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社区首页 >专栏 >挑战程序竞赛系列(72):4.7高度数组(2)

挑战程序竞赛系列(72):4.7高度数组(2)

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用户1147447
发布2018-01-02 11:05:49
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发布2018-01-02 11:05:49
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文章被收录于专栏:机器学习入门

挑战程序竞赛系列(72):4.7高度数组(2)

传送门:POJ 3415: Common Substrings

题意:

公共子串:统计A和B长度不小于K的公共子串个数。

思路: 一开始想当然的求LCP数组,把LCP遍历一遍,大于K的,ans不断累加ans += lcp[i] - k + 1,但这只是一部分解,因为所求的只是相邻后缀的最长公共前缀。

一种直观的做法时,两个for循环,对于当前位置属于S的LCP时,向下找属于T的后缀,把每个后缀的最长对应公共前缀加一遍,但TLE了,此处需要利用单调性来简化时间复杂度。采用记忆化手段,用栈。

自己写了一种,但各别样例过不了,并不清楚原因。此处代码参考hankcs的代码,具体思路如下:对应于S的lcp,先不管三七二十一,贡献值都以最大的加,但我们知道,中间如果lcp变小,意味着后缀的公共前缀在不断减小,此时需要按照最小的算,只需要在贡献值上,删除原先多加的即可。针对T的lcp,同样处理。

代码如下:

代码语言:javascript
复制
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.Comparator;
import java.util.StringTokenizer;

public class Main{

    String INPUT = "./data/judge/201709/P3415.txt";

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

    class SuffixArray{
        int k = 1;
        int n;
        Integer[] sa;
        int[] rank, tmp, lcp;

        SuffixArray(char[] cs){
            n    = cs.length; 
            sa   = new Integer[n + 1];
            rank = new int[n + 1];
            tmp  = new int[n + 1];
            lcp  = new int[n];

            for (int i = 0; i <= n; ++i) {
                sa[i] = i;
                rank[i] = i < n ? cs[i] : -1;
            }

            for (k = 1; k <= n; k <<= 1) {
                Arrays.sort(sa, cmp);
                tmp[sa[0]] = 0;
                for (int i = 1; i <= n; ++i) {
                    tmp[sa[i]] = tmp[sa[i - 1]] + (cmp.compare(sa[i - 1], sa[i]) < 0 ? 1 : 0);
                }
                for (int i = 0; i <= n; ++i) {
                    rank[i] = tmp[i];
                }
            }

            // lcp
            int h = 0;
            for (int i = 0; i <= n; ++i) rank[sa[i]] = i;
            for (int i = 0; i < n; ++i) {
                int j = sa[rank[i] - 1];
                if (h > 0) h --;
                for (;j + h < n && i + h < n; ++h) {
                    if (cs[j + h] != cs[i + h]) break;
                }
                lcp[rank[i] - 1] = h;
            }
        }

        Comparator<Integer> cmp = new Comparator<Integer>() {
            @Override
            public int compare(Integer o1, Integer o2) {
                int i = o1;
                int j = o2;
                if (rank[i] != rank[j]) return rank[i] - rank[j];
                else {
                    int ri = i + k <= n ? rank[i + k] : -1;
                    int rj = j + k <= n ? rank[j + k] : -1;
                    return ri - rj;
                }
            }
        };
    }

    void read() {
        while (true) {
            int k = ni();
            if (k == 0) break;
            String s = ns();
            String t = ns();
            SuffixArray sa = new SuffixArray((s + '$' + t).toCharArray());
            long ans = 0;
            ans += solve(true, s.length(), k, sa);
            ans += solve(false, s.length(), k, sa);
            out.println(ans);
        }
    }

    int[][] stack;
    int top;
    long sum;
    long solve(boolean isS, int sLen, int k, SuffixArray sa) {
        long ans = 0;
        sum = 0;
        top = 0;
        stack = new int[sa.n + 16][2];
        for (int i = 0; i < sa.n; ++i) {
            if (sa.lcp[i] < k) {
                top = 0;
                sum = 0;
            }
            else {
                int size = 0;
                if ((isS && sa.sa[i] < sLen) || (!isS && sa.sa[i] > sLen)) {
                    size ++;
                    sum += sa.lcp[i] - k + 1;
                }
                while (top > 0 && sa.lcp[i] < stack[top - 1][0]) {
                    --top;
                    sum -= stack[top][1] * (stack[top][0] - sa.lcp[i]);
                    size += stack[top][1];
                }
                if (size > 0) {
                    stack[top][0] = sa.lcp[i];
                    stack[top][1] = size;
                    top ++;
                }

                if ((isS && sa.sa[i + 1] > sLen) || (!isS && sa.sa[i + 1] < sLen)) {
                    ans += sum;
                }
            }
        }
        return 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);
        }
    }
}
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