POJ--1064 Cable master(二分搜索/稍微变通)

标签：Cable -- 1064 number int length pieces cables

记录
0:28 2023-2-9

reference:《挑战程序设计竞赛(第2版)》3.1.2 p140

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

Sample Output

2.00

二分搜索。最基础的二分搜索比如有:在给定顺序数组中查找某个值(在给定顺序数组中查找满足条件最小/最大的下标)，稍微变通可以将判断条件使用函数来表达。
比如函数C(x)，这种情况下需要函数与x成正比或者反比。举个例子，对于x0 < x1，需要有C(x0) < C(x1) 或者 C(x0) > C(x1)
这道题中C(x)为:得到K条长度为x的绳子(也就是判断在绳子长度为x的条件下能否得到K条绳子)。题目要求是求最大的x。
从x0 = 0.0 x1 = INF开始二分搜索，找到满足条件最小的K就得到了最大的x(其实表达成最大的x得到满足条件最小的K更好理解)。

#include<cstdio>
#include<cmath>
#define MAX_N 10000
const int INF = 0x3f3f3f3f;
int N, K;
double L[MAX_N + 1];

bool check(double x) {
    int res = 0;
    for(int i = 0; i < N; i++) {
        res += floor(L[i] / x);
    }
    if(res >= K) {
        return true;
    } else {
        return false;
    }
}

void solve() {
    double lb = 0.0, ub = INF;

    while (ub - lb > 0.00001) {
        double mid = (lb + ub) / 2;
        if(check(mid)) {
            lb = mid;
        } else {
            ub = mid;
        }
    }
    
    printf("%.2f\n", floor(ub * 100) / 100);
}

int main() {
    scanf("%d %d", &N, &K);
    for(int i = 0; i < N; i++) {
        scanf("%lf", &L[i]);
    }
    solve();
}

标签：Cable,--,1064,number,int,length,pieces,cables
From： https://www.cnblogs.com/57one/p/17103864.html