# [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:

Note:

• 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.

https://discuss.leetcode.com/topic/76221/java-o-n-clean-solution-easy-to-understand