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字符串排序算法

不懒人   2020-02-12 我要评论

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

 


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