《算法》第五章部分程序 part 3

▶ 书中第五章部分程序，包括在加上自己补充的代码，字符串高位优先排序（美国国旗排序）

● 美国国旗排序

package package01;

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

public class class01
{
    private static final int BITS_PER_BYTE = 8;
    private static final int BITS_PER_INT = 32;
    private static final int R = 256;
    private static final int CUTOFF = 15;

    private class01() {}

    public static void sort(String[] a)
    {
        sortKernel(a, 0, a.length - 1);
    }

    public static void sortKernel(String[] a, int lo, int hi)
    {
        Stack<Integer> st = new Stack<Integer>();
        int[] first = new int[R + 2], next = new int[R + 2];
        int d = 0;
        for (st.push(lo), st.push(hi), st.push(d); !st.isEmpty();)
        {
            d = st.pop(); hi = st.pop(); lo = st.pop();
            if (hi <= lo + CUTOFF)
            {
                insertion(a, lo, hi, d);
                continue;
            }
            for (int i = lo; i <= hi; i++)      // 以字符串的第 d 位进行统计
                first[charAt(a[i], d) + 2]++;
            first[0] = lo;                      // 前部垫起
            for (int c = 0; c <= R; c++)        // 前缀和与子问题分配
            {
                first[c + 1] += first[c];
                if (c > 0 && first[c + 1] - 1 > first[c])       // 存在至少 2 个第 d 位为 c 的字符串，注意排除 c == 0 的情况
                {
                    st.push(first[c]);                          // 添加子问题，对第 d 位为 c 的所有字符串关于第 d+1 位进行排序
                    st.push(first[c + 1] - 1);
                    st.push(d + 1);
                }
            }
            for (int c = 0; c < R + 2; c++)     // 拷贝 first 到 next 中，next 用于搬运字符串过程中的变化索引
                next[c] = first[c];
            for (int k = lo; k <= hi; k++)      // 搬运字符串到指定位置，循环将 a[k] 作为交换的临时位置
            {
                int c = charAt(a[k], d) + 1;                    // 取 a[k] 的第 d 位的下一个字符
                for (; first[c] > k; c = charAt(a[k], d) + 1)   // 只要 c 出现的位置排在 k 后面，就交换 a[k] 和 a[next[c]]，并且 next[c]向后移一个位置
                    exch(a, k, next[c]++);
                next[c]++;                                      // 全部移完了，next[c] 再自增 1，表示 c 开头的索引已经等于 first[c+1]，避免重复排序
            }
            for (int c = 0; c < R + 2; c++)     // 清除 first 和 next
                first[c] = next[c] = 0;
        }
    }

    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);
        }
    }

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

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

    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))
                continue;
            return v.charAt(i) < w.charAt(i);
        }
        return v.length() < w.length();
    }

    public static void sort(int[] a)                            // 数组排序
    {
        sortKernel(a, 0, a.length - 1);
    }

    private static void sortKernel(int[] a, int lo, int hi)
    {
        Stack<Integer> st = new Stack<Integer>();
        int[] first = new int[R + 1], next = new int[R + 1];
        int mask = R - 1, d = 0;
        for (st.push(lo), st.push(hi), st.push(d); !st.isEmpty();)
        {
            d = st.pop(); hi = st.pop(); lo = st.pop();
            if (hi <= lo + CUTOFF)
            {
                insertion(a, lo, hi, d);
                continue;
            }
            int shift = BITS_PER_INT - BITS_PER_BYTE * (d + 1); // 取从左往右的第 d 字节
            for (int i = lo; i <= hi; i++)
                first[((a[i] >> shift) & mask) + 1]++;
            first[0] = lo;
            for (int c = 0; c < R; c++)
            {
                first[c + 1] += first[c];
                if (d < 3 && first[c + 1] - 1 > first[c])       // c > 0 条件改为，当前字节不是最低字节
                {
                    st.push(first[c]);
                    st.push(first[c + 1] - 1);
                    st.push(d + 1);
                }
            }
            for (int c = 0; c < R + 1; c++)
                next[c] = first[c];
            for (int k = lo; k <= hi; k++)
            {
                int c = (a[k] >> shift) & mask;
                for (; first[c] > k; c = (a[k] >> shift) & mask)
                    exch(a, k, next[c]++);
                next[c]++;
            }
            for (int c = 0; c < R + 1; c++)
                first[c] = next[c] = 0;
        }
    }

    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 && less(a[j], a[j - 1], d); j--)
                exch(a, j, j - 1);
        }
    }

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

    private static boolean less(int v, int w, int d)
    {
        int mask = R - 1;
        for (int i = d; i < 4; i++)
        {
            int shift = BITS_PER_INT - BITS_PER_BYTE * (i + 1);
            int a = (v >> shift) & mask, b = (w >> shift) & mask;
            if (a == b)
                continue;
            return a < b;
        }
        return false;
    }

    public static void main(String[] args)
    {
        if (args.length > 0 && args[0].equals("int"))
        {
            int[] a = StdIn.readAllInts();
            sort(a);

            for (int i = 0; i < a.length; i++)
                StdOut.println(a[i]);
        }
        else
        {
            String[] a = StdIn.readAllStrings();
            sort(a);

            for (int i = 0; i < a.length; i++)
                StdOut.println(a[i]);
        }
    }
}

● 美国国旗排序 2

package package01;

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

public class class01
{
    private static final int R = 256;
    private static final int CUTOFF = 15;

    private class01() {}

    public static void sort(String[] a)
    {
        sortKernel(a, 0, a.length - 1);
    }

    public static void sortKernel(String[] a, int lo, int hi)
    {
        Stack<Integer> st = new Stack<Integer>();
        int[] count = new int[R + 1];
        int d = 0;
        for (st.push(lo), st.push(hi), st.push(d); !st.isEmpty();)
        {
            d = st.pop(); hi = st.pop(); lo = st.pop();
            if (hi <= lo + CUTOFF)
            {
                insertion(a, lo, hi, d);
                continue;
            }
            for (int i = lo; i <= hi; i++)
                count[charAt(a[i], d) + 1]++;
            count[0] += lo;
            for (int c = 0; c < R; c++)
            {
                count[c + 1] += count[c];                   // count[c] 表示键值不大于 c 的元素个数（相当于字符 c+1 起始位置先前 1 格）
                if (c > 0 && count[c + 1] - 1 > count[c])
                {
                    st.push(count[c]);
                    st.push(count[c + 1] - 1);
                    st.push(d + 1);
                }
            }
            for (int r = hi; r >= lo; r--)                  // r 从后向前
            {
                int c = charAt(a[r], d) + 1;
                for (; r >= lo && count[c] - 1 <= r;)
                {
                    if (count[c] - 1 == r)
                        count[c]--;
                    r--;
                    if (r >= lo)
                        c = charAt(a[r], d) + 1;
                }
                if (r < lo)                                 // r 已经降到 lo 以下，调整完成
                    break;
                for (count[c]--; count[c] != r; c = charAt(a[r], d) + 1, count[c]--)
                    exch(a, r, count[c]);
            }
        }
        for (int c = 0; c < R + 1; c++)                     // 清除 count
            count[c] = 0;
    }

    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);
        }
    }

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

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

    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))
                continue;
            return v.charAt(i) < w.charAt(i);
        }
        return v.length() < w.length();
    }

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

        for (int i = 0; i < a.length; i++)
            StdOut.println(a[i]);
    }
}