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Hard1-D Dynamic ProgrammingLC 903

Valid Permutations for DI Sequence

You are given a string s of length n where s[i] is either: 'D' means decreasing, or 'I' means increasing. A permutation perm of n + 1 integers of all the integers in the range [0, n] is called a valid permutation if for all valid i: If s[i] == 'D', then perm[i] > perm[i + 1], and If s[i] == 'I', then perm[i] < perm[i + 1]. Return the number of valid permutations perm. Since the answer may be large, return it modulo 109 + 7.

Hints
  • 1.Think about which data structure fits best
  • 2.Consider the time complexity of your approach
  • 3.Look for patterns in the constraints
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