Submission #1720552

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Source Code Expand

#include <bits/stdc++.h>
using namespace std;

#ifdef DEBUG
#define NDEBUG
#include "cout11.h"
#endif
#undef NDEBUG
#include <cassert>

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> ii;
typedef pair<ll,ll> llll;
typedef pair<double,double> dd;

typedef vector<int> vi;


#define sz(a)  int((a).size())
#define pb  push_back
#define FOR(var,from,to) for(int var=(from);var<=(to);++var)
#define rep(var,n)  for(int var=0;var<(n);++var)
#define rep1(var,n)  for(int var=1;var<=(n);++var)
#define repC2(vari,varj,n)  for(int vari=0;vari<(n)-1;++vari)for(int varj=vari+1;varj<(n);++varj)
#define ALL(c)  (c).begin(),(c).end()
#define RALL(c)  (c).rbegin(),(c).rend()
#define tr(i,c)  for(auto i=(c).begin(); i!=(c).end(); ++i)
#define found(s,e)  ((s).find(e)!=(s).end())
#define mset(arr,val)  memset(arr,val,sizeof(arr))
#define mid(x,y) ((x)+((y)-(x))/2)
#define IN(x,a,b) ((a)<=(x)&&(x)<=(b))

#define INTSPACE 12
char _buf[INTSPACE*1000000 + 3];

int loadint() {
    if (fgets(_buf, INTSPACE+3, stdin)==NULL) return 0;
    return atoi(_buf);
}
int loadvec(vector<int>& v, int N=-1) {
    if (N == -1) {
        N = loadint();
        if (N==0) return 0;
    }
    int bufsize = INTSPACE*N + 3;
    if (fgets(_buf, bufsize, stdin)==NULL) return 0;
    v.resize(N);

    int i=0;
    bool last = false;
    for (char *p=&_buf[0]; ;) {
        char *q = p;
        while (*q > ' ') ++q;
        if (*q == 0x0D || *q == 0x0A) last = true;
        *q = 0;
        v[i++] = atoi(p);
        if (last || i == N) break;
        p = q+1;
    }
    // assert(i <= N);
    return i;
}

vector<int> t, v;

double maxs(int i, int a, int b) {
    // printf("[%d %d %d]\n", i, a, b);
    if (a > v[i] || b > v[i]) return -1;
    int w = t[i];
    if (abs(a - b) > w) return -1;
    double m = 0.5 * (b - a + w);
    double h = a + m;
    // t:0 -> m -> w
    // v:a -> h -> b
    if (h <= v[i]) {
        double S = (0.5 * (a + h) * m) + (0.5 * (h + b) * (w - m));
        // cout << S << endl;
        return S;
    }
    else {
        double u1 = v[i] - a, u2 = v[i] - b, mid = w - (u1 + u2);
        // printf("w=%d, u1=%g, u2=%g, mid=%g\n", w, u1,u2,mid);
        double S = (0.5 * (a + v[i]) * u1) + (v[i] * mid) + (0.5 * (b + v[i]) * u2);
        // cout << S << endl;
        return S;
    }
}

double solve(int N) {
    vector<double> d(101, -1);
    d[0] = 0;

    rep(i, N) {
        vector<double> d2(101, -1);
        rep(a, 101) {
            if (d[a] < 0) continue;
            rep(b, 101) {
                double f = maxs(i, a, b);
                if (f < 0) continue;
                d2[b] = max(d2[b], d[a]+f);
            }
        }
        /// cout << i << d2 << endl;
        d = d2;
    }
    return d[0];
}


int main() {
    int N = loadint();
    t.resize(N); v.resize(N);
    loadvec(t, N);
    loadvec(v, N);
    double ans = solve(N);
    printf("%.6f\n", ans);
    return 0;
}

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