LightOj 1079 (Just Another Robbery)
Idea⌗
DP
- Probability of robbing bank
a1 , a2 ... an = (1-p1) * (1-p2) * ... (1-pn)wherepi= the probability of getting caught from robbing banki - Use this idea to implement a variation of coin change dp .
/**Which of the favors of your Lord will you deny ?**/
#include<bits/stdc++.h>
using namespace std;
#define LL long long
#define PII pair<int,int>
#define PLL pair<LL,LL>
#define MP make_pair
#define F first
#define S second
#define INF INT_MAX
#define ALL(x) (x).begin(), (x).end()
#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<class TIn>
using indexed_set = tree<TIn, null_type, less<TIn>,rb_tree_tag, tree_order_statistics_node_update>;
/*
PBDS
-------------------------------------------------
1) insert(value)
2) erase(value)
3) order_of_key(value) // 0 based indexing
4) *find_by_order(position) // 0 based indexing
*/
inline void optimizeIO()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
}
const int nmax = 2e5+7;
const LL LINF = 1e17;
template<class T>
string to_str(T x)
{
stringstream ss;
ss<<x;
return ss.str();
}
//bool cmp(const PII &A,const PII &B)
//{
//
//}
double dp[10005]; /** dp[s] = Probability of robbing 's' millions i.e not getting caught robbing 's' millions **/
int money[105];
double p[105];
int main()
{
//freopen("out.txt","w",stdout);
optimizeIO();
int tc;
cin>>tc;
for(int qq=1; qq<=tc; qq++)
{
memset(dp,0,sizeof dp);
int n;
double thresh;
cin>>thresh>>n;
LL sum = 0;
for(int i=1;i<=n;i++)
cin>>money[i]>>p[i] , sum += money[i];
dp[0] = 1.0; /** Probability of robbing 0 million **/
for(int i=1;i<=n;i++)
for(int s=sum;s-money[i]>=0;s--)
dp[s] = max(dp[s],dp[s-money[i]]*(1-p[i])); /** As prob of not getting caught , So, (1-p[i]) is multiplied **/
// for(int s=sum;s>=0;s--)
// cout<<s<<" : "<<dp[s]<<endl;
for(int s=sum;s>=0;s--)
if(1-dp[s]<thresh) /** Prob of getting caught < threshold value **/
{cout<<"Case "<<qq<<": "<<s<<endl;break;}
}
return 0;
}
/**
1
0.29 4
7 0.04
10 0.69
2 0.78
2 0.78
Ans = 7
**/
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