字符串排序算法

字母表数据结构

package string;

import edu.princeton.cs.algs4.StdOut;

public class Alphabet {

    public static final Alphabet BINARY = new Alphabet("01");

    public static final Alphabet OCTAL = new Alphabet("01234567");

    public static final Alphabet DECIMAL = new Alphabet("0123456789");

    public static final Alphabet HEXADECIMAL = new Alphabet("0123456789ABCDEF");

    public static final Alphabet DNA = new Alphabet("ACGT");

    public static final Alphabet LOWERCASE = new Alphabet("abcdefghijklmnopqrstuvwxyz");

    public static final Alphabet UPPERCASE = new Alphabet("ABCDEFGHIJKLMNOPQRSTUVWXYZ");

    public static final Alphabet PROTEIN = new Alphabet("ACDEFGHIKLMNPQRSTVWY");

    public static final Alphabet BASE64 = new Alphabet("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/");

    public static final Alphabet ASCII = new Alphabet(128);

    public static final Alphabet EXTENDED_ASCII = new Alphabet(256);

    public static final Alphabet UNICODE16      = new Alphabet(65536);


    private char[] alphabet;     // the characters in the alphabet
    private int[] inverse;       // indices
    private final int R;         // the radix of the alphabet

    public Alphabet(String alpha) {

        // check that alphabet contains no duplicate chars
        boolean[] unicode = new boolean[Character.MAX_VALUE];
        for (int i = 0; i < alpha.length(); i++) {
            char c = alpha.charAt(i);
            if (unicode[c])
                throw new IllegalArgumentException("Illegal alphabet: repeated character = '" + c + "'");
            unicode[c] = true;
        }

        alphabet = alpha.toCharArray();
        R = alpha.length();
        inverse = new int[Character.MAX_VALUE];
        for (int i = 0; i < inverse.length; i++)
            inverse[i] = -1;

        // can't use char since R can be as big as 65,536
        for (int c = 0; c < R; c++)
            inverse[alphabet[c]] = c;
    }

    private Alphabet(int radix) {
        this.R = radix;
        alphabet = new char[R];
        inverse = new int[R];

        // can't use char since R can be as big as 65,536
        for (int i = 0; i < R; i++)
            alphabet[i] = (char) i;
        for (int i = 0; i < R; i++)
            inverse[i] = i;
    }

    public Alphabet() {
        this(256);
    }

    public boolean contains(char c) {
        return inverse[c] != -1;
    }

    @Deprecated
    public int R() {
        return R;
    }

    public int radix() {
        return R;
    }

    public int lgR() {
        int lgR = 0;
        for (int t = R-1; t >= 1; t /= 2)
            lgR++;
        return lgR;
    }

    public int toIndex(char c) {
        if (c >= inverse.length || inverse[c] == -1) {
            throw new IllegalArgumentException("Character " + c + " not in alphabet");
        }
        return inverse[c];
    }

    public int[] toIndices(String s) {
        char[] source = s.toCharArray();
        int[] target  = new int[s.length()];
        for (int i = 0; i < source.length; i++)
            target[i] = toIndex(source[i]);
        return target;
    }

    public char toChar(int index) {
        if (index < 0 || index >= R) {
            throw new IllegalArgumentException("index must be between 0 and " + R + ": " + index);
        }
        return alphabet[index];
    }

    public String toChars(int[] indices) {
        StringBuilder s = new StringBuilder(indices.length);
        for (int i = 0; i < indices.length; i++)
            s.append(toChar(indices[i]));
        return s.toString();
    }

    public static void main(String[] args) {
        int[]  encoded1 = Alphabet.BASE64.toIndices("NowIsTheTimeForAllGoodMen");
        String decoded1 = Alphabet.BASE64.toChars(encoded1);
        StdOut.println(decoded1);

        int[]  encoded2 = Alphabet.DNA.toIndices("AACGAACGGTTTACCCCG");
        String decoded2 = Alphabet.DNA.toChars(encoded2);
        StdOut.println(decoded2);

        int[]  encoded3 = Alphabet.DECIMAL.toIndices("01234567890123456789");
        String decoded3 = Alphabet.DECIMAL.toChars(encoded3);
        StdOut.println(decoded3);
    }
}

一.字符串排序

1.键索引计数法

2.低位优先的字符串排序（字符串长度相同）

package string;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class LSD {
    private static final int BITS_PER_BYTE = 8;

    private LSD() { }

    public static void sort(String[] a, int w) {
        int n = a.length;
        int R = 256;   // extend ASCII alphabet size
        String[] aux = new String[n];

        for (int d = w-1; d >= 0; d--) {
            // sort by key-indexed counting on dth character

            // compute frequency counts
            int[] count = new int[R+1];
            for (int i = 0; i < n; i++)
                count[a[i].charAt(d) + 1]++;

            // compute cumulates
            for (int r = 0; r < R; r++)
                count[r+1] += count[r];

            // move data
            for (int i = 0; i < n; i++)
                aux[count[a[i].charAt(d)]++] = a[i];

            // copy back
            for (int i = 0; i < n; i++)
                a[i] = aux[i];
        }
    }

    public static void sort(int[] a) {
        final int BITS = 32;                 // each int is 32 bits
        final int R = 1 << BITS_PER_BYTE;    // each bytes is between 0 and 255
        final int MASK = R - 1;              // 0xFF
        final int w = BITS / BITS_PER_BYTE;  // each int is 4 bytes

        int n = a.length;
        int[] aux = new int[n];

        for (int d = 0; d < w; d++) {

            // compute frequency counts
            int[] count = new int[R+1];
            for (int i = 0; i < n; i++) {
                int c = (a[i] >> BITS_PER_BYTE*d) & MASK;
                count[c + 1]++;
            }

