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更新频率_MySQL优化之如何了解SQL的执行频率
查看>>
mysql替换表的字段里面内容
查看>>
MySQL最多能有多少连接
查看>>
MySQL最大建议行数 2000w,靠谱吗?
查看>>
MySQL有哪些锁
查看>>
MySQL服务器安装(Linux)
查看>>
mysql服务器查询慢原因分析方法
查看>>
mysql服务无法启动的问题
查看>>
MySQL杂谈
查看>>
mysql权限
查看>>
mysql条件查询
查看>>
MySQL条件查询
查看>>
MySQL架构与SQL的执行流程_1
查看>>
MySQL架构与SQL的执行流程_2
查看>>
MySQL架构介绍
查看>>
MySQL架构优化
查看>>
mysql架构简介、及linux版的安装
查看>>
MySQL查看数据库相关信息
查看>>
MySQL查看表结构和表中数据
查看>>
MySQL查询优化:LIMIT 1避免全表扫描
查看>>