Codeforces 782B The Meeting Place Cannot Be Changed(二分答案)

题目链接 The Meeting Place Cannot Be Changed

二分答案即可。

check的时候先算出每个点可到达的范围的区间，然后求并集。判断一下是否满足l <= r就好了。

eps我设了1e-7。

#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b)              for(int i(a); i <= (b); ++i)

const int N      =    100000      +       10;
const double eps =    1e-7;

double mi, ma;

struct node{
    double x, y;
    friend bool operator < (const node &a, const node &b){
        return a.x < b.x;
    }
}a[N];
int n;

double c[N], d[N];

bool check(double x){
    rep(i, 1, n){
        c[i] = a[i].x - a[i].y * x;
        d[i] = a[i].x + a[i].y * x;
    }

    double l = c[1], r = d[1];
    rep(i, 2, n){
        l = max(l, c[i]);
        r = min(r, d[i]);
    }

    return l <= r;
}

int main(){

    mi = 2e9, ma = -mi;
    scanf("%d", &n);
    rep(i, 1, n){
        scanf("%lf", &a[i].x);
        mi = min(mi, a[i].x);
        ma = max(ma, a[i].x);
    }

    rep(i, 1, n){
        scanf("%lf", &a[i].y);
    }

    sort(a + 1, a + n + 1);

    double l = 0, r = 1000000000;
    while (abs(l - r) > eps){

        double mid = (l + r) / 2;

        if (check(mid)) r = mid; else l = mid;
    }
        
    printf("%.10f
", l);
    return 0;

}