《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]);
     }
 }