This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
const int N = 1e6 + 100;
int n, op[N];
vector < int > g[N];
double a[N], z[51];
inline double add(vector < int > &v){
double sum = 0;
for(int i = 0; i < (int)v.size(); i++){
sum += a[v[i]];
}
return min(sum, z[(int)v.size()]);
}
inline bool cmp(int x, int y){
return a[x] < a[y];
}
inline double mult(vector < int > &v){
sort(v.begin(), v.end(), cmp);
double sum = z[(int)v.size()], res = 1;
for(int i = 0; i < (int)v.size(); i++){
double mn = min(a[v[i]], sum / (double)((int)v.size() - i));
res *= mn;
sum -= mn;
}
return res;
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin >> n;
for(int i = 1; i <= n; i++){
cin >> z[i];
}
string s;
cin >> s;
stack < int > q;
int cur = 0;
for(auto it : s){
if(it == '('){
if(!q.empty()){
g[q.top()].push_back(cur);
}
q.push(cur++);
}
else if(it == ')'){
int x = q.top();
q.pop();
if(g[x].empty()){
a[x] = z[1];
}
else{
a[x] = (op[x] == 1 ? add(g[x]) : mult(g[x]));
}
}
else if(it == '+'){
op[q.top()] = 1;
}
else if(it == '*'){
op[q.top()] = 2;
}
}
cout << fixed << setprecision(6) << a[0];
}
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