挑战程序竞赛系列（63）：4.7字符串上的动态规划（1）

挑战程序竞赛系列（63）：4.7字符串上的动态规划（1）

传送门：POJ 3691: DNA Pair

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题意：

考虑只由A, G, C, T四种字符组成的DNA字符串。给定一个原字符串S，和n个禁止模式字符串 P1,P2,...,Pn 。请修改字符串S，使得其中不包含任何禁止模式。每次修改操作只能将S中的某个字符修改为其他字符。如果不存在这样的修改，请输出-1，否则，输出所需要的最少修改回数。

AC自动机真好用，暴力的做法是对于字符串的每个字符修改一遍，再去看看是否有禁止模式，这种做法求最小编辑距离也不好做。

但思路还是从暴力出，对于每个字符都有四种状态A,T,C,G，那么两个字符就意味着4 * 4 = 16种状态，其实不然，AC自动机的思想在于对状态的抽象，比如P = ｛“AA”｝，那么对于match = ｛”TG”,”GT”,…｝,这些状态可以完全看做一个状态。而我们知道阶段数总共就是字符串的长度，我们只要列出同质状态，以及各状态之间的转移过程，此问题就解决了。

对DP新的认识，DP其实很暴力，但之所以比暴力优在于它对状态的抽象，啧啧啧。

参考《挑战》P371：

书中代码出现了一个小错误，在求解不可达的状态时，后缀和禁止模式匹配中，subString的裁剪长度有误。

正确版本如下：

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.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;

public class Main {

    String INPUT = "./data/judge/201709/P3691.txt";

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

    static final int MAX_N = 50 + 2;
    static final int INF   = 0x3f3f3f3f;

    static char[] ATCG = {'A','G','C','T'};

    void read() {
        int cnt = 0;    
        while (true) {
            int N = ni();
            if (N == 0) break;
            String[] p = new String[N];
            for (int i = 0; i < N; ++i) p[i] = ns();
            String match = ns();
            out.println("Case " + (++cnt) + ": " + solve(match, p));
        }
    }


    int solve(String match, String[] p) {
        Set pfx = new HashSet();
        pfx.add("");
        for (String forb : p) {
            for (int i = 0; i <= forb.length(); ++i) {
                pfx.add(forb.substring(0, i));
            }
        }

        int K = pfx.size();
        String[] pfxs = pfx.toArray(new String[0]);
        Map mem = new HashMap();
        for (int i = 0; i < K; ++i) mem.put(pfxs[i], i);

        boolean[] ng = new boolean[K + 1];

        //不可达状态
        for (int i = 0; i < K; ++i) {
            ng[i] = false;
            for (int j = 0; j < p.length; ++j) {
                ng[i] |= p[j].length() <= pfxs[i].length() 
                        && pfxs[i].substring(pfxs[i].length() - p[j].length() , pfxs[i].length()).equals(p[j]);
            }
        }

        int[][] next = new int[K + 1][4];
        for (int i = 0; i < K; ++i) {
            for (int j = 0; j < 4; ++j) {
                String s = pfxs[i] + ATCG[j];
                while (!mem.containsKey(s)) {
                    s = s.substring(1);
                }
                next[i][j] = mem.get(s);
            }
        }

        int[][] dp = new int[match.length() + 16][K + 16];
        dp[0][0] = 1;
        for (int i = 1; i < K; ++i) dp[0][i] = 0;
        for (int i = 1; i <= match.length(); ++i) {
            for (int j = 0; j < K; ++j) dp[i][j] = INF;
            for (int j = 0; j < K; ++j) {
                if (ng[j]) continue;
                for (int l = 0; l < 4; ++l) {
                    int ns = next[j][l];
                    dp[i][ns] = Math.min(dp[i][ns], dp[i - 1][j] + (match.charAt(i - 1) == ATCG[l] ? 0 : 1));
                }
            }
        }

        int ans = INF;
        for (int i = 0; i < K; ++i) {
            if (ng[i]) continue;
            ans = Math.min(ans, dp[match.length()][i]);
        }

        return ans == INF ? -1 : ans;
    }

    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();
        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 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);
            }
        }
    }
}

书中关于状态的转移用了二分，实际可以用Map更快的定位，稍许优化了一下。