            // compute cumulates
            for (int r = 0; r < R; r++)
                count[r+1] += count[r];

            // for most significant byte, 0x80-0xFF comes before 0x00-0x7F
            if (d == w-1) {
                int shift1 = count[R] - count[R/2];
                int shift2 = count[R/2];
                for (int r = 0; r < R/2; r++)
                    count[r] += shift1;
                for (int r = R/2; r < R; r++)
                    count[r] -= shift2;
            }

            // move data
            for (int i = 0; i < n; i++) {
                int c = (a[i] >> BITS_PER_BYTE*d) & MASK;
                aux[count[c]++] = a[i];
            }

            // copy back
            for (int i = 0; i < n; i++)
                a[i] = aux[i];
        }
    }

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        int n = a.length;

        // check that strings have fixed length
        int w = a[0].length();
        for (int i = 0; i < n; i++)
            assert a[i].length() == w : "Strings must have fixed length";

        // sort the strings
        sort(a, w);

        // print results
        for (int i = 0; i < n; i++)
            StdOut.println(a[i]);
    }
}

3.高位优先的字符串排序

package string;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class MSD {
    private static final int BITS_PER_BYTE =   8;
    private static final int BITS_PER_INT  =  32;   // each Java int is 32 bits 
    private static final int R             = 256;   // extended ASCII alphabet size
    private static final int CUTOFF        =  15;   // cutoff to insertion sort

    // do not instantiate
    private MSD() { }

    public static void sort(String[] a) {
        int n = a.length;
        String[] aux = new String[n];
        sort(a, 0, n-1, 0, aux);
    }

    // return dth character of s, -1 if d = length of string
    private static int charAt(String s, int d) {
        assert d >= 0 && d <= s.length();
        if (d == s.length()) return -1;
        return s.charAt(d);
    }

    // sort from a[lo] to a[hi], starting at the dth character
    private static void sort(String[] a, int lo, int hi, int d, String[] aux) {

        // cutoff to insertion sort for small subarrays
        if (hi <= lo + CUTOFF) {
            insertion(a, lo, hi, d);
            return;
        }

        // compute frequency counts
        int[] count = new int[R+2];
        for (int i = lo; i <= hi; i++) {
            int c = charAt(a[i], d);
            count[c+2]++;
        }

        // transform counts to indicies
        for (int r = 0; r < R+1; r++)
            count[r+1] += count[r];

        // distribute
        for (int i = lo; i <= hi; i++) {
            int c = charAt(a[i], d);
            aux[count[c+1]++] = a[i];
        }

        // copy back
        for (int i = lo; i <= hi; i++)
            a[i] = aux[i - lo];


        // recursively sort for each character (excludes sentinel -1)
        for (int r = 0; r < R; r++)
            sort(a, lo + count[r], lo + count[r+1] - 1, d+1, aux);
    }


    // insertion sort a[lo..hi], starting at dth character
    private static void insertion(String[] a, int lo, int hi, int d) {
        for (int i = lo; i <= hi; i++)
            for (int j = i; j > lo && less(a[j], a[j-1], d); j--)
                exch(a, j, j-1);
    }

    // exchange a[i] and a[j]
    private static void exch(String[] a, int i, int j) {
        String temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    // is v less than w, starting at character d
    private static boolean less(String v, String w, int d) {
        // assert v.substring(0, d).equals(w.substring(0, d));
        for (int i = d; i < Math.min(v.length(), w.length()); i++) {
            if (v.charAt(i) < w.charAt(i)) return true;
            if (v.charAt(i) > w.charAt(i)) return false;
        }
        return v.length() < w.length();
    }

    public static void sort(int[] a) {
        int n = a.length;
        int[] aux = new int[n];
        sort(a, 0, n-1, 0, aux);
    }

    // MSD sort from a[lo] to a[hi], starting at the dth byte
    private static void sort(int[] a, int lo, int hi, int d, int[] aux) {

        // cutoff to insertion sort for small subarrays
        if (hi <= lo + CUTOFF) {
            insertion(a, lo, hi, d);
            return;
        }

        // compute frequency counts (need R = 256)
        int[] count = new int[R+1];
        int mask = R - 1;   // 0xFF;
        int shift = BITS_PER_INT - BITS_PER_BYTE*d - BITS_PER_BYTE;
        for (int i = lo; i <= hi; i++) {
            int c = (a[i] >> shift) & mask;
            count[c + 1]++;
        }

        // transform counts to indicies
        for (int r = 0; r < R; r++)
            count[r+1] += count[r];

        for (int i = lo; i <= hi; i++) {
            int c = (a[i] >> shift) & mask;
            aux[count[c]++] = a[i];
        }

        // copy back
        for (int i = lo; i <= hi; i++)
            a[i] = aux[i - lo];

        // no more bits
        if (d == 4) return;

        // recursively sort for each character
        if (count[0] > 0)
            sort(a, lo, lo + count[0] - 1, d+1, aux);
        for (int r = 0; r < R; r++)
            if (count[r+1] > count[r])
                sort(a, lo + count[r], lo + count[r+1] - 1, d+1, aux);
    }

