Codeforces Round #409 Div.2(C. Voltage Keepsake)二分

C. Voltage Keepsake
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard 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.
题意：n个电器。一个每秒充P的充电器。给出每个电器的耗电速度和当前电量。问在其中一个机器用完电之前最多用多久时间。
题解：二分时间，判断是否可行，小数二分用判断次数的方法更佳！。注意上界要足够大。
代码：

#include
#include
#include
#include
#define ll long long
using namespace std;
int cnt;
int n;
double m;
struct node
{
    double x,y;
}a[100100];
int solve(double mid)
{
    double mx=mid*m;
    for(int i=1;i<=n;i++)
    {
        double q=a[i].x*mid;
        q-=a[i].y;
        if(q<=0) continue;
        if(mx>=q)
        {
            mx-=q;
        }
        else
        {
            return 0;
        }
    }
    return 1;
}
int main()
{
    cin>>n>>m;
    for(int i=1;i<=n;i++)
        cin>>a[i].x>>a[i].y;
    cnt=0;
    double ans=-1;
    double l=0;
    double r=100000000005;
    while(cnt<=150)
    {
        cnt++;
        double mid=(l+r)/2;
        if(solve(mid))
        {
            l=mid;
            ans=mid;
        }
        else r=mid;
    }
    if(ans>=10000000005) printf("-1\n");
    else
    printf("%.9lf\n",ans);
}