HDU 4055 Number String (dp的思想)
Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) Problem Description
The signature of a permutation is a string that is computed as follows: for each pair of consecutive elements of the permutation, write down the letter 'I' (increasing) if the second element is greater than the first one, otherwise write down the letter 'D'
(decreasing). For example, the signature of the permutation {3,1,2,7,4,6,5} is "DIIDID".
Input
Each test case consists of a string of 1 to 1000 characters long, containing only the letters 'I', 'D' or '?', representing a permutation signature.
Output
For each test case, print the number of permutations satisfying the signature on a single line. In case the result is too large, print the remainder modulo 1000000007.
Sample Input II ID DI DD ?D ??
Sample Output 1 2 2 1 3 6
Author HONG, Qize
Source 2011 Asia Dalian Regional Contest
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#include <iostream> #include <cstring> #include <cstdio> #include <string> using namespace std; const int maxn=1010; const int mod=1000000007; string st; long long dp[maxn][maxn],sum[maxn]; void computing(){ int len=st.length(); dp[1][1]=1; sum[1]=1;sum[0]=0; for(int i=2;i<=1+len;i++){ for(int j=1;j<=i;j++){ if(st[i-2]=='D') dp[i][j]=sum[j-1]; else if(st[i-2]=='I') dp[i][j]=((sum[i-1]-sum[j-1])%mod+mod)%mod; else dp[i][j]=sum[i-1]; } sum[0]=0; for(int j=1;j<=i;j++){ sum[j]=(sum[j-1]+dp[i][j])%mod; } } cout<<sum[len+1]<<endl; } int main(){ while(cin>>st){ computing(); } return 0; }