    // TODO: insertion sort a[lo..hi], starting at dth character
    private static void insertion(int[] a, int lo, int hi, int d) {
        for (int i = lo; i <= hi; i++)
            for (int j = i; j > lo && a[j] < a[j-1]; j--)
                exch(a, j, j-1);
    }

    // exchange a[i] and a[j]
    private static void exch(int[] a, int i, int j) {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        int n = a.length;
        sort(a);
        for (int i = 0; i < n; i++)
            StdOut.println(a[i]);
    }
}

4.三向字符串快速排序

package string;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import edu.princeton.cs.algs4.StdRandom;

public class Quick3string {
    private static final int CUTOFF =  15;   // cutoff to insertion sort

    // do not instantiate
    private Quick3string() { }

    public static void sort(String[] a) {
        StdRandom.shuffle(a);
        sort(a, 0, a.length-1, 0);
        assert isSorted(a);
    }

    // return the dth character of s, -1 if d = length of s
    private static int charAt(String s, int d) {
        assert d >= 0 && d <= s.length();
        if (d == s.length()) return -1;
        return s.charAt(d);
    }


    // 3-way string quicksort a[lo..hi] starting at dth character
    private static void sort(String[] a, int lo, int hi, int d) {

        // cutoff to insertion sort for small subarrays
        if (hi <= lo + CUTOFF) {
            insertion(a, lo, hi, d);
            return;
        }

        int lt = lo, gt = hi;
        int v = charAt(a[lo], d);
        int i = lo + 1;
        while (i <= gt) {
            int t = charAt(a[i], d);
            if      (t < v) exch(a, lt++, i++);
            else if (t > v) exch(a, i, gt--);
            else              i++;
        }

        // a[lo..lt-1] < v = a[lt..gt] < a[gt+1..hi]. 
        sort(a, lo, lt-1, d);
        if (v >= 0) sort(a, lt, gt, d+1);
        sort(a, gt+1, hi, d);
    }

    // sort from a[lo] to a[hi], starting at the dth character
    private static void insertion(String[] a, int lo, int hi, int d) {
        for (int i = lo; i <= hi; i++)
            for (int j = i; j > lo && less(a[j], a[j-1], d); j--)
                exch(a, j, j-1);
    }

    // exchange a[i] and a[j]
    private static void exch(String[] a, int i, int j) {
        String temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    // is v less than w, starting at character d
    // DEPRECATED BECAUSE OF SLOW SUBSTRING EXTRACTION IN JAVA 7
    // private static boolean less(String v, String w, int d) {
    //    assert v.substring(0, d).equals(w.substring(0, d));
    //    return v.substring(d).compareTo(w.substring(d)) < 0; 
    // }

    // is v less than w, starting at character d
    private static boolean less(String v, String w, int d) {
        assert v.substring(0, d).equals(w.substring(0, d));
        for (int i = d; i < Math.min(v.length(), w.length()); i++) {
            if (v.charAt(i) < w.charAt(i)) return true;
            if (v.charAt(i) > w.charAt(i)) return false;
        }
        return v.length() < w.length();
    }

    // is the array sorted
    private static boolean isSorted(String[] a) {
        for (int i = 1; i < a.length; i++)
            if (a[i].compareTo(a[i-1]) < 0) return false;
        return true;
    }

    public static void main(String[] args) {

        // read in the strings from standard input
        String[] a = StdIn.readAllStrings();
        int n = a.length;

        // sort the strings
        sort(a);

        // print the results
        for (int i = 0; i < n; i++)
            StdOut.println(a[i]);
    }
}

二.单词查找树

 1.基于单词查找树的符号表

package string;

import edu.princeton.cs.algs4.Queue;
import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class TrieST<Value> {
    private static final int R = 256;        // extended ASCII

    private Node root;      // root of trie
    private int n;          // number of keys in trie

    private static class Node {
        private Object val;
        private Node[] next = new Node[R];
    }

    public TrieST() {
    }

    public Value get(String key) {
        if (key == null) throw new IllegalArgumentException("argument to get() is null");
        Node x = get(root, key, 0);
        if (x == null) return null;
        return (Value) x.val;
    }

    public boolean contains(String key) {
        if (key == null) throw new IllegalArgumentException("argument to contains() is null");
        return get(key) != null;
    }

    private Node get(Node x, String key, int d) {
        if (x == null) return null;
        if (d == key.length()) return x;
        char c = key.charAt(d);
        return get(x.next[c], key, d+1);
    }

    public void put(String key, Value val) {
        if (key == null) throw new IllegalArgumentException("first argument to put() is null");
        if (val == null) delete(key);
        else root = put(root, key, val, 0);
    }

    private Node put(Node x, String key, Value val, int d) {
        if (x == null) x = new Node();
        if (d == key.length()) {
            if (x.val == null) n++;
            x.val = val;
            return x;
        }
        char c = key.charAt(d);
        x.next[c] = put(x.next[c], key, val, d+1);
        return x;
    }

    public int size() {
        return n;
    }

    public boolean isEmpty() {
        return size() == 0;
    }

    public Iterable<String> keys() {
        return keysWithPrefix("");
    }

    public Iterable<String> keysWithPrefix(String prefix) {
        Queue<String> results = new Queue<String>();
        Node x = get(root, prefix, 0);
        collect(x, new StringBuilder(prefix), results);
        return results;
    }

