Submission #2866023

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Source Code Expand

#include <iostream>
#include <sstream>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <stack>
#include <memory>
#include <complex>
#include <numeric>
#include <cstdio>
#include <iomanip>

#define REP(i,m,n) for(int i=int(m);i<int(n);i++)
#define RREP(i,m,n) for(int i=int(n)-1;i>=int(m);--i)
#define EACH(i,c) for (auto &(i): c)
#define all(c) begin(c),end(c)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort(begin(c),end(c))
#define pb emplace_back
#define MP make_pair
#define SZ(a) int((a).size())

#ifdef LOCAL
#define DEBUG(s) cout << (s) << endl
#define dump(x)  cerr << #x << " = " << (x) << endl
#define BR cout << endl;
#else
#define DEBUG(s) do{}while(0)
#define dump(x) do{}while(0)
#define BR 
#endif
using namespace std;

using UI = unsigned int;
using UL = unsigned long;
using LL = long long int;
using ULL = unsigned long long;
using VI = vector<int>;
using VVI = vector<VI>;
using VLL = vector<LL>;
using VS = vector<string>;
using PII = pair<int,int>;
using VP = vector<PII>;

//struct edge {int from, to, cost;};

constexpr double EPS = 1e-10;
constexpr double PI  = acos(-1.0);
//constexpr int INF = INT_MAX;

template<class T> inline T sqr(T x) {return x*x;}

void solve() {
    int n;
    cin >> n;
    vector<double> t(n), v(n), s(n);
    REP(i,0,n) cin >> t[i];
    REP(i,0,n) cin >> v[i];
    /*
    s[0] = min({v[0], t[0], v[1]});
    REP(i,1,n-1) {
        s[i] = min({s[i-1]+t[i],v[i],v[i+1]});
        if (s[i] + t[i] < s[i-1]) {
            RREP(j,0,i-1) {
                s[j] = min(s[j], s[j+1] + t[j+1]);
            }
        }
    }
    */
    int ti = 0;
    VI ru(n);
    ru[0] = t[0];
    REP(i,1,n) ru[i] = ru[i-1] + t[i];
    REP(i,0,n) {
        ti += t[i];
        s[i] = ti;
        REP(j,0,n) {
            if (j == 0) {
                if (ti <= t[0]) s[i] = min(s[i], v[0]);
                else s[i] = min(s[i], v[0] + ti - t[0]);
            } else {
                if (ti <= ru[j-1]) s[i] = min(s[i], v[j] + ru[j-1] - ti);
                else if (ti <= ru[j]) s[i] = min(s[i], v[j]);
                else s[i] = min(s[i], v[j] + ti - ru[j]);
            }
        }
        s[i] = min(s[i], 0.0 + ru[n-1] - ti);
    }
    // REP(i,0,n) cerr << s[i] << endl;
    double ans = 0.0;
    double y = min(0.5 * (t[0] + s[0]), 1.0 * v[0]);
    ans += 1.0 * t[0] * y - 0.5 * (y * y + (y - s[0]) * (y - s[0]));
    //cerr << 1.0 * t[0] * y - 0.5 * (y * y + (y - s[0]) * (y - s[0])) << endl;
    REP(i,1,n) {
        y = min(0.5 * (t[i] + s[i] + s[i-1]), 1.0 * v[i]);
        ans += 1.0 * t[i] * y - 0.5 * ((y - s[i-1]) * (y - s[i-1]) + (y - s[i]) * (y - s[i]));
        //cerr << 1.0 * t[i] * y - 0.5 * (y * y + (y - s[i]) * (y - s[i])) << endl;
    }
    printf("%.12lf\n", ans);
}

int main() {
    solve();
    
    return 0;
}

Submission Info

Judge Result