挑战程序竞赛系列（63）：4.7字符串上的动态规划（1）

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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

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：
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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<String> pfx = new HashSet<String>();        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<String, Integer> mem = new HashMap<String, Integer>();        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。

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