    private void collect(Node x, StringBuilder prefix, Queue<String> results) {
        if (x == null) return;
        if (x.val != null) results.enqueue(prefix.toString());
        for (char c = 0; c < R; c++) {
            prefix.append(c);
            collect(x.next[c], prefix, results);
            prefix.deleteCharAt(prefix.length() - 1);
        }
    }

    public Iterable<String> keysThatMatch(String pattern) {
        Queue<String> results = new Queue<String>();
        collect(root, new StringBuilder(), pattern, results);
        return results;
    }

    private void collect(Node x, StringBuilder prefix, String pattern, Queue<String> results) {
        if (x == null) return;
        int d = prefix.length();
        if (d == pattern.length() && x.val != null)
            results.enqueue(prefix.toString());
        if (d == pattern.length())
            return;
        char c = pattern.charAt(d);
        if (c == '.') {
            for (char ch = 0; ch < R; ch++) {
                prefix.append(ch);
                collect(x.next[ch], prefix, pattern, results);
                prefix.deleteCharAt(prefix.length() - 1);
            }
        }
        else {
            prefix.append(c);
            collect(x.next[c], prefix, pattern, results);
            prefix.deleteCharAt(prefix.length() - 1);
        }
    }

    public String longestPrefixOf(String query) {
        if (query == null) throw new IllegalArgumentException("argument to longestPrefixOf() is null");
        int length = longestPrefixOf(root, query, 0, -1);
        if (length == -1) return null;
        else return query.substring(0, length);
    }

    // returns the length of the longest string key in the subtrie
    // rooted at x that is a prefix of the query string,
    // assuming the first d character match and we have already
    // found a prefix match of given length (-1 if no such match)
    private int longestPrefixOf(Node x, String query, int d, int length) {
        if (x == null) return length;
        if (x.val != null) length = d;
        if (d == query.length()) return length;
        char c = query.charAt(d);
        return longestPrefixOf(x.next[c], query, d+1, length);
    }

    public void delete(String key) {
        if (key == null) throw new IllegalArgumentException("argument to delete() is null");
        root = delete(root, key, 0);
    }

    private Node delete(Node x, String key, int d) {
        if (x == null) return null;
        if (d == key.length()) {
            if (x.val != null) n--;
            x.val = null;
        }
        else {
            char c = key.charAt(d);
            x.next[c] = delete(x.next[c], key, d+1);
        }

        // remove subtrie rooted at x if it is completely empty
        if (x.val != null) return x;
        for (int c = 0; c < R; c++)
            if (x.next[c] != null)
                return x;
        return null;
    }

    public static void main(String[] args) {

        // build symbol table from standard input
        TrieST<Integer> st = new TrieST<Integer>();
        for (int i = 0; !StdIn.isEmpty(); i++) {
            String key = StdIn.readString();
            st.put(key, i);
        }

        // print results
        if (st.size() < 100) {
            StdOut.println("keys(""):");
            for (String key : st.keys()) {
                StdOut.println(key + " " + st.get(key));
            }
            StdOut.println();
        }

        StdOut.println("longestPrefixOf("shellsort"):");
        StdOut.println(st.longestPrefixOf("shellsort"));
        StdOut.println();

        StdOut.println("longestPrefixOf("quicksort"):");
        StdOut.println(st.longestPrefixOf("quicksort"));
        StdOut.println();

        StdOut.println("keysWithPrefix("shor"):");
        for (String s : st.keysWithPrefix("shor"))
            StdOut.println(s);
        StdOut.println();

        StdOut.println("keysThatMatch(".he.l."):");
        for (String s : st.keysThatMatch(".he.l."))
            StdOut.println(s);
    }
}

2.基于三向单词查找树的符号表

package string;

import edu.princeton.cs.algs4.Queue;
import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class TST<Value> {
    private int n;              // size
    private Node<Value> root;   // root of TST

    private static class Node<Value> {
        private char c;                        // character
        private Node<Value> left, mid, right;  // left, middle, and right subtries
        private Value val;                     // value associated with string
    }

    public TST() {
    }

    public int size() {
        return n;
    }

    public boolean contains(String key) {
        if (key == null) {
            throw new IllegalArgumentException("argument to contains() is null");
        }
        return get(key) != null;
    }

    public Value get(String key) {
        if (key == null) {
            throw new IllegalArgumentException("calls get() with null argument");
        }
        if (key.length() == 0) throw new IllegalArgumentException("key must have length >= 1");
        Node<Value> x = get(root, key, 0);
        if (x == null) return null;
        return x.val;
    }

    // return subtrie corresponding to given key
    private Node<Value> get(Node<Value> x, String key, int d) {
        if (x == null) return null;
        if (key.length() == 0) throw new IllegalArgumentException("key must have length >= 1");
        char c = key.charAt(d);
        if      (c < x.c)              return get(x.left,  key, d);
        else if (c > x.c)              return get(x.right, key, d);
        else if (d < key.length() - 1) return get(x.mid,   key, d+1);
        else                           return x;
    }

    public void put(String key, Value val) {
        if (key == null) {
            throw new IllegalArgumentException("calls put() with null key");
        }
        if (!contains(key)) n++;
        else if(val == null) n--;       // delete existing key
        root = put(root, key, val, 0);
    }

