博客
关于我
Codeforces Round #456 (Div. 2) D. Fishes
阅读量:530 次
发布时间:2019-03-08

本文共 2855 字,大约阅读时间需要 9 分钟。

D. Fishes
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

While Grisha was celebrating New Year with Ded Moroz, Misha gifted Sasha a small rectangular pond of sizen × m, divided into cells of size1 × 1, inhabited by tiny evil fishes (no more than one fish per cell, otherwise they'll strife!).

The gift bundle also includes a square scoop of size r × r, designed for fishing. If the lower-left corner of the scoop-net is located at cell(x, y), all fishes inside the square(x, y)...(x + r - 1, y + r - 1) get caught. Note that the scoop-net should lie completely inside the pond when used.

Unfortunately, Sasha is not that skilled in fishing and hence throws the scoop randomly. In order to not frustrate Sasha, Misha decided to releasek fishes into the empty pond in such a way that the expected value of the number of caught fishes is as high as possible. Help Misha! In other words, putk fishes in the pond into distinct cells in such a way that when the scoop-net is placed into a random position among(n - r + 1)·(m - r + 1) possible positions, the average number of caught fishes is as high as possible.

Input

The only line contains four integers n, m, r, k (1 ≤ n, m ≤ 105,1 ≤ r ≤ min(n, m),1 ≤ k ≤ min(n·m, 105)).

Output

Print a single number — the maximum possible expected number of caught fishes.

You answer is considered correct, is its absolute or relative error does not exceed10 - 9. Namely, let your answer bea, and the jury's answer be b. Your answer is considered correct, if .

Examples
Input
3 3 2 3
Output
2.0000000000
Input
12 17 9 40
Output
32.8333333333
Note

In the first example you can put the fishes in cells (2, 1),(2, 2), (2, 3). In this case, for any of four possible positions of the scoop-net (highlighted with light green), the number of fishes inside is equal to two, and so is the expected value.

题目大意:用r*r的矩阵去套k条鱼,问期望值是多少?

思路:中间放一条鱼对答案贡献肯定最大,根据对称性,上下左右可得下一个最大值,向四个方向BFS,贡献值逐级递减

#include 
typedef long long ll;using namespace std;int n,m,r,k;ll sum;map
,bool> vis;int dir[4][2]={0,1, 0,-1, 1,0, -1,0};struct node{ int x,y; ll v; bool operator <(const node & obj) const{ //为了排序 return v
que; que.push(temp); while(!que.empty()){ node t,tt; t=que.top(); que.pop(); sum+=t.v; k--; if(k==0) break; for(int i=0;i<4;i++){ int nx=dir[i][0]+t.x; int ny=dir[i][1]+t.y; if(!vis[make_pair(nx,ny)]&&nx>=1&&nx<=n&&ny>=1&&ny<=m){ tt.x=nx,tt.y=ny,tt.v=cul(nx,ny); que.push(tt); vis[make_pair(nx,ny)]=true; } } //puts(""); } return sum;}int main(void){ cin>>n>>m>>r>>k; ll tot=1LL*(n-r+1)*(m-r+1); ll sum=solve(); printf("%.12f\n",sum*1.0/tot);}

转载地址:http://pgziz.baihongyu.com/

你可能感兴趣的文章
MySQL数据库优化总结
查看>>
Mysql数据库函数contac_函数:函数删除操作语法&使用例——《mysql 从入门到内卷再到入土》...
查看>>
mysql数据库命令备份还原
查看>>
mysql数据库基础教程
查看>>
MySQL数据库备份
查看>>
mysql数据库备份与恢复
查看>>
MySQL数据库备份实战
查看>>
Mysql数据库备份的问题:mysqldump: Got error: 1049: Unknown_无需整理
查看>>
mysql数据库如何重置密码是多少钱_MySQL数据库忘记root密码如何重置修改
查看>>
MySQL数据库安装配置与常用命令
查看>>
MySQL数据库实现主从同步数据
查看>>
mysql数据库导入导出_windows系统以及linux系统下的操作---linux工作笔记042
查看>>
mysql数据库导出导入
查看>>
MySQL数据库工具类之——DataTable批量加入MySQL数据库(Net版)
查看>>
mysql数据库常用命令
查看>>
MySQL数据库必会的增删查改操作(CRUD)
查看>>
MySQL数据库性能分析与调优实践
查看>>
mysql数据库扫盲,你真的知道什么是数据库嘛
查看>>
mysql数据库批量插入数据shell脚本实现
查看>>
MySQL数据库操作
查看>>