POJ 刷题系列:3041. Asteroids

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POJ 刷题系列:3041. Asteroids

传送门:3041. Asteroids

题意:

在NxN的网格中有K颗小行星。小行星i的位置是Ri,Ci。现在有一个强力武器能够有一发光束将一整行或一整列的小行星轰为灰烬。想要利用这个武器摧毁所有小行星最少需要几发光束。

思路: 思路参考《挑战》P229,简单说说,小行星的行和列可以代表二分图中的左侧结点和右侧结点。所以当确定一条匹配边后,左结点的其他边都失效,或者右结点的其他边都失效,这意味着攻击一条匹配边就可以攻击对应的行或列。但这还不够,我们需要匹配最大的边,因为我们要消灭所有的行星。

简单说说二分图DFS的思路吧,首先如果对于待匹配点S,在它的邻接顶点中,存在未匹配的to,就直接匹配。不过如果to被其他w匹配了怎么办?并不是说不能匹配to了,只要w还能匹配其它顶点,就能让to和S匹配,这就是增广路径。(只要还能找到w的匹配路径,就让to和S重新配对)

代码如下:

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/P3041.txt";

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    int[] match;
    int N, K;
    List<Integer>[] graph;

    boolean dfs(int s, boolean[] vis) {
        vis[s] = true;
        for (int to : graph[s]) {
            int w = match[to];
            if (w == -1 || !vis[w] && dfs(w, vis)) {
                match[to] = s;
                match[s] = to;
                return true;
            }
        }
        return false;
    }

    int bipartite_match() {
        int res = 0;
        match = new int[2 * N];
        Arrays.fill(match, -1);
        for (int i = 0; i < 2 * N; ++i) {
            if (match[i] < 0) {
                if (dfs(i, new boolean[2 * N])) {
                    res += 1;
                }
            }
        }
        return res;
    }

    void read() {
        N = ni();
        K = ni();
        graph = new ArrayList[2 * N];
        for (int i = 0; i < 2 * N; ++i) graph[i] = new ArrayList<Integer>();
        for (int i = 0; i < K; ++i) {
            int u = ni();
            int v = ni();
            u = u - 1;
            v = N + v - 1;
            graph[u].add(v);
            graph[v].add(u);
        }
        out.println(bipartite_match());
    }

    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);
        }
    }
}

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