    private Node<Value> put(Node<Value> x, String key, Value val, int d) {
        char c = key.charAt(d);
        if (x == null) {
            x = new Node<Value>();
            x.c = c;
        }
        if      (c < x.c)               x.left  = put(x.left,  key, val, d);
        else if (c > x.c)               x.right = put(x.right, key, val, d);
        else if (d < key.length() - 1)  x.mid   = put(x.mid,   key, val, d+1);
        else                            x.val   = val;
        return x;
    }

    public String longestPrefixOf(String query) {
        if (query == null) {
            throw new IllegalArgumentException("calls longestPrefixOf() with null argument");
        }
        if (query.length() == 0) return null;
        int length = 0;
        Node<Value> x = root;
        int i = 0;
        while (x != null && i < query.length()) {
            char c = query.charAt(i);
            if      (c < x.c) x = x.left;
            else if (c > x.c) x = x.right;
            else {
                i++;
                if (x.val != null) length = i;
                x = x.mid;
            }
        }
        return query.substring(0, length);
    }

    public Iterable<String> keys() {
        Queue<String> queue = new Queue<String>();
        collect(root, new StringBuilder(), queue);
        return queue;
    }

    public Iterable<String> keysWithPrefix(String prefix) {
        if (prefix == null) {
            throw new IllegalArgumentException("calls keysWithPrefix() with null argument");
        }
        Queue<String> queue = new Queue<String>();
        Node<Value> x = get(root, prefix, 0);
        if (x == null) return queue;
        if (x.val != null) queue.enqueue(prefix);
        collect(x.mid, new StringBuilder(prefix), queue);
        return queue;
    }

    // all keys in subtrie rooted at x with given prefix
    private void collect(Node<Value> x, StringBuilder prefix, Queue<String> queue) {
        if (x == null) return;
        collect(x.left,  prefix, queue);
        if (x.val != null) queue.enqueue(prefix.toString() + x.c);
        collect(x.mid,   prefix.append(x.c), queue);
        prefix.deleteCharAt(prefix.length() - 1);
        collect(x.right, prefix, queue);
    }

    public Iterable<String> keysThatMatch(String pattern) {
        Queue<String> queue = new Queue<String>();
        collect(root, new StringBuilder(), 0, pattern, queue);
        return queue;
    }

    private void collect(Node<Value> x, StringBuilder prefix, int i, String pattern, Queue<String> queue) {
        if (x == null) return;
        char c = pattern.charAt(i);
        if (c == '.' || c < x.c) collect(x.left, prefix, i, pattern, queue);
        if (c == '.' || c == x.c) {
            if (i == pattern.length() - 1 && x.val != null) queue.enqueue(prefix.toString() + x.c);
            if (i < pattern.length() - 1) {
                collect(x.mid, prefix.append(x.c), i+1, pattern, queue);
                prefix.deleteCharAt(prefix.length() - 1);
            }
        }
        if (c == '.' || c > x.c) collect(x.right, prefix, i, pattern, queue);
    }

    public static void main(String[] args) {

        // build symbol table from standard input
        TST<Integer> st = new TST<Integer>();
        for (int i = 0; !StdIn.isEmpty(); i++) {
            String key = StdIn.readString();
            st.put(key, i);
        }

        // print results
        if (st.size() < 100) {
            StdOut.println("keys(""):");
            for (String key : st.keys()) {
                StdOut.println(key + " " + st.get(key));
            }
            StdOut.println();
        }

        StdOut.println("longestPrefixOf("shellsort"):");
        StdOut.println(st.longestPrefixOf("shellsort"));
        StdOut.println();

        StdOut.println("longestPrefixOf("shell"):");
        StdOut.println(st.longestPrefixOf("shell"));
        StdOut.println();

        StdOut.println("keysWithPrefix("shor"):");
        for (String s : st.keysWithPrefix("shor"))
            StdOut.println(s);
        StdOut.println();

        StdOut.println("keysThatMatch(".he.l."):");
        for (String s : st.keysThatMatch(".he.l."))
            StdOut.println(s);
    }
}

三.子字符串查找

1.Knuth-Morris-Pratt字符串查找算法

package string;

import edu.princeton.cs.algs4.StdOut;

public class KMP {
    private final int R;       // the radix
    private int[][] dfa;       // the KMP automoton

    private char[] pattern;    // either the character array for the pattern
    private String pat;        // or the pattern string

    public KMP(String pat) {
        this.R = 256;
        this.pat = pat;

        // build DFA from pattern
        int m = pat.length();
        dfa = new int[R][m];
        dfa[pat.charAt(0)][0] = 1;
        for (int x = 0, j = 1; j < m; j++) {
            for (int c = 0; c < R; c++)
                dfa[c][j] = dfa[c][x];     // Copy mismatch cases.
            dfa[pat.charAt(j)][j] = j+1;   // Set match case.
            x = dfa[pat.charAt(j)][x];     // Update restart state.
        }
    }

    public KMP(char[] pattern, int R) {
        this.R = R;
        this.pattern = new char[pattern.length];
        for (int j = 0; j < pattern.length; j++)
            this.pattern[j] = pattern[j];

