Given a number **N** in the form of string. The task is to find the greatest number that has same set of digits as N and is smaller than N. If it is not possible to find any such numebr, then print “not possible”.

**Examples**:

Input: N = "218765"Output: 218756Input: N = "1234"Output: Not PossibleInput: N = "262345"Output: 256432

Following are few observations about the greatest number smaller than N:

- If all digits sorted in ascending order, then output is always “Not Possible”. For example, 1234.
- If all digits are sorted in descending order, then we need to swap last two digits. For example, 4321.
- For other cases, we need to process the number from rightmost side (why? because we need to find the greatest of all smaller numbers).

**Algorithm**:

- Traverse the given number from rightmost digit, keep traversing till you find a digit which is greater than the previously traversed digit. For example, if the input number is “262345”, we stop at 6 because 6 is greater than previous digit 5. If we do not find such a digit, then output is “Not Possible”.
- Now search the right side of above found digit ‘d’ for the greatest digit smaller than ‘d’. For “262345?, the right side of 6 contains “2345”. The greatest digit smaller than 6 is 5.
- Swap the above found two digits, we get “252346” in above example.
- Now sort all digits from position next to ‘d’ to the end of number in descending order. The number that we get after sorting is the output. For above example, we sort digits in bold 25
**2346**. We get**256432**which is the previous smaller number for input**262345**.</li

Below is the implementation of the above approach:

`// C++ implementation of the above approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find previous number ` `void` `findPrevious(string number, ` `int` `n) ` `{ ` ` ` `int` `i, j; ` ` ` ` ` `// I) Start from the right most digit ` ` ` `// and find the first digit that is ` ` ` `// smaller than the digit next to it. ` ` ` `for` `(i = n - 1; i > 0; i--) ` ` ` `if` `(number[i] < number[i - 1]) ` ` ` `break` `; ` ` ` ` ` `// If no such digit is found ` ` ` `// then all digits are in ascending order ` ` ` `// means there cannot be a smallest number ` ` ` `// with same set of digits ` ` ` `if` `(i == 0) { ` ` ` `cout << ` `"Previous number is not possible"` `; ` ` ` `return` `; ` ` ` `} ` ` ` ` ` `// II) Find the greatest digit on ` ` ` `// right side of (i-1)'th digit that is ` ` ` `// smaller than number[i-1] ` ` ` `int` `x = number[i - 1], greatest = i; ` ` ` `for` `(j = i; j < n; j++) ` ` ` `if` `(number[j] < x && number[j] > number[greatest]) ` ` ` `greatest = j; ` ` ` ` ` `// III) Swap the above found smallest digit with number[i-1] ` ` ` `swap(number[greatest], number[i - 1]); ` ` ` ` ` `// IV) Sort the digits after (i-1) in descending order ` ` ` `sort(number.begin() + i, number.begin() + n, greater<` `char` `>()); ` ` ` ` ` `cout << ` `"Greatest smaller number with same set of digits is "` `<< number; ` ` ` ` ` `return` `; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `string digits = ` `"262345"` `; ` ` ` `int` `n = digits.length(); ` ` ` ` ` `findPrevious(digits, n); ` ` ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

**Output:**

Greatest smaller number with same set of digits is 256432

## Recommended Posts:

- Largest number smaller than or equal to n and digits in non-decreasing order
- Find the Largest number with given number of digits and sum of digits
- Find the Largest Cube formed by Deleting minimum Digits from a number
- Largest number smaller than or equal to N divisible by K
- Largest smaller number possible using only one swap operation
- Largest number not greater than N all the digits of which are odd
- Largest number with prime digits
- Largest number with the given set of N digits that is divisible by 2, 3 and 5
- Find the largest multiple of 3 from array of digits | Set 2 (In O(n) time and O(1) space)
- Find the closest and smaller tidy number
- Find the largest good number in the divisors of given number N
- Find count of digits in a number that divide the number
- Find maximum number that can be formed using digits of a given number
- Find the smallest number whose digits multiply to a given number n
- Find first and last digits of a number