挑战程序竞赛系列（49）：4.2 推理与动态规划算法（2）

详细代码可以fork下Github上leetcode项目，不定期更新。

练习题如下：

• POJ 2068: Nim

POJ 2068: Nim

团体尼姆赛：传统的尼姆游戏由两名玩家进行，在一堆石头中，双方轮流取走任意合法数量块石头，取走最后一块石头的玩家落败。多人尼姆游戏将参赛人数拓展至两个队伍，每支队伍有n名队员交错入座，单次分别能最多取走Mi块石头，取走S块石头中的最后一块的队伍失败，求第一支队伍是否有必胜策略？

动态规划题，如果单纯的两个人轮流取，直接利用数学公式直接求出，但此题多轮多人且每人取的石头数也不同，这貌似只能动规了。

dp[i][j][k] 第i支队伍第k个人，剩余k个石子时，能否赢得当前轮注意当k = 0，表明是必胜态，而当k = 1时，一定为必输态。

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.StringTokenizer;public class Main{    String INPUT = "./data/judge/201709/P2068.txt";    public static void main(String[] args) throws IOException {        new Main().run();    }    static final int MAX_S = 1 << 13;    boolean[][][] dp; //第k只队伍 第j个队员 剩余i个石头的状态    void solve() {        while (true) {            int n = ni();            if (n == 0) break;            int s = ni();            dp = new boolean[2][12][MAX_S + 16];            int[] team = new int[2 * n];            for (int i = 0; i < 2 * n; ++i) {                team[i] = ni();            }            for (int i = 0; i < 2 * n; ++i) {                dp[i & 1][i / 2 + 1][0] = true;                dp[i & 1][i / 2 + 1][1] = false; // 必输态            }            for (int i = 2; i <= s; ++i) {                for (int now = 0; now < 2 * n; ++now) {                    int nxt = (now + 1) % (2 * n);                    for (int j = team[now]; j >= 1; --j) {                        if (i - j >= 0) {                            dp[now & 1][now / 2 + 1][i] |= !dp[nxt & 1][nxt / 2 + 1][i - j];                            if (dp[now & 1][now / 2 + 1][i]) break;                        }                    }                }            }            out.println(dp[0][1][s] ? "1" : "0");        }    }    FastScanner in;    PrintWriter out;    void run() throws IOException {        boolean oj;        try {            oj = ! System.getProperty("user.dir").equals("F:\\java_workspace\\leetcode");        } 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();        solve();        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);        }    }}