        // build DFA from pattern
        int m = pattern.length;
        dfa = new int[R][m];
        dfa[pattern[0]][0] = 1;
        for (int x = 0, j = 1; j < m; j++) {
            for (int c = 0; c < R; c++)
                dfa[c][j] = dfa[c][x];     // Copy mismatch cases.
            dfa[pattern[j]][j] = j+1;      // Set match case.
            x = dfa[pattern[j]][x];        // Update restart state.
        }
    }

    public int search(String txt) {

        // simulate operation of DFA on text
        int m = pat.length();
        int n = txt.length();
        int i, j;
        for (i = 0, j = 0; i < n && j < m; i++) {
            j = dfa[txt.charAt(i)][j];
        }
        if (j == m) return i - m;    // found
        return n;                    // not found
    }

    public int search(char[] text) {

        // simulate operation of DFA on text
        int m = pattern.length;
        int n = text.length;
        int i, j;
        for (i = 0, j = 0; i < n && j < m; i++) {
            j = dfa[text[i]][j];
        }
        if (j == m) return i - m;    // found
        return n;                    // not found
    }

    public static void main(String[] args) {
        String pat = args[0];
        String txt = args[1];
        char[] pattern = pat.toCharArray();
        char[] text    = txt.toCharArray();

        KMP kmp1 = new KMP(pat);
        int offset1 = kmp1.search(txt);

        KMP kmp2 = new KMP(pattern, 256);
        int offset2 = kmp2.search(text);

        // print results
        StdOut.println("text:    " + txt);

        StdOut.print("pattern: ");
        for (int i = 0; i < offset1; i++)
            StdOut.print(" ");
        StdOut.println(pat);

        StdOut.print("pattern: ");
        for (int i = 0; i < offset2; i++)
            StdOut.print(" ");
        StdOut.println(pat);
    }
}

2.Boyer-Moore字符串匹配算法

package string;

import edu.princeton.cs.algs4.StdOut;

public class BoyerMoore {
    private final int R;     // the radix
    private int[] right;     // the bad-character skip array

    private char[] pattern;  // store the pattern as a character array
    private String pat;      // or as a string

    public BoyerMoore(String pat) {
        this.R = 256;
        this.pat = pat;

        // position of rightmost occurrence of c in the pattern
        right = new int[R];
        for (int c = 0; c < R; c++)
            right[c] = -1;
        for (int j = 0; j < pat.length(); j++)
            right[pat.charAt(j)] = j;
    }

    public BoyerMoore(char[] pattern, int R) {
        this.R = R;
        this.pattern = new char[pattern.length];
        for (int j = 0; j < pattern.length; j++)
            this.pattern[j] = pattern[j];

        // position of rightmost occurrence of c in the pattern
        right = new int[R];
        for (int c = 0; c < R; c++)
            right[c] = -1;
        for (int j = 0; j < pattern.length; j++)
            right[pattern[j]] = j;
    }

    public int search(String txt) {
        int m = pat.length();
        int n = txt.length();
        int skip;
        for (int i = 0; i <= n - m; i += skip) {
            skip = 0;
            for (int j = m-1; j >= 0; j--) {
                if (pat.charAt(j) != txt.charAt(i+j)) {
                    skip = Math.max(1, j - right[txt.charAt(i+j)]);
                    break;
                }
            }
            if (skip == 0) return i;    // found
        }
        return n;                       // not found
    }

    public int search(char[] text) {
        int m = pattern.length;
        int n = text.length;
        int skip;
        for (int i = 0; i <= n - m; i += skip) {
            skip = 0;
            for (int j = m-1; j >= 0; j--) {
                if (pattern[j] != text[i+j]) {
                    skip = Math.max(1, j - right[text[i+j]]);
                    break;
                }
            }
            if (skip == 0) return i;    // found
        }
        return n;                       // not found
    }

    public static void main(String[] args) {
        String pat = args[0];
        String txt = args[1];
        char[] pattern = pat.toCharArray();
        char[] text    = txt.toCharArray();

        BoyerMoore boyermoore1 = new BoyerMoore(pat);
        BoyerMoore boyermoore2 = new BoyerMoore(pattern, 256);
        int offset1 = boyermoore1.search(txt);
        int offset2 = boyermoore2.search(text);

        // print results
        StdOut.println("text:    " + txt);

        StdOut.print("pattern: ");
        for (int i = 0; i < offset1; i++)
            StdOut.print(" ");
        StdOut.println(pat);

        StdOut.print("pattern: ");
        for (int i = 0; i < offset2; i++)
            StdOut.print(" ");
        StdOut.println(pat);
    }
}

3.Rabin-Karp指纹字符串查找算法

package string;

import edu.princeton.cs.algs4.StdOut;

import java.math.BigInteger;
import java.util.Random;

public class RabinKarp {
    private String pat;      // the pattern  // needed only for Las Vegas
    private long patHash;    // pattern hash value
    private int m;           // pattern length
    private long q;          // a large prime, small enough to avoid long overflow
    private int R;           // radix
    private long RM;         // R^(M-1) % Q

    public RabinKarp(char[] pattern, int R) {
        this.pat = String.valueOf(pattern);
        this.R = R;
        throw new UnsupportedOperationException("Operation not supported yet");
    }

    public RabinKarp(String pat) {
        this.pat = pat;      // save pattern (needed only for Las Vegas)
        R = 256;
        m = pat.length();
        q = longRandomPrime();

        // precompute R^(m-1) % q for use in removing leading digit
        RM = 1;
        for (int i = 1; i <= m-1; i++)
            RM = (R * RM) % q;
        patHash = hash(pat, m);
    }

    // Compute hash for key[0..m-1]. 
    private long hash(String key, int m) {
        long h = 0;
        for (int j = 0; j < m; j++)
            h = (R * h + key.charAt(j)) % q;
        return h;
    }

