Find largest number smaller than N with same set of digits
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 number, then print “not possible”.
Input: N = "218765" Output: 218756 Input: N = "1234" Output: Not Possible Input: 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).
- 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 252346. We get 256432 which is the previous smaller number for input 262345.
Below is the implementation of the above approach:
Greatest smaller number with same set of digits is 256432