Codeforces801C Voltage Keepsake 2017-04-19 00:26 109人阅读 评论(0) 收藏

C. Voltage Keepsake

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You have n devices that you want to use simultaneously.

The i-th device uses ai units
of power per second. This usage is continuous. That is, in λ seconds, the device will use λ·ai units
of power. The i-th device currently has bi units
of power stored. All devices can store an arbitrary amount of power.

You have a single charger that can plug to any single device. The charger will add p units of power per second to a device. This charging
is continuous. That is, if you plug in a device for λ seconds, it will gain λ·p units
of power. You can switch which device is charging at any arbitrary unit of time (including real numbers), and the time it takes to switch is negligible.

You are wondering, what is the maximum amount of time you can use the devices until one of them hits 0 units of power.

If you can use the devices indefinitely, print -1. Otherwise, print the maximum amount of time before any one device hits 0 power.

Input

The first line contains two integers, n and p (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 109) —
the number of devices and the power of the charger.

This is followed by n lines which contain two integers each. Line i contains
the integers ai and bi (1 ≤ ai, bi ≤ 100 000) —
the power of the device and the amount of power stored in the device in the beginning.

Output

If you can use the devices indefinitely, print -1. Otherwise, print the maximum amount of time before any one device hits 0 power.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 4.

Namely, let's assume that your answer is a and the answer of the jury is b.
The checker program will consider your answer correct if .

Examples

input

2 1
2 2
2 1000

output

2.0000000000

input

1 100
1 1

output

-1

input

3 5
4 3
5 2
6 1

output

0.5000000000

Note

In sample test 1, you can charge the first device for the entire time until it hits zero power. The second device has enough power to last this time without being charged.

In sample test 2, you can use the device indefinitely.

In sample test 3, we can charge the third device for 2 / 5 of a second, then switch to charge the second device for a 1 / 10 of
a second

————————————————————————————————————

题目给出n台设备每分钟耗电量和初始电量，再给出充电器每分钟提供电量，问最长

能坚持多少时间每台设备都有电

思路：二分所需时间，验证是否够坚持这么久时间，题目的数据很大很大，控制精度

徘徊了无数次TLE和WA之后终于AC了

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <string>
#include <set>
#include <map>
#include <queue>

using namespace std;
#define inf 0x3f3f3f3f3f

struct node{
double x,y;
}p[100005];
int n;
double m;

bool check(double t)
{

    double ans=0;
    for(int i=0;i<n;i++)
    {
        ans+=max(0.0,p[i].x*t-p[i].y);
    }
    if(ans<=m*t)
        return 1;
    return 0;
}

int main()
{
    while(~scanf("%d%lf",&n,&m))
    {
        double cnt=0;
        for(int i=0;i<n;i++)
        {
            scanf("%lf%lf",&p[i].x,&p[i].y);
            cnt+=p[i].x;
        }
        if(m>=cnt)
            printf("-1\n");
        else
        {
              double l=0,r=inf;
              while(r-l>1e-4)
              {
                  double mid=(l+r)/2;
                  if(check(mid))
                    l=mid;
                  else
                    r=mid;
              }
              printf("%.10lf\n",l);
        }
    }
    return 0;
}