    // Las Vegas version: does pat[] match txt[i..i-m+1] ?
    private boolean check(String txt, int i) {
        for (int j = 0; j < m; j++)
            if (pat.charAt(j) != txt.charAt(i + j))
                return false;
        return true;
    }

    // Monte Carlo version: always return true
    // private boolean check(int i) {
    //    return true;
    //}

    public int search(String txt) {
        int n = txt.length();
        if (n < m) return n;
        long txtHash = hash(txt, m);

        // check for match at offset 0
        if ((patHash == txtHash) && check(txt, 0))
            return 0;

        // check for hash match; if hash match, check for exact match
        for (int i = m; i < n; i++) {
            // Remove leading digit, add trailing digit, check for match. 
            txtHash = (txtHash + q - RM*txt.charAt(i-m) % q) % q;
            txtHash = (txtHash*R + txt.charAt(i)) % q;

            // match
            int offset = i - m + 1;
            if ((patHash == txtHash) && check(txt, offset))
                return offset;
        }

        // no match
        return n;
    }

    // a random 31-bit prime
    private static long longRandomPrime() {
        BigInteger prime = BigInteger.probablePrime(31, new Random());
        return prime.longValue();
    }

    public static void main(String[] args) {
        String pat = args[0];
        String txt = args[1];

        RabinKarp searcher = new RabinKarp(pat);
        int offset = searcher.search(txt);

        // print results
        StdOut.println("text:    " + txt);

        // from brute force search method 1
        StdOut.print("pattern: ");
        for (int i = 0; i < offset; i++)
            StdOut.print(" ");
        StdOut.println(pat);
    }
}

四.正则表达式

package string;

import edu.princeton.cs.algs4.*;

public class NFA {

    private Digraph graph;     // digraph of epsilon transitions
    private String regexp;     // regular expression
    private final int m;       // number of characters in regular expression

    public NFA(String regexp) {
        this.regexp = regexp;
        m = regexp.length();
        Stack<Integer> ops = new Stack<Integer>();
        graph = new Digraph(m+1);
        for (int i = 0; i < m; i++) {
            int lp = i;
            if (regexp.charAt(i) == '(' || regexp.charAt(i) == '|')
                ops.push(i);
            else if (regexp.charAt(i) == ')') {
                int or = ops.pop();

                // 2-way or operator
                if (regexp.charAt(or) == '|') {
                    lp = ops.pop();
                    graph.addEdge(lp, or+1);
                    graph.addEdge(or, i);
                }
                else if (regexp.charAt(or) == '(')
                    lp = or;
                else assert false;
            }

            // closure operator (uses 1-character lookahead)
            if (i < m-1 && regexp.charAt(i+1) == '*') {
                graph.addEdge(lp, i+1);
                graph.addEdge(i+1, lp);
            }
            if (regexp.charAt(i) == '(' || regexp.charAt(i) == '*' || regexp.charAt(i) == ')')
                graph.addEdge(i, i+1);
        }
        if (ops.size() != 0)
            throw new IllegalArgumentException("Invalid regular expression");
    }

    public boolean recognizes(String txt) {
        DirectedDFS dfs = new DirectedDFS(graph, 0);
        Bag<Integer> pc = new Bag<Integer>();
        for (int v = 0; v < graph.V(); v++)
            if (dfs.marked(v)) pc.add(v);

        // Compute possible NFA states for txt[i+1]
        for (int i = 0; i < txt.length(); i++) {
            if (txt.charAt(i) == '*' || txt.charAt(i) == '|' || txt.charAt(i) == '(' || txt.charAt(i) == ')')
                throw new IllegalArgumentException("text contains the metacharacter '" + txt.charAt(i) + "'");

            Bag<Integer> match = new Bag<Integer>();
            for (int v : pc) {
                if (v == m) continue;
                if ((regexp.charAt(v) == txt.charAt(i)) || regexp.charAt(v) == '.')
                    match.add(v+1);
            }
            dfs = new DirectedDFS(graph, match);
            pc = new Bag<Integer>();
            for (int v = 0; v < graph.V(); v++)
                if (dfs.marked(v)) pc.add(v);

            // optimization if no states reachable
            if (pc.size() == 0) return false;
        }

        // check for accept state
        for (int v : pc)
            if (v == m) return true;
        return false;
    }

    public static void main(String[] args) {
        String regexp = "(" + args[0] + ")";
        String txt = args[1];
        NFA nfa = new NFA(regexp);
        StdOut.println(nfa.recognizes(txt));
    }

}

五.数据压缩

1.霍夫曼压缩

package string;

import edu.princeton.cs.algs4.BinaryStdIn;
import edu.princeton.cs.algs4.BinaryStdOut;
import edu.princeton.cs.algs4.MinPQ;

public class Huffman {
    // alphabet size of extended ASCII
    private static final int R = 256;

    // Do not instantiate.
    private Huffman() { }

    // Huffman trie node
    private static class Node implements Comparable<Node> {
        private final char ch;
        private final int freq;
        private final Node left, right;

        Node(char ch, int freq, Node left, Node right) {
            this.ch    = ch;
            this.freq  = freq;
            this.left  = left;
            this.right = right;
        }

        // is the node a leaf node?
        private boolean isLeaf() {
            assert ((left == null) && (right == null)) || ((left != null) && (right != null));
            return (left == null) && (right == null);
        }

