1037_Agent_47.md

Algorithm: DP

Problem: 1037 Agent 47

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define vi vector<int>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vvi vector<vi>
#define vll vector<ll>
#define vvll vector<vector<ll>>
#define vpii vector<pair<int,int>>
#define vpll vector<pair<ll,ll>>
#define vb vector<bool>
#define vs vector<string>
///............x...........///
#define all(a) a.begin(), a.end()
#define allr(a) a.rbegin(), a.rend()
#define mp(a, b) make_pair(a, b)
#define pb push_back
#define ff first
#define ss second
#define bg begin()
#define UNIQUE(X) (X).erase(unique(all(X)), (X).end())
#define ft cout << "for test"<<endl;
#define read(v, a, n) for (int i = a; i<n; i++)cin>>v[i];
#define print(v) for (auto it : v)cout << it<<' ';cout << endl;
#define PI acos(-1.0)
#define yes cout <<"Yes"<< endl
#define no cout<<"No"<<endl
#define FIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define t_c int test, cs = 1;cin>>test;while (test--)
#define casep cout<<"Case "<< cs++<<": ";
///................function.....................///

#define D(a) (double)(a)
#define sqr(a) (a * a)
#define siz(s) (int)(s.size())
#define max3(a, b, c) max(a, max(b, c))
#define min3(a, b, c) min(a, min(b, c))
#define Min(a) *min_element(all(a))
///#define mod 1000000007
///.........Graph.........///
int X[] = {1, -1, 0, 0};
int Y[] = {0, 0, 1, -1};
///........constant........///
const ll N = 1e6+5;
class C{
public:
	int n;
	vector<string>s;
	vll v;
	vll dp;
	C(int _n){
		n=_n;
		s.resize(n);
		v.resize(n);
		for(int i=0; i<n; i++)cin>>v[i];
		for(int i=0; i<n; i++)cin>>s[i];
		dp.resize(1<<n,-1);
	}
	ll val(int pos, int bit){
		ll ret=v[pos];
		for(int i=0; i<n; i++){
			if(bit&(1<<i)){
				ll perShot = s[i][pos]-'0';
				if(perShot==0)continue;
				ret = min(ret,(v[pos]+perShot-1)/perShot);
			}	
		}
		return ret;
	}
	ll f(int bit){
		if(__builtin_popcountll(bit)==n)return 0;
		ll &ret = dp[bit];
		if(ret!=-1)return ret;
		ret=LLONG_MAX;
		for(int i=0; i<n; i++){
			if(bit&(1<<i))continue;
			ll cost =val(i,bit);
			ret = min(ret,cost+f(bit|(1<<i)));
		}
		return ret;
	}
};
int main(){
	FIO;
	t_c{
		int n;
		cin>>n;
		C ob(n);
		casep;cout<<ob.f(0)<<endl;
	}
}
/**
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**/