Codeforces 909 C. Python Indentation (dp+ Tree array optimization)

Topic Link: Python indentation

Test instructions

Python does not have curly braces to indicate a block of statements, but rather a strict indentation. There is now a simplified version of Python, with only two statements:

(1) ' s ' statement: simple statements. Equivalent to a general statement. (2) ' F ' statement: for statements. Corresponds to A For loop and specifies that its loop body cannot be empty.

Then give you a non-indented Python program, a total of n rows (n <= 5000). Ask you how many legitimate and different Python programs are available after you add indentation.

Solution: Problem Analysis

DP in the past, if the first position is ' F ', dp[i][j] only add to dp[i+1][j+1], if it is ' s ' can be added to all the numbers from dp[i][0,j]. Interval wigs can be optimized with a tree-like array to reduce the complexity to (Nxnxlog (n)). This problem let me find a long long operation is a bit slower than int, there is a mod operation is really slow, encounter mod operation can reduce the time with If.

1#include <bits/stdc++.h>2 using namespacestd;3 Const intMax_n = 5e3+9;4 Const intMOD = 1e9+7;5 CharVec[max_n];6 intDp[max_n][max_n];7 voidAddintPosintXintnum)8 {9     if(num<0) num+=MOD;Ten      for(; x<max_n;x+= (x&-x)) One     { Adp[pos][x]=dp[pos][x]+num; -         if(Dp[pos][x]>=mod) dp[pos][x]-=MOD; -     } the } - intSumintPosintx) - { -     intAns =0; +      for(;x>0; x-= (x&-x)) -     { +ans=ans+Dp[pos][x]; A         if(Ans>=mod) ans-=MOD; at     } -     returnans; - } - intMain () - { -     intn,m,t; in      while(cin>>N) -     { toMemset (DP,0,sizeof(DP)); +          for(intI=1; i<=n;i++) -         { theCin>>Vec[i]; *         } $dp[1][1] =1;Panax Notoginseng          for(intI=1; i<=n;i++) -         { the              for(intj=1; j<=i;j++) +             { A                 intt =sum (i,j); the                 if(Vec[i] = ='F') +                 { -Add (i+1, j+1, T); $Add (i+1, j+2,-t); $                 } -                 Else -                 { theAdd (i+1,1, T); -Add (i+1, j+1,-t);Wuyi                 } the             } -         } Wu         intAns =0; -          for(intI=1; i<=n;i++) About         { $Ans = ans+sum (n,i); -             if(Ans>=mod) ans-=MOD; -         } -cout<< (Ans+mod)%mod<<Endl; A     } +     return 0; the}

Codeforces 909 C. Python Indentation (dp+ Tree array optimization)