[Leetcode] Find Permutation

By now, you are given a secret signature consisting of character ‘D’ and ‘I’. ‘D’ represents a decreasing relationship between two numbers, ‘I’ represents an increasing relationship between two numbers. And our secret signature was constructed by a special integer array, which contains uniquely all the different number from 1 to n (n is the length of the secret signature plus 1). For example, the secret signature “DI” can be constructed by array [2,1,3] or [3,1,2], but won’t be constructed by array [3,2,4] or [2,1,3,4], which are both illegal constructing special string that can’t represent the “DI” secret signature.

On the other hand, now your job is to find the lexicographically smallest permutation of [1, 2, … n] could refer to the given secret signature in the input.

Example 1:

Example 2:



  • The input string will only contain the character ‘D’ and ‘I’.
  • The length of input string is a positive integer and will not exceed 10,000

A simple solution is to use dfs search and back tracking. See the following code:

However, the above method does not work when the input is too long. 

The following is a much better solution:

For example, given IDIIDD we start with sorted sequence 1234567

Then for each k continuous D starting at index i we need to reverse [i, i+k] portion of the sorted sequence.