMOST digit to minimum expect 0
            for (int i = 1 ; i <= 9 ; i++)
            {
                    if (freq[i] != 0)
                {
                        result = i;
                        freq[i]--;
                    break;
                }
            }

            // arrange all remaining digits
            // in ascending order
            for (int i = 0 ; i <= 9 ; i++)
                while (freq[i]-- != 0)
                    result = result * 10 + i;
         }
          else  // If negative then number should be Largest
        {
          // Set the Rightmost digit to maximum
          for (int i = 9 ; i >= 1 ; i--)
          {
             if (freq[i] !=0)
             {
                result = i;
                freq[i]--;
                break;
             }
          }

          // arrange all remaining digits
          // in descending order
          for (int i = 9 ; i >=0 ; i--)
             while (freq[i]-- != 0)
                result = result * 10 + i;

          // Negative number should be returned here
          result = -result;
        }
        return result;
    }

    // Driver Program
    public static void main(String args[])
    {
        int num = 570107;
        System.out.println(smallest(num));

        int num2 = -691005;
        System.out.println(smallest(num2));
    }
}
// This code is contributed by Sumit Ghosh

Python3

# Function to find the smallest number
def smallest(lst):

    # Here i is index and n is the number of the list
    for i,n in enumerate(lst):

        # Checking for the first non-zero digit in the sorted list
        if n != '0':

            # Remove and store the digit from the lst
            tmp = lst.pop(i)
            break

    # Place the first non-zero digit at the starting
    # and return the final number
    return str(tmp) + ''.join(lst)


# Driver program
if __name__ == '__main__':

    # Converting the given numbers into string to form a list
    lst = list(str(570107))
    lst.sort()

    # Calling the function using the above list
    print (smallest(lst))

# This code is contributed by Mahendra Yadav

C#

// C# program for finding smallest
// number from digits of given
// number
using System;

public class GFG {

    // function to find the smallest
    // number
    static int smallest(int num)
    {

        // initialize frequency of
        // each digit to Zero
        int[] freq = new int[10];

        // count frequency of each
        // digit in the number
        while (num > 0)
        {

            // extract last digit
            int d = num % 10;

            // increment counting
            freq[d]++;

            //remove last digit
            num = num / 10;
        }

        // Set the LEFTMOST digit to
        // minimum expect 0
        int result = 0;
        for (int i = 1 ; i <= 9 ; i++)
        {
            if (freq[i] != 0)
            {
                result = i;
                freq[i]--;
                break;
            }
        }

        // arrange all remaining digits
        // in ascending order
        for (int i = 0 ; i <= 9 ; i++)
            while (freq[i]-- != 0)
                result = result * 10 + i;

        return result;
    }

    // Driver Program
    public static void Main()
    {
        int num = 570107;
        Console.WriteLine(smallest(num));
    }
}

// This code is contributed by anuj_67.

PHP

<?php
// PHP program for finding smallest
// number from digits of given number

// function to find the smallest number
function smallest($num)
{
    // initialize frequency of
    // each digit to Zero
    $freq = array_fill(0, 10, 0);

    // count frequency of each
    // digit in the number
    while ($num)
    {
        $d = $num % 10; // extract last digit
        $freq[$d]++; // increment counting
        $num = (int)($num / 10); // remove last digit
    }

    // Set the LEFTMOST digit
    // to minimum expect 0
    $result = 0;
    for ($i = 1 ; $i <= 9 ; $i++)
    {
        if ($freq[$i])
        {
            $result = $i;
            $freq[$i]--;
            break;
        }
    }

    // arrange all remaining digits
    // in ascending order
    for ($i = 0 ; $i <= 9 ; $i++)
        while ($freq[$i] > 0)
        {
            $result = $result * 10 + $i;
            $freq[$i] -= 1;
        }

    return $result;
}

// Driver Code
$num = 570107;
echo smallest($num);

// This code is contributed by mits
?>

Javascript

<script>

// Javascript program for finding smallest number
// from digits of given number

// function to find the smallest number
function smallest(num)
{
    // initialize frequency of each digit to Zero
    var freq = Array(10).fill(0);

    // count frequency of each digit in the number
    while (num)
    {
        var d = num % 10; // extract last digit
        freq[d]++; // increment counting
        num = parseInt(num / 10); //remove last digit
    }

    // Set the LEFTMOST digit to minimum expect 0
    var result = 0;
    for (var i = 1 ; i <= 9 ; i++)
    {
        if (freq[i])
        {
            result = i;
            freq[i]--;
            break;
        }
    }

    // arrange all remaining digits
    // in ascending order
    for (var i = 0 ; i <= 9 ; i++)
        while (freq[i]--)
            result = result * 10 + i;

    return result;
}

// Driver Program
var num = 570107;
document.write(smallest(num));

// This code is contributed by rutvik_56.
</script>

Output

100577
-965100

Time complexity: O(n), where n is the number of digits in the given number.

Space complexity: O(1), as only a constant amount of memory is used for the freq array.

Another Approach:Find smallest permutation of given number
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