"Probability dp" ZOJ 3380 patchouli ' s Spell Cards

Channel

Test instructions: There is a M position, each position fills in a number, the number of the range is 1~n, ask at least a number of the same probability

Ideas:

The total is n^m, we ask for the probability of not having the same number as the L position * Set DP[I][J] means the number of the number of the first I, filling the J position of the scheme (to meet no l position is the same number) * DP[I][J]=DP[I-1][J]+SIGM (dp[i-1][j-k]*c[m- (J-K)] [K]  ) k<=j&&k<l * is actually looking at the number of I, can not fill, fill a position, two locations ... This accumulates. * Then the final answer is (N^m-dp[1~n][m])/(N^M)

Code:

ImportJava.util.*;ImportJava.io.*;Importjava.math.*; Public classmain{StaticBiginteger[][] Dp=Newbiginteger[110][110]; StaticBiginteger[][] C=NewBIGINTEGER[110][110];//Number of combinations     Public Static voidMain (String arg[]) {Scanner cin=NewScanner (NewBufferedinputstream (system.in));  for(inti=0;i<105;i++) {c[i][0]=c[i][i]=Biginteger.one;  for(intj=1;j<i;j++) C[i][j]=c[i-1][j-1].add (c[i-1][j]); }        intn,m,l;  while(Cin.hasnext ()) {M=Cin.nextint (); N=Cin.nextint (); L=Cin.nextint (); BigInteger Tol=biginteger.valueof (N). POW (M); if(l>M) {System.out.println ("Mukyu~"); Continue; }            if(L&GT;M/2)//this time you can use the combination number to find out.{BigInteger ans=Biginteger.zero;  for(inti=l;i<=m;i++) ans=ans.add (C[m][i].multiply (biginteger.valueof (N-1). Pow (M-i))); Ans=ans.multiply (biginteger.valueof (N)); BigInteger GCD=ANS.GCD (tol); System.out.println (Ans.divide (GCD)+"/"+tol.divide (GCD)); Continue; }             for(inti=0;i<=n;i++)                  for(intj=0;j<=m;j++) {Dp[i][j]=Biginteger.zero; } dp[0][0]=Biginteger.one;  for(inti=1;i<=n;i++)                 for(intj=1;j<=m;j++)                {                     for(intk=0;k<l&&k<=j;k++) Dp[i][j]=dp[i][j].add (Dp[i-1][j-k].multiply (c[m-(J-K)]                [K])); } BigInteger ans=Biginteger.zero;  for(inti=1;i<=n;i++) ans=Ans.add (dp[i][m]); Ans=tol.subtract (ans); BigInteger GCD=ANS.GCD (tol); System.out.println (Ans.divide (GCD)+"/"+tol.divide (GCD)); }    }}

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"Probability dp" ZOJ 3380 patchouli ' s Spell Cards