Difficult problem....DP referenced tutorial and solution report
This problem gives n, l, k
So we use these three to do DP state transition
dp[i][j][m] win j of the first i days and get total bag Probability
So
If we get a bag
dp[i+1][j+1][m+w[i]]=dp[i][j][m]*p[i]
If we get a trophy
dp[i+1][j+1][m-1]=dp[i][j][m]*p[i]
If we get nothing
dp[i+1][j][m]=dp[i][j][m]*(1-p[i])
So after calculating, as long as we get l or more days in n days, and the bag is not empty, we can add up the probabilities
Because it means you can get them all back, just add up all the probabilities of getting them back~~~~~
//
// GGGGGGGGGGGGG CCCCCCCCCCCCC AAA
// GGG::::::::::::G CCC::::::::::::C A:::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::::A
// G:::::G GGGGGG C:::::C CCCCCC A:::::::::A
//G:::::G C:::::C A:::::A:::::A
//G:::::G C:::::C A:::::A A:::::A
//G:::::G GGGGGGGGGGC:::::C A:::::A A:::::A
//G:::::G G::::::::GC:::::C A:::::A A:::::A
//G:::::G GGGGG::::GC:::::C A:::::AAAAAAAAA:::::A
//G:::::G G::::GC:::::C A:::::::::::::::::::::A
// G:::::G G::::G C:::::C CCCCCC A:::::AAAAAAAAAAAAA:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::A A:::::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A A:::::A
// GGG::::::GGG:::G CCC::::::::::::C A:::::A A:::::A
// GGGGGG GGGG CCCCCCCCCCCCCAAAAAAA AAAAAAA
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <cctype>
#include <utility>
#include <ctime>
using namespace std;
#ifdef DEBUG
#define VAR(a,b) decltype(b) a=(b)
#define debug(...) printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)
#define gettime() end\_time=clock();printf("now running time is %.7f\\n",(float)(end\_time - start\_time)/CLOCKS\_PER\_SEC);
#else
#define VAR(a,b) \_\_typeof(b) a=(b)
#define debug(...)
#define gettime()
#endif
typedef unsigned int uint;
typedef long long int Int;
typedef unsigned long long int UInt;
#define Set(a,s) memset(a,s,sizeof(a))
#define Write(w) freopen(w,"w",stdout)
#define Read(r) freopen(r,"r",stdin)
#define Pln() printf("\\n")
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()
#define De(x)printf(#x"%d\\n",x)
#define For(i,x)for(int i=0;i<x;i++)
#define CON(x,y) x##y
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\
printf("%d ",dp\[htx\]\[hty\]);}Pln();}
#define M 30005
#define PII pair<int,int\>
#define PB push\_back
#define oo INT\_MAX
#define Set\_oo 0x3f
#define FOR(a,b) for(VAR(a,(b).begin());a!=(b).end();++a)
#define eps 1e-6
#define X first
#define Y second
clock\_t start\_time=clock(), end\_time;
bool xdy(double x,double y){return x>y+eps;}
bool xddy(double x,double y){return x>y-eps;}
bool xcy(double x,double y){return x<y-eps;}
bool xcdy(double x,double y){return x<y+eps;}
int min3(int x,int y,int z){
int tmp=min(x,y);
return min(tmp,z);
}
int max3(int x,int y,int z){
int tmp=max(x,y);
return max(tmp,z);
}
double dp\[205\]\[205\]\[420\];
int n,l,k;
int no=200;
int ed=400;
int a\[205\];
int w\[205\];
int main() {
ios\_base::sync\_with\_stdio(0);
while(~scanf("%d%d%d",&n,&l,&k)){
for(int i=1;i<=n;i++)scanf("%d",&a\[i\]);
for(int i=1;i<=n;i++)scanf("%d",&w\[i\]);
Set(dp,0);
dp\[0\]\[0\]\[no+k\]=1;
for(int i=1;i<=n;i++){
for(int j=0;j<i;j++){
for(int k=0;k<=ed;k++){
if(w\[i\]!=-1){
int t=min(k+w\[i\],ed);
dp\[i\]\[j+1\]\[t\]+=dp\[i-1\]\[j\]\[k\]\*(a\[i\]/100.);
}else if(k>0){
dp\[i\]\[j+1\]\[k-1\]+=dp\[i-1\]\[j\]\[k\]\*(a\[i\]/100.);
}
dp\[i\]\[j\]\[k\]+=dp\[i-1\]\[j\]\[k\]\*((100-a\[i\])/100.);
}
}
}
double ans=0;
for(int i=l;i<=n;i++){
for(int j=no;j<=ed;j++){
ans+=dp\[n\]\[i\]\[j\];
}
}
printf("%.12f\\n",ans);
}
}