This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
//#include <ext/pb_ds/tree_policy.hpp>
//#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
//using namespace __gnu_pbds;
#define FOR(i,start,end) for(int i=start;i<(int)(end);i++)
#define FORE(i,start,end) for(int i=start;i<=(int)end;i++)
#define RFOR(i,start,end) for(int i = start; i>end; i--)
#define RFORE(i,start,end) for(int i = start; i>=end; i--)
#define all(a) a.begin(), a.end()
#define mt make_tuple
#define v vector
#define sf scanf
#define pf printf
#define dvar(x) cout << #x << " := " << x << "\n"
#define darr(x,n) FOR(i,0,n) cout << #x << "[" << i << "]" << " := " << x[i] << "\n"
typedef long long ll;
typedef long double ld;
typedef pair<int, int > pii;
typedef pair<ll, ll> pll;
const ll MOD = 1000000007LL;
const ll PRIME = 105943LL;
const ll INF = 1e18;
//template <class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T> void minn(T &a, T b) { a = min(a, b); }
template<class T> void maxx(T &a, T b) { a = max(a, b); }
void io() {
#ifdef LOCAL_PROJECT
freopen("input.in", "r", stdin); freopen("output.out", "w", stdout);
#else
/* online submission */
#endif
ios_base::sync_with_stdio(false); cin.tie(NULL);
}
/**************************COCI 2016-2017 Contest 3 Problem 4 *************************/
string expr;
int ending[1000000];
int K;
ll Z[55];
double calculateSum(v<double> &vals) {
double sum = 0;
for (auto d : vals)
sum += d;
return min((double)Z[vals.size()], sum);
}
double calculateProduct(v<double> &vals) {
sort(all(vals));
reverse(all(vals));
double targetSum = Z[vals.size()];
double prod = 1;
while (!vals.empty()) {
double avg = targetSum / vals.size();
if (vals.back() < avg) {
prod *= vals.back();
targetSum -= vals.back();
vals.pop_back();
continue;
}
FOR(i, 0, vals.size())
prod *= avg;
break;
}
return prod;
}
double solve(int l, int r) {
v<double> vals;
char op = '|';
for (int i = l + 1; i < r; i++) {
if (expr[i] == '(') {
vals.push_back(solve(i, ending[i]));
i = ending[i];
}
else if (expr[i] == '+'){
assert(op == '|' || op == '+');
op = '+';
}
else if (expr[i] == '*') {
assert(op == '|' || op == '*');
op = '*';
}
else if (expr[i] == '?')
return Z[1];
else
assert(0);
}
assert(vals.size() > 1);
return (op == '+' ? calculateSum(vals) : calculateProduct(vals));
}
void genEnding() {
stack<int> open;
FOR(i, 0, expr.size()) {
char c = expr[i];
if (c == '(')
open.push(i);
else if (c == ')') {
ending[open.top()] = i;
open.pop();
}
}
}
int main() {
io();
cin >> K;
FORE(i, 1, K) cin >> Z[i];
cin >> expr;
genEnding();
cout << std::fixed << std::setprecision(9) << solve(0, expr.size() - 1) << "\n";
return 0;
}
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