Smallest number by rearranging digits of a given number

Last Updated : 07 Apr, 2025

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.

Count the frequency of each digit in the number.
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.
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

Python

# 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# 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.

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>

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 ?>

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

Find smallest number formed by inverting digits of given number N

Ajay Kumar Agrahari(aJy aGr)

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Smallest number by rearranging digits of a given number

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