UVA11021 tribles[discrete probability DP]

Uva-11021tribles

Gravitation, N. "The tendency of all bodies to approach one another with a strength proportion to the quantity of matter T Hey contain–the quantity of matter they contain being ascertained by the strength of their tendency to approach one anot Her. This is a lovely and edifying illustration of what science, have made a the proof of B, makes B the proof of a. "

                                                                       Ambrose Bierce

You have a population of K tribbles. This particular species of tribbles live for exactly one day and then die. Just before death, a single tribble have the probability Pi of giving birth to I more tribbles. What's the probability that after M generations, every tribble would be dead?

Input

The first line of input gives the number of cases, N. n test Cases follow. Each one starts with a line CONTAININGN (1≤n≤1000), K (0≤k≤1000) Andm (0≤m≤1000). Thenextnlineswillgivethe probabilities P0, P1, ..., pn−1.

Output

For each test case, the output one line containing ' case #x: ' followed by the answer, correct-to-an absolute or relative ER Ror of 10−6.

Sample Input

4 3 1 1 0.33 0.34 0.33 3 1 2 0.33 0.34 0.33 3 1 2 0.5 0.0 0.5 4 2 2 0.5 0.0 0.0 0.5

Sample Output

Case #1:0.3300000Case #2:0.4781370Case #3:0.6250000Case #4:0.3164062

Each ball is independent of each other, and one can be asked.
F[i] Indicates the probability of the total death of 1 balls and offspring after I days
F[i]=p[0]+p[1]*f[i-1]+p[2]*f[i-1]^2+ .....
Boundary f[0]=0

////main.cpp//uva11021////Created by Candy on 26/10/2016.//copyright©2016 Candy. All rights reserved.//#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#include<cmath>using namespacestd;Const intn=1005;intt,n,m,k;DoubleF[n],p[n];inlineDoublefpDoubleAintb) {    Doubleans=1.0;  for(; b;b>>=1, a*=a)if(b&1) ans*=A; returnans;}voiddp () {f[0]=0;  for(intI=1; i<=m;i++) {F[i]=p[0];  for(intj=1; j<n;j++) F[I]+=P[J]*FP (f[i-1],j); }}intMainintargcConst Char*argv[]) {scanf ("%d",&T);  for(intcas=1; cas<=t;cas++) {scanf ("%d%d%d",&n,&k,&m);  for(intI=0; i<n;i++) scanf ("%LF",&P[i]);        DP (); printf ("Case #%d:%.7lf\n", CAS,FP (f[m],k)); }        return 0;}

UVA11021 tribles[discrete probability DP]