F-Cable master

最新推荐文章于 2024-03-28 12:58:54 发布

TimEckel

最新推荐文章于 2024-03-28 12:58:54 发布

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分类专栏：二分贪心

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本文介绍了一个经典的算法问题——切绳子问题，旨在帮助参赛者在编程比赛中均匀地分配网络电缆，确保每位选手间的最大距离。文章详细解释了如何通过二分搜索算法找到最优解，并给出了完整的C++代码实现。

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Description
Inhabitants of the Wonderland have decided to hold a regional programming contest. The Judging Committee has volunteered and has promised to organize the most honest contest ever. It was decided to connect computers for the contestants using a “star” topology - i.e. connect them all to a single central hub. To organize a truly honest contest, the Head of the Judging Committee has decreed to place all contestants evenly around the hub on an equal distance from it.
To buy network cables, the Judging Committee has contacted a local network solutions provider with a request to sell for them a specified number of cables with equal lengths. The Judging Committee wants the cables to be as long as possible to sit contestants as far from each other as possible.
The Cable Master of the company was assigned to the task. He knows the length of each cable in the stock up to a centimeter,and he can cut them with a centimeter precision being told the length of the pieces he must cut. However, this time, the length is not known and the Cable Master is completely puzzled.
You are to help the Cable Master, by writing a program that will determine the maximal possible length of a cable piece that can be cut from the cables in the stock, to get the specified number of pieces.
Input
The first line of the input file contains two integer numb ers N and K, separated by a space. N (1 = N = 10000) is the number of cables in the stock, and K (1 = K = 10000) is the number of requested pieces. The first line is followed by N lines with one number per line, that specify the length of each cable in the stock in meters. All cables are at least 1 meter and at most 100 kilometers in length. All lengths in the input file are written with a centimeter precision, with exactly two digits after a decimal point.
Output
Write to the output file the maximal length (in meters) of the pieces that Cable Master may cut from the cables in the stock to get the requested number of pieces. The number must be written with a centimeter precision, with exactly two digits after a decimal point.
If it is not possible to cut the requested number of pieces each one being at least one centimeter long, then the output file must contain the single number “0.00” (without quotes).
Sample Input
4 11
8.02
7.43
4.57
5.39
Sample Output
2.00

这题就是一个切绳子的问题n条剪成m条等长的绳子，普通二分就行，但是有细节，一个是精度要控制，另一个是类型转换的问题，c默认四舍五入而题目要求不能四舍五入，所以要特殊处理r=(int)(r*100)/100.0

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<math.h>
using namespace std;
double L[100500];
int a,b,i;
bool F(double x)
{
    int sum=0;
    for(i=0;i<a;i++)
        sum +=(int)(L[i]/x);
    return sum >= b;
}
void ww()
{
    double l=0,r=1100000,mid;
    while(r-l>1e-10)
    {
        mid=(r+l)/2;
        if(F(mid))
            l=mid;
        else
            r=mid;
    }
     r=(int)(r*100)/100.0;
     printf("%.2f\n",r);    
 }
 int main() 
 {
    scanf("%d%d",&a,&b);
    for(i=0;i<a;i++)
        scanf("%lf",&L[i]);
    ww();    
    return 0;
}