poj 3020 --最小路径覆盖
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H - Antenna Placement
Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%lld & %lluDescription
The Global Aerial Research Centre has been allotted the task of building the fifth generation of mobile phone nets in Sweden. The most striking reason why they got the job, is their discovery of a new, highly noise resistant, antenna. It is called 4DAir, and comes in four types. Each type can only transmit and receive signals in a direction aligned with a (slightly skewed) latitudinal and longitudinal grid, because of the interacting electromagnetic field of the earth. The four types correspond to antennas operating in the directions north, west, south, and east, respectively. Below is an example picture of places of interest, depicted by twelve small rings, and nine 4DAir antennas depicted by ellipses covering them.
Obviously, it is desirable to use as few antennas as possible, but still provide coverage for each place of interest. We model the problem as follows: Let A be a rectangular matrix describing the surface of Sweden, where an entry of A either is a point of interest, which must be covered by at least one antenna, or empty space. Antennas can only be positioned at an entry in A. When an antenna is placed at row r and column c, this entry is considered covered, but also one of the neighbouring entries (c+1,r),(c,r+1),(c-1,r), or (c,r-1), is covered depending on the type chosen for this particular antenna. What is the least number of antennas for which there exists a placement in A such that all points of interest are covered?
Obviously, it is desirable to use as few antennas as possible, but still provide coverage for each place of interest. We model the problem as follows: Let A be a rectangular matrix describing the surface of Sweden, where an entry of A either is a point of interest, which must be covered by at least one antenna, or empty space. Antennas can only be positioned at an entry in A. When an antenna is placed at row r and column c, this entry is considered covered, but also one of the neighbouring entries (c+1,r),(c,r+1),(c-1,r), or (c,r-1), is covered depending on the type chosen for this particular antenna. What is the least number of antennas for which there exists a placement in A such that all points of interest are covered?
Input
On the first row of input is a single positive integer n, specifying the number of scenarios that follow. Each scenario begins with a row containing two positive integers h and w, with 1 <= h <= 40 and 0 < w <= 10. Thereafter is a matrix presented, describing the points of interest in Sweden in the form of h lines, each containing w characters from the set ['*','o']. A '*'-character symbolises a point of interest, whereas a 'o'-character represents open space.
Output
For each scenario, output the minimum number of antennas necessary to cover all '*'-entries in the scenario's matrix, on a row of its own.
Sample Input
27 9ooo**oooo**oo*ooo*o*oo**o**ooooooooo*******ooo*o*oo*oo*******oo10 1***o******
Sample Output
175
题意:在一个n*m的棋盘中,* 表示城市,o表示空地,要把所有城市安装上天线,每个天线可以覆盖相邻的两个城市
问至少要建多少天线
很明显 ,求最小路径覆盖嘛,每条路径两个点(显然二分图),问最少几条路径可以覆盖所有点,给每个城市标号,相邻城市
建边,建双向边,求最大匹配,最小路径覆盖=节点个数-最大匹配数
#include <iostream>#include <string.h>using namespace std;int g[405][405],nmp[200][200];char mp[200][200];int dx[5]={1,0,-1,0};int dy[4]={0,1,0,-1};int uN,vN;int linker[500],used[500];bool dfs(int u){ for(int v=1;v<=vN;v++) { if(g[u][v]&&!used[v]) { used[v]=true; if(linker[v]==-1||dfs(linker[v])) { linker[v]=u; return true; } } } return false;}int solve(){ int res=0; memset(linker,-1,sizeof(linker)); for(int u=1;u<=uN;u++) { memset(used,false,sizeof(used)); if(dfs(u)) res++; } return res;}int main(){ int t; int n,m; cin>>t; while(t--) { cin>>n>>m; int tot=1; memset(mp,0,sizeof(mp)); memset(nmp,0,sizeof(nmp)); for(int i=1;i<=n;i++) { for(int j=1;j<=m;j++) { cin>>mp[i][j]; if(mp[i][j]=='*') { nmp[i][j]=tot++; } } } memset(g,0,sizeof(g)); for(int i=1;i<=n;i++) { for(int j=1;j<=m;j++) { if(mp[i][j]=='*') for(int k=0;k<4;k++) { int nx=dx[k]+i; int ny=dy[k]+j; if(mp[nx][ny]=='*') g[nmp[i][j]][nmp[nx][ny]]=1; } } } uN=tot-1; vN=tot-1; int ans=solve(); //cout<<ans<<endl; cout<<tot-1-ans/2<<endl; } return 0;}
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