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
- Place the smallest digit (except 0) at the left most of the required number.
and decrement the frequency of that digit by 1. - Place all remaining digits in ascending order from left to right.
- Else if it is a negative number then
- Place the largest digit at the left most of the required number. and decrement the frequency of that digit by 1.
- 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;
}
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
# 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.
<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 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
?>
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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