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 signaturewas 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:
Input: "I" Output: [1,2] Explanation: [1,2] is the only legal initial spectial string can construct secret signature "I", where the number 1 and 2 construct an increasing relationship.
Example 2:
Input: "DI" Output: [2,1,3] Explanation: Both [2,1,3] and [3,1,2] can construct the secret signature "DI",
but since we want to find the one with the smallest lexicographical permutation, you need to output [2,1,3]
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
这道题给了我们一个由D和I两个字符组成的字符串，分别表示对应位置的升序和降序，要我们根据这个字符串生成对应的数字字符串。由于受名字中的permutation的影响，感觉做法应该是找出所有的全排列然后逐个数字验证，这种方法十有八九无法通过OJ。其实这题用贪婪算法最为简单，我们来看一个例子：
D D I I D I
1 2 3 4 5 6 7
3 2 1 4 6 5 7
我们不难看出，只有D对应的位置附近的数字才需要变换，而且变换方法就是倒置一下字符串，我们要做的就是通过D的位置来确定需要倒置的子字符串的起始位置和长度即可。通过观察，我们需要记录D的起始位置i，还有D的连续个数k，那么我们只需要在数组中倒置[i, i+k]之间的数字即可，根据上述思路可以写出代码如下：
解法一：
class Solution { public: vector<int> findPermutation(string s) { int n = s.size(); vector<int> res(n + 1); for (int i = 0; i < n + 1; ++i) res[i] = i + 1; for (int i = 0; i < n; ++i) { if (s[i] != 'D') continue; int j = i; while (s[i] == 'D' && i < n) ++i; reverse(res.begin() + j, res.begin() + i + 1); --i; } return res; } };
下面这种方法没有用到数组倒置，而是根据情况来往结果res中加入正确顺序的数字，我们遍历s字符串，遇到D直接跳过，遇到I进行处理，我们每次先记录下结果res的长度size，然后从i+1的位置开始往size遍历，将数字加入结果res中即可，参见代码如下：
解法二：
class Solution { public: vector<int> findPermutation(string s) { vector<int> res; for (int i = 0; i < s.size() + 1; ++i) { if (i == s.size() || s[i] == 'I') { int size = res.size(); for (int j = i + 1; j > size; --j) { res.push_back(j); } } } return res; } };
类似题目：
参考资料：
https://leetcode.com/problems/find-permutation/
https://leetcode.com/problems/find-permutation/discuss/96644/c-simple-solution-in-72ms-and-9-lines