Cable master（二分-求可行解）

Posted 2020-12-24 moomcake

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

2.0

题意：有n段长度分别为Li的电缆，要求把它们分割成K条长度为X的电缆，问X的最大值为多少。

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<stack>
 4 #include<queue>
 5 #include<algorithm>
 6 #include<map>
 7 #include<cmath>
 8 #include<vector>
 9 #define PI acos(-1.0)
10 using namespace std;
11 #define Inf 0x3f3f3f3f
12 #define exp 1e-8
13 typedef long long ll;
14 int m,n;
15 double str[58899];
16 int visit[50][50][50][50];
17 int dis[500][500];
18 int di[8][4]= {{0,0,0,1},{0,0,0,-1},{0,0,1,0},{0,0,-1,0},{0,1,0,0},{0,-1,0,0},{1,0,0,0},{-1,0,0,0}};
19 map<ll,ll>::iterator it;
20 bool solve(double mid)
21 {
22     int ans=0;
23     for(int i=0;i<m;i++)
24     {
25         ans+=(int)(str[i]/mid);
26     }
27     return ans>=n;
28 }
29 int main()
30 {
31     int i,j;
32    while( scanf("%d%d",&m,&n)!=-1){
33     for(i=0;i<m;i++)
34     {
35         scanf("%lf",&str[i]);
36     }
37     double left=0,right=Inf,mid;
38     int ans;
39     i=1000;
40     while(i--)
41     {
42         mid=(left+right)/2;
43         if(solve(mid))
44         {
45             left=mid;
46         }
47         else
48         {
49             right=mid;
50         }
51     }
52     printf("%0.2lf
",floor(right*100)/100.0);
53    }
54     return 0;
55 }

View Code

 

题解：将X视为变量，可知它的范围为0~max;  那么问题就变成了电缆长度取X时，所得的电缆条数大于，还是等于，或小于K的问题。  用二分查找法能很快的找出K的值，不过要注意精度，直接输出时会四舍五入，五入时的结果肯定是错的，注意向下取整。