        // compare, based on frequency
        public int compareTo(Node that) {
            return this.freq - that.freq;
        }
    }

    public static void compress() {
        // read the input
        String s = BinaryStdIn.readString();
        char[] input = s.toCharArray();

        // tabulate frequency counts
        int[] freq = new int[R];
        for (int i = 0; i < input.length; i++)
            freq[input[i]]++;

        // build Huffman trie
        Node root = buildTrie(freq);

        // build code table
        String[] st = new String[R];
        buildCode(st, root, "");

        // print trie for decoder
        writeTrie(root);

        // print number of bytes in original uncompressed message
        BinaryStdOut.write(input.length);

        // use Huffman code to encode input
        for (int i = 0; i < input.length; i++) {
            String code = st[input[i]];
            for (int j = 0; j < code.length(); j++) {
                if (code.charAt(j) == '0') {
                    BinaryStdOut.write(false);
                }
                else if (code.charAt(j) == '1') {
                    BinaryStdOut.write(true);
                }
                else throw new IllegalStateException("Illegal state");
            }
        }

        // close output stream
        BinaryStdOut.close();
    }

    // build the Huffman trie given frequencies
    private static Node buildTrie(int[] freq) {

        // initialze priority queue with singleton trees
        MinPQ<Node> pq = new MinPQ<Node>();
        for (char c = 0; c < R; c++)
            if (freq[c] > 0)
                pq.insert(new Node(c, freq[c], null, null));

        // merge two smallest trees
        while (pq.size() > 1) {
            Node left  = pq.delMin();
            Node right = pq.delMin();
            Node parent = new Node('', left.freq + right.freq, left, right);
            pq.insert(parent);
        }
        return pq.delMin();
    }


    // write bitstring-encoded trie to standard output
    private static void writeTrie(Node x) {
        if (x.isLeaf()) {
            BinaryStdOut.write(true);
            BinaryStdOut.write(x.ch, 8);
            return;
        }
        BinaryStdOut.write(false);
        writeTrie(x.left);
        writeTrie(x.right);
    }

    // make a lookup table from symbols and their encodings
    private static void buildCode(String[] st, Node x, String s) {
        if (!x.isLeaf()) {
            buildCode(st, x.left,  s + '0');
            buildCode(st, x.right, s + '1');
        }
        else {
            st[x.ch] = s;
        }
    }

    public static void expand() {

        // read in Huffman trie from input stream
        Node root = readTrie();

        // number of bytes to write
        int length = BinaryStdIn.readInt();

        // decode using the Huffman trie
        for (int i = 0; i < length; i++) {
            Node x = root;
            while (!x.isLeaf()) {
                boolean bit = BinaryStdIn.readBoolean();
                if (bit) x = x.right;
                else     x = x.left;
            }
            BinaryStdOut.write(x.ch, 8);
        }
        BinaryStdOut.close();
    }

    private static Node readTrie() {
        boolean isLeaf = BinaryStdIn.readBoolean();
        if (isLeaf) {
            return new Node(BinaryStdIn.readChar(), -1, null, null);
        }
        else {
            return new Node('', -1, readTrie(), readTrie());
        }
    }

    public static void main(String[] args) {
        if      (args[0].equals("-")) compress();
        else if (args[0].equals("+")) expand();
        else throw new IllegalArgumentException("Illegal command line argument");
    }

}

 2.LZW算法的压缩

package string;

import edu.princeton.cs.algs4.BinaryStdIn;
import edu.princeton.cs.algs4.BinaryStdOut;

public class LZW {
    private static final int R = 256;        // number of input chars
    private static final int L = 4096;       // number of codewords = 2^W
    private static final int W = 12;         // codeword width

    // Do not instantiate.
    private LZW() { }

    public static void compress() {
        String input = BinaryStdIn.readString();
        TST<Integer> st = new TST<Integer>();
        for (int i = 0; i < R; i++)
            st.put("" + (char) i, i);
        int code = R+1;  // R is codeword for EOF

        while (input.length() > 0) {
            String s = st.longestPrefixOf(input);  // Find max prefix match s.
            BinaryStdOut.write(st.get(s), W);      // Print s's encoding.
            int t = s.length();
            if (t < input.length() && code < L)    // Add s to symbol table.
                st.put(input.substring(0, t + 1), code++);
            input = input.substring(t);            // Scan past s in input.
        }
        BinaryStdOut.write(R, W);
        BinaryStdOut.close();
    }

    public static void expand() {
        String[] st = new String[L];
        int i; // next available codeword value

        // initialize symbol table with all 1-character strings
        for (i = 0; i < R; i++)
            st[i] = "" + (char) i;
        st[i++] = "";                        // (unused) lookahead for EOF

        int codeword = BinaryStdIn.readInt(W);
        if (codeword == R) return;           // expanded message is empty string
        String val = st[codeword];

        while (true) {
            BinaryStdOut.write(val);
            codeword = BinaryStdIn.readInt(W);
            if (codeword == R) break;
            String s = st[codeword];
            if (i == codeword) s = val + val.charAt(0);   // special case hack
            if (i < L) st[i++] = val + s.charAt(0);
            val = s;
        }
        BinaryStdOut.close();
    }

    public static void main(String[] args) {
        if      (args[0].equals("-")) compress();
        else if (args[0].equals("+")) expand();
        else throw new IllegalArgumentException("Illegal command line argument");
    }

}