leetcode903 Valid Permutations for DI Sequence

Ideas:

dp [i] [j] indicates up to i + 1-position, and with all the remaining figures small section j + 1 is valid for all digital number sequence end.

achieve:

 1 class Solution
 2 {
 3 public:
 4     int numPermsDISequence(string S)
 5     {
 6         if (S.empty()) return 0;
 7         int n = S.length(), MOD = 1e9 + 7;
 8         vector<vector<int>> dp(2, vector<int>(n + 1, 0));
 9         for (int i = 0; i <= n; i++) dp[0][i] = 1;
10         for (int i = 1; i <= n; i++)
11         {
12             if (S[i - 1] == 'D')
13             {
14                 dp[i & 1][n - i] = dp[i - 1 & 1][n - i + 1];
15                 for (int j = n - i - 1; j >= 0; j--)
16                     dp[i & 1][j] = (dp[i & 1][j + 1] + dp[i - 1 & 1][j + 1]) % MOD;
17             }
18             else
19             {
20                 dp[i & 1][0] = dp[i - 1 & 1][0];
21                 for (int j = 1; j <= n - i; j++)
22                     dp[i & 1][j] = (dp[i - 1 & 1][j] + dp[i & 1][j - 1]) % MOD;
23             }
24         }
25         return dp[n & 1][0];
26     }
27 }