POJ 刷题系列：1753. Flip Game

POJ 刷题系列：1753. Flip Game

传送门：POJ 1753. Filp Game

题意：

一个4*4的矩阵，每一格要么是白色，要么是黑色。现在你可以选择任意一个格变成相反的颜色，则这个格的上，下，左，右四个格也会跟着变成相反的色（如果存在的话）。问要把矩阵的所有格子变成同一个颜色，你最少需执行几次上面的操作。

思路：
讲真，难度一下上来了，不过既然提示枚举了，那么采用BFS或者DFS暴搜即可。关键在于抓住棋盘演变的状态，因为只有16个小格，每个小格0或者1，所以总共有2^16种状态，所以棋盘状态可以用一个16位的二进制数表示，这样状态的重复访问可以由一个HashSet快速记录了。BFS有个很好的性质，一旦找到END状态可以立即返回。所以如果答案普遍“深度较浅”，可以采用BFS，但空间毕竟摆在那。

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.Arrays;import java.util.HashSet;import java.util.Map;import java.util.Queue;import java.util.Set;import java.util.StringTokenizer;public class Main{    String INPUT = "./data/judge/201712/P1753.txt";    public static void main(String[] args) throws IOException {        new Main().run();    }    class State{        boolean[][] board;        State(boolean[][] board){            this.board = board;        }        int hash() {            int n = 4;            int hash = 0;            int k = 0;            for (int i = 0; i < n; ++i) {                for (int j = 0; j < n; ++j) {                    boolean f = board[i][j];                    int bit = f == true ? 1 : 0;                    hash ^= bit << k;                    k++;                }            }            return hash;        }        @Override        public String toString() {            StringBuilder sb = new StringBuilder();            for (int i = 0; i < 4; ++i) {                for (int j = 0; j < 4; ++j) {                    sb.append((board[i][j] ? 1 : 0) + (j + 1 == 4 ? "\n" : " "));                }            }            return sb.toString();        }    }    void read() {        int n = 4;        int START = 0;        int END   = 65535;        boolean[][] board = new boolean[n][n];        for (int i = 0; i < n; ++i) {            String line = ns();            for (int j = 0; j < n; ++j) {                char c = line.charAt(j);                board[i][j] = c == 'b';            }        }        Queue<State> queue = new ArrayDeque<State>();        Set<Integer> vis   = new HashSet<Integer>();        int[][] dir = {{0, 1},{0, -1},{1, 0},{-1, 0},{0, 0}};        State hello = new State(board);        queue.offer(hello);        vis.add(hello.hash());        int ans  = -1;        int turn = 0;        outer: while (!queue.isEmpty() && ans == -1) {            int size = queue.size();            for (int i = 0; i < size; ++i) {                State cur = queue.poll();                if (cur.hash() == START || cur.hash() == END) {                    ans = turn;                    break outer;                }                for (int x = 0; x < n; ++x) {                    for (int y = 0; y < n; ++y) {                        State nxt = new State(flip(cur.board, x, y, dir));                        if (!vis.contains(nxt.hash())) {                            queue.offer(nxt);                            vis.add(nxt.hash());                        }                    }                }            }            turn ++;        }        if (ans == -1) out.println("Impossible");        else out.println(ans);    }    boolean[][] flip(boolean[][] board, int x, int y, int[][] dir){        int n = 4;        boolean[][] ans = new boolean[n][n];        for (int i = 0; i < n; ++i) {            for (int j = 0; j < n; ++j) {                ans[i][j] = board[i][j];            }        }        for (int[] d : dir) {            int nx = d[0] + x;            int ny = d[1] + y;            if (nx >= 0 && nx < n && ny >= 0 && ny < n) {                ans[nx][ny] = !board[nx][ny];            }        }        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);        }    }}

咋能排在那么后面。。。