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: 对换(替换)两条记录的同一个字段值
查看>>
mysql:Can‘t connect to local MySQL server through socket ‘/var/run/mysqld/mysqld.sock‘解决方法
查看>>
MYSQL:基础——3N范式的表结构设计
查看>>
MYSQL:基础——触发器
查看>>
Mysql:连接报错“closing inbound before receiving peer‘s close_notify”
查看>>
mysqlbinlog报错unknown variable ‘default-character-set=utf8mb4‘
查看>>
mysqldump 参数--lock-tables浅析
查看>>
mysqldump 导出中文乱码
查看>>
mysqldump 导出数据库中每张表的前n条
查看>>
mysqldump: Got error: 1044: Access denied for user ‘xx’@’xx’ to database ‘xx’ when using LOCK TABLES
查看>>
Mysqldump参数大全(参数来源于mysql5.5.19源码)
查看>>
mysqldump备份时忽略某些表
查看>>
mysqldump实现数据备份及灾难恢复
查看>>
mysqldump数据库备份无法进行操作只能查询 --single-transaction
查看>>
mysqldump的一些用法
查看>>
mysqli
查看>>
MySQLIntegrityConstraintViolationException异常处理
查看>>
mysqlreport分析工具详解
查看>>
MySQLSyntaxErrorException: Unknown error 1146和SQLSyntaxErrorException: Unknown error 1146
查看>>
Mysql_Postgresql中_geometry数据操作_st_astext_GeomFromEWKT函数_在java中转换geometry的16进制数据---PostgreSQL工作笔记007
查看>>