2017级寒假讲座二分三分训练题A - Cable master （浮点数二分法将其转化成整数进行）

题目：A - Cable master
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

大意：就是从所给出的每一个绳子，要分出11段彻底相同的，而后输出能分的最大的长度；

思路：这里用二分法进行，能分出来的长度只可能从0到最大的绳子的长度之间，因此二分时只须要在这个范围内二分便可；而后二分出来的值看可否让其凑出11段；

注意：这个由于是要求比较精确的状况，即保留两位小数点的时候，因此尽可能避免直接用浮点数来进行，而是要转换成整型来进行；（由于浮点数的精度问题会很难受，因此要特别注意！）（这个转化成整型，即成100来进行）；

新技巧：之后对于这类的浮点数的二分时，将其转化成整型进行二分；（若是扩大倍数的，以后别忘再缩回来）；

代码：

#include <iostream>
#include<cstring>
#include<stdio.h>
using namespace std;
        int len[10005];
int main(){
    long n,k,ks,i;
    while(scanf("%ld%ld",&n,&k)!=EOF){
        int  ans,left=0,maxs=0,mid;

        double input[10005];
        for(i=0;i<n;i++){
            scanf("%lf",&input[i]);
            len[i]=input[i]*100;
            maxs=maxs>len[i]?maxs:len[i];
        }
        while(maxs>=left){
            ks=0;
            ans=(maxs+left)/2;
            if(!ans){
                mid=ans;
                break;
            }
            for(i=0;i<n;i++)
                ks+=len[i]/ans;
            if(ks>=k){
                left=ans+1;
                mid=ans;
            }
            else
                maxs=ans-1;
        }
        printf("%.2f\n",(double)mid/100);
    }
    return 0;
}