POJ 1064 Cable master

Cable master

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 34728		Accepted: 7391

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

假定一个解并判断是否可行

题意：

有n条绳子，他们的长度分别为Li。如果从他们中切割出k条长度相同的绳子的话，这k条绳子每条最长能有多长？答案保留到小数点后2位。

 

像这样，如果在求解最大化或最小化问题中，能够比较简单地判断条件是否满足，那么使用二分搜索法就可以很好的解决问题。

#include <cstdio>
#include <cmath>
using namespace std;
const int maxn = 10000 + 10;
const int INF = 100000000;
int n, k;
double L[maxn];

//判断是否满足条件
bool C(double x)
{
    int num = 0;
    for (int i = 0; i < n; i++){
        num += (int)(L[i] / x);
    }
    return num >= k;
}

void solve()
{
    //初始化解的范围
    double lb = 0, ub = INF;

    //重复循环，直到解的范围足够小
    for (int i = 0; i < 100; i++){
        double mid = (lb + ub) / 2;
        if (C(mid))
            lb = mid;
        else
            ub = mid;
    }
    printf("%.2f\n", floor(ub * 100) / 100);  /*其功能是“向下取整”，或者说“向下舍入”，即取不大于x的最大整数
                                            （与“四舍五入”不同，下取整是直接取按照数轴上最接近要求的值左边的值，
                                            也就是不大于要求的值的最大的那个）。*/
}

int main()
{
    while (scanf("%d%d", &n, &k) != EOF){
        for (int i = 0; i < n; i++){
            scanf("%lf", &L[i]);
        }
        solve();
    }
    return 0;
}