POJ 刷题系列:2965. The Pilots Brothers' refrigerator

POJ 刷题系列:2965. The Pilots Brothers’ refrigerator

传送门:POJ 2965. The Pilots Brothers’ refrigerator

题意:

一个4*4的矩阵,每一格要么是”+”,要么是”-“。现在你可以选择任意一个格翻转,则这个格的同行和同列也会跟着翻转。问要把矩阵的所有格子变成全”-“所需要的最短步骤。

思路: 此题实际上和flip game类似,不过flip game 采用BFS的暴力做法在这里就不奏效了。说白了,少考虑了一些性质呗。观察flip game中BFS中的代码,会发现有两层for循环来遍历所有可能的位置,此处非常冗余。原因如下:flip 这个操作,对于每个位置而言全局只需要翻转一次即可,因为一个位置翻转两次就会回到原先的状态。所以问题就转化为:16个位置,每个位置可能翻转和不翻转两种情况,遍历2^16种状态,每个状态遇到翻转位则翻转,看最后能否抵达END状态即可。

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.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Set;
import java.util.StringTokenizer;

public class Main{

    String INPUT = "./data/judge/201712/P2965.txt";

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

    static final int[][] MAP = {{0, 1, 2, 3}, {4, 5, 6, 7}, {8, 9, 10, 11}, {12, 13, 14, 15}};

    int hash(char[][] board) {
        int n = 4;
        int k = 0;
        int ans = 0;
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                int bit = board[i][j] == '+' ? 0 : 1;
                ans |= bit << k;
                k ++;
            }
        }
        return ans;
    }

    void read() {
        int n = 4;
        char[][] board = new char[n][n];
        for (int i = 0; i < n; ++i) {
            String line = ns();
            for (int j = 0; j < n; ++j) {
                board[i][j] = line.charAt(j); 
            }
        }

        int END = 65535;
        int hash = hash(board);

        int ans = 0;
        int len = 0;
        for (int i = 0; i < 1 << 16; ++i) {
            int count = 0;
            int tmp = hash;
            for (int j = 0; j < 16; ++j) {
                if (((i >> j) & 1) == 1) {
                    count ++;
                    tmp = flip(tmp, j / n, j % n);
                }
            }

            if (tmp == END) {
                len = count;
                ans = i;
                break;
            }
        }

        out.println(len);
        for (int j = 0; j < 16; ++j) {
            if (((ans >> j) & 1) == 1) {
                out.println((j / n + 1) + " " + (j % n + 1));
            }
        }
    }

    int flip(int hash, int x, int y){
        int n = 4;
        int ans = hash;

        for (int i = 0; i < n; ++i) {
            ans ^= (1 << MAP[i][y]);
            ans ^= (1 << MAP[x][i]);
        }
        ans ^= (1 << MAP[x][y]);
        return ans;
    }

    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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