ZOJ 3329-one Person Game (probabilistic DP, iterative processing ring)

Test instructions

Three dice have k1,2,k3 face each side of the label (1-K1,1-K2,1-K3), three dice at a time, the positive upward of three numbers, if the three designator and the given three number a1,b1,c1 corresponds to the sum of zero, otherwise the sum plus three dice marking and, until the sum is not less than n when the end, The desired number of times to ask for a parabolic boson.

Analysis:

The state of the problem is good analysis

Dp[i] represents and is the desired number of times for I, dp[0] is the answer

Dp[i]=sum (Dp[i+tmp]*p[tmp]) +dp[0]*p0+1 (TMP is the three dice can be obtained the marking and);

The first time to see such an equation is not solved, see the solution to know with the iterative method, each dp[i] includes dp[0];

Dp[i]=a[i]*dp[0]+b[i], brought into the above equation can be dp[i]= (sum (a[i+tmp]*p[tmp]) +p0) *dp[0]+sum (b[i+tmp]*p[tmp]) +1;

Then A[i]=sum (a[i+tmp]*p[tmp]) +p0,b[i]=sum (b[i+tmp]*p[tmp]) +1;

Then dp[0]=a[0]*dp[0]+b[0], to find out the answer;

#include <map>#include<Set>#include<list>#include<cmath>#include<queue>#include<stack>#include<cstdio>#include<vector>#include<string>#include<cctype>#include<complex>#include<cassert>#include<utility>#include<cstring>#include<cstdlib>#include<iostream>#include<algorithm>using namespaceStd;typedef pair<int,int>Pii;typedefLong Longll;#defineLson l,m,rt<<1#definePi ACOs (-1.0)#defineRson m+1,r,rt<<11#defineAll 1,n,1#defineRead Freopen ("In.txt", "R", stdin)Constll infll =0x3f3f3f3f3f3f3f3fll;Const intinf=0x7ffffff;Const intMoD =1000000007;Doublea[1010],b[1010],p[ -];intn,k1,k2,k3,a1,b1,c1;voidsolve () {Doubletp=1.0/(k1*k2*K3); Memset (P,0,sizeof(p)); Memset (A,0,sizeof(a)); memset (b,0,sizeof(b));  for(intI=1; i<=k1;++i) for(intj=1; j<=k2;++j) for(intk=1; k<=k3;++k)if(i!=a1| | j!=b1| | k!=C1) P[i+j+k]+=TP;  for(inti=n;i>=0;--i) {     for(intj=3;(i+j) <=n&&j<=k1+k2+k3;++j) {A[i]+=a[i+j]*P[j]; B[i]+=b[i+j]*P[j]; } A[i]+=TP; B[i]+=1.0; } printf ("%.15lf\n", b[0]/(1.0-a[0]));}intMain () {intT; scanf ("%d",&t);  while(t--) {scanf ("%d%d%d%d%d%d%d",&n,&k1,&k2,&k3,&a1,&b1,&C1);    Solve (); }return 0;}

ZOJ 3329-one Person Game (probabilistic DP, iterative processing ring)