POJ 刷题系列：3020. Antenna Placement
题意：
一个矩形中，有N个城市’*’，现在这n个城市都要覆盖无线，若放置一个基站，那么它至多可以覆盖相邻的两个城市。问至少放置多少个基站才能使得所有的城市都覆盖无线？
思路： 看了discuss，咋有那么多人纠结无向图和有向图的区别。而且我也并没有理解所谓的答案： 顶点数 - 最大匹配数 / 2，说说我的思路吧。首先在二维矩阵中，对邻接城市进行建图时，它一定可以建成二分图，所以这里也没有所谓的无向图和有向图区分，个人认为无向图和有向图做匹配答案是一样的。
此处参考《挑战》P221页。我们实际要求一个图的最小边覆盖，最小边覆盖为： 顶点数-最大匹配数。简单证明下，首先最大匹配数的顶点集为 2 * match，由于是二分图，所以它们每个匹配顶点对彼此之间是不相邻的，那么剩余的顶点也需要有边连接，如果是孤立的顶点，也要建天线，所以是孤立点就 1。此外，从最大匹配数的顶点集出发，连一条边到其余顶点，而这个数刚好是：所有顶点数 - 2 * 最大匹配数 匹配数。
代码如下：
代码语言：javascript复制import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;
public class Main{
String INPUT = "./data/judge/201801/P3020.txt";
public static void main(String[] args) throws IOException {
new Main().run();
}
boolean[][] map;
int[] match;
boolean dfs(int v, boolean[] vis, int num) {
vis[v] = true;
for (int to = 0; to < num; to) {
if (map[v][to]) {
int w = match[to];
if (w == -1 || !vis[w] && dfs(w, vis, num)) {
match[v] = to;
match[to] = v;
return true;
}
}
}
return false;
}
int bipatite_match(int V) {
match = new int[V];
Arrays.fill(match, -1);
int res = 0;
for (int i = 0; i < V; i) {
if (match[i] < 0) {
if (dfs(i, new boolean[V], V))
res ;
}
}
return res;
}
void read() {
int T = ni();
while (T --> 0) {
int n = ni();
int m = ni();
char[][] board = new char[n][m];
List<int[]> star = new ArrayList<int[]>();
for (int i = 0; i < n; i) {
String ns = ns();
for (int j = 0; j < m; j) {
board[i][j] = ns.charAt(j);
if (board[i][j] == '*') star.add(new int[] {i, j});
}
}
int tot = star.size();
// build map
map = new boolean[n * m][n * m];
boolean[][] vis = new boolean[n][m];
int[][] dir = {{1, 0},{-1, 0},{0, 1},{0, -1}};
for (int[] now : star) {
int i = now[0];
int j = now[1];
if (!vis[i][j]) {
for (int[] d : dir) {
int ni = i d[0];
int nj = j d[1];
if (ni >= 0 && ni < n && nj >= 0 && nj < m && board[ni][nj] == '*' && !vis[ni][nj]) {
map[ni * m nj][i * m j] = true;
map[i * m j][ni * m nj] = true;
vis[i][j] = true;
}
}
}
}
out.println(tot - (bipatite_match(n * m)));
}
}
FastScanner in;
PrintWriter out;
void run() throws IOException {
boolean oj;
try {
oj = ! System.getProperty("user.dir").equals("F:\oxygen_workspace\Algorithm");
} catch (Exception e) {
oj = System.getProperty("ONLINE_JUDGE") != null;
}
InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));
in = new FastScanner(is);
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
read();
out.flush();
if (!oj){
System.out.println("[" (System.currentTimeMillis() - s) "ms]");
}
}
public boolean more(){
return in.hasNext();
}
public int ni(){
return in.nextInt();
}
public long nl(){
return in.nextLong();
}
public double nd(){
return in.nextDouble();
}
public String ns(){
return in.nextString();
}
public char nc(){
return in.nextChar();
}
class FastScanner {
BufferedReader br;
StringTokenizer st;
boolean hasNext;
public FastScanner(InputStream is) throws IOException {
br = new BufferedReader(new InputStreamReader(is));
hasNext = true;
}
public String nextToken() {
while (st == null || !st.hasMoreTokens()) {
try {
st = new StringTokenizer(br.readLine());
} catch (Exception e) {
hasNext = false;
return "##";
}
}
return st.nextToken();
}
String next = null;
public boolean hasNext(){
next = nextToken();
return hasNext;
}
public int nextInt() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Integer.parseInt(more);
}
public long nextLong() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Long.parseLong(more);
}
public double nextDouble() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Double.parseDouble(more);
}
public String nextString(){
if (next == null){
hasNext();
}
String more = next;
next = null;
return more;
}
public char nextChar(){
if (next == null){
hasNext();
}
String more = next;
next = null;
return more.charAt(0);
}
}
static class D{
public static void pp(int[][] board, int row, int col) {
StringBuilder sb = new StringBuilder();
for (int i = 0; i < row; i) {
for (int j = 0; j < col; j) {
sb.append(board[i][j] (j 1 == col ? "n" : " "));
}
}
System.out.println(sb.toString());
}
public static void pp(char[][] board, int row, int col) {
StringBuilder sb = new StringBuilder();
for (int i = 0; i < row; i) {
for (int j = 0; j < col; j) {
sb.append(board[i][j] (j 1 == col ? "n" : " "));
}
}
System.out.println(sb.toString());
}
}
static class ArrayUtils {
public static void fill(int[][] f, int value) {
for (int i = 0; i < f.length; i) {
Arrays.fill(f[i], value);
}
}
public static void fill(int[][][] f, int value) {
for (int i = 0; i < f.length; i) {
fill(f[i], value);
}
}
public static void fill(int[][][][] f, int value) {
for (int i = 0; i < f.length; i) {
fill(f[i], value);
}
}
}
static class Num{
public static <K> void inc(Map<K, Integer> mem, K k) {
if (!mem.containsKey(k)) mem.put(k, 0);
mem.put(k, mem.get(k) 1);
}
}
}
