[LeetCode] 903. Valid Permutations for DI Sequence DI序列的有效排列

We are given?S, a length?n?string of characters from the set?{‘D‘, ‘I‘}. (These letters stand for "decreasing" and "increasing".)

A?valid permutation?is a permutation?P[0], P[1], ..., P[n]?of integers?{0, 1, ..., n}, such that for all?i:

• If?S[i] == ‘D‘, then?P[i] > P[i+1], and;
• If?S[i] == ‘I‘, then?P[i] < P[i+1].

How many valid permutations are there?? Since the answer may be large,?return your answer modulo?10^9 + 7.

Example 1:

Input: "DID"
Output: 5
Explanation:
The 5 valid permutations of (0, 1, 2, 3) are:
(1, 0, 3, 2)
(2, 0, 3, 1)
(2, 1, 3, 0)
(3, 0, 2, 1)
(3, 1, 2, 0)

Note:

1. 1 <= S.length <= 200
2. S?consists only of characters from the set?{‘D‘, ‘I‘}.

Github 同步地址:

https://github.com/grandyang/leetcode/issues/CHANGE_ME

参考资料：

https://leetcode.com/problems/valid-permutations-for-di-sequence/

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原文地址：https://www.cnblogs.com/grandyang/p/11094525.html