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UVA 12549 Sentry Robots 最小点集覆盖

2015-05-29 14:28 363 查看
这题的模型是二分图最小点集覆盖 即选择最少的行或列来覆盖所有的点

二分图最小点集覆盖 = 最大匹配数

本题需要注意的是障碍物会把行和列分隔开来 所以要拆行拆列

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

const int maxn = 2500 + 10;
const int N = 100 + 10;

int X, Y;
int g[maxn][maxn], linker[maxn];
bool vis[maxn];

bool dfs(int u){
for(int v = 0; v < Y; v++)if(g[u][v] && !vis[v]){
vis[v] = true;
if(linker[v] == -1 || dfs(linker[v])){
linker[v] = u;
return true;
}
}
return false;
}

int hungary(){
int ans = 0;
memset(linker, -1, sizeof(linker));
for(int u = 0; u < X; u++){
memset(vis, false, sizeof(vis));
if(dfs(u)) ans++;
}
return ans;
}

int map

, n, m;
pair<int, int> Map

;

void input(){
int N, x, y;
memset(map, 0, sizeof(map));
scanf("%d%d%d", &n, &m, &N);
while(N--){
scanf("%d%d", &x, &y);
map[x][y] = 1;
}
scanf("%d", &N);
while(N--){
scanf("%d%d", &x, &y);
map[x][y] = 2;
}
}

void solve(){
int row_num = -1, col_num = -1;
for(int i = 1; i <= n; i++){
bool flag = true;
for(int j = 1; j <= m; j++){
if(map[i][j] == 1){
if(flag) ++row_num;
Map[i][j].first = row_num;
flag = false;
}
if(map[i][j] == 2) flag = true;
}
}
for(int j = 1; j <= m; j++){
bool flag = true;
for(int i = 1; i <= n; i++){
if(map[i][j] == 1){
if(flag) ++col_num;
Map[i][j].second = col_num;
flag = false;
}
if(map[i][j] == 2) flag = true;
}
}
X = row_num + 1;
Y = col_num + 1;
memset(g, 0, sizeof(g));
for(int i = 1; i <= n; i++)
for(int j = 1; j <= m; j++)if(map[i][j] == 1){
g[Map[i][j].first][Map[i][j].second] = 1;
}
printf("%d\n", hungary());
}

int main()
{
//          freopen("in.txt", "r", stdin);
int T;
scanf("%d", &T);
while(T--){
input();
solve();
}
return 0;
}
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