Description
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?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
2 7 9 ooo**oooo **oo*ooo* o*oo**o** ooooooooo *******oo o*o*oo*oo *******oo 10 1 * * * o * * * * * *Sample Output
17 5Source
//题意：给一个图，用两个格子覆盖全部*，可以重复题解：只是需要把多余的*加上就行了，所有的城市数减去二分最大匹配数就是答案
//需要把图转换成二分图
！get个技能 ：如何 加快cin、cout的输入输出速度 #include<cstdio> #include<iostream> #include<cstdlib> #include<cstring> using namespace std; const int N=400+5,maxn=100000+5,inf=0x3f3f3f3f; int n,m,col,row; char ma[N][N]; int color[N],u[N][N];//u分别记录两个集合的编号 bool used[N],ok[N][N];//标记数组，标记边是否可行 bool match(int x) { for(int i=1;i<=row;i++) { if(ok[x][i]&&!used[i]) { used[i]=1; if(color[i]==0||match(color[i])) { color[i]=x; return 1; } } } return 0; } int solve()//匈牙利算法 { int ans=0; memset(color,0,sizeof(color)); for(int i=1;i<=col;i++) { memset(used,0,sizeof(used)); ans+=match(i); } return ans; } int main() { ios::sync_with_stdio(false);//加快cin,cout的速度 cin.tie(0); int t; cin>>t; while(t--) { cin>>n>>m; int res=0; for(int i=1;i<=n;i++) for(int j=1;j<=m;j++) { cin>>ma[i][j]; if(ma[i][j]=='*')res++; } memset(u,0,sizeof(u)); col=row=0; for(int i=1;i<=n;i++) { for(int j=1;j<=m;j++) { if((i+j)%2==0&&ma[i][j]=='*')u[i][j]=++col;//集合_1 if((i+j)%2==1&&ma[i][j]=='*')u[i][j]=++row;//集合_2 } } memset(ok,0,sizeof(ok));//制作二分图 for(int i=1;i<=n;i++) { for(int j=1;j<=m;j++) { if((i+j)%2==0)//集合_1添加元素 { if(i+1<=n&&ma[i+1][j]=='*')ok[u[i][j]][u[i+1][j]]=1; if(j+1<=n&&ma[i][j+1]=='*')ok[u[i][j]][u[i][j+1]]=1; if(i-1>=1&&ma[i-1][j]=='*')ok[u[i][j]][u[i-1][j]]=1; if(j-1>=1&&ma[i][j-1]=='*')ok[u[i][j]][u[i][j-1]]=1; } else//集合_2添加元素 { if(i+1<=n&&ma[i+1][j]=='*')ok[u[i+1][j]][u[i][j]]=1; if(j+1<=n&&ma[i][j+1]=='*')ok[u[i][j+1]][u[i][j]]=1; if(i-1>=1&&ma[i-1][j]=='*')ok[u[i-1][j]][u[i][j]]=1; if(j-1>=1&&ma[i][j-1]=='*')ok[u[i][j-1]][u[i][j]]=1; } } } cout<<res-solve()<<endl; } }