TimSort.java implementation

src/main/java/edu/princeton/cs/algs4/TimSort.java

@@ -0,0 +1,257 @@
+/******************************************************************************
+ *  Compilation:  javac TimSort.java
+ *  Execution:    java TimSort < input.txt
+ *  Dependencies: StdOut.java StdIn.java Insertion.java
+ *  Data files:   https://algs4.cs.princeton.edu/23quicksort/tiny.txt
+ *                https://algs4.cs.princeton.edu/23quicksort/words3.txt
+ *
+ *  A hybrid sorting algorithm derived from merge sort and insertion sort.
+ *  It was designed to perform well on many kinds of real-world data.
+ *
+ *  % more tiny.txt
+ *  S O R T E X A M P L E
+ *
+ *  % java TimSort < tiny.txt
+ *  A E E L M O P R S T X                 [ one string per line ]
+ *
+ *  % more words3.txt
+ *  bed bug dad yes zoo ... all bad yet
+ *
+ *  % java TimSort < words3.txt
+ *  all bad bed bug dad ... yes yet zoo    [ one string per line ]
+ *
+ ******************************************************************************/
+
+package edu.princeton.cs.algs4;
+
+/**
+ * The {@code TimSort} class provides static methods for sorting an
+ * array using the TimSort algorithm, a hybrid stable sorting algorithm
+ * derived from merge sort and insertion sort. It is designed to perform
+ * efficiently on many kinds of real-world data.
+ * <p>
+ * This implementation takes &Theta;(<em>n</em> log <em>n</em>) time
+ * to sort an array of length <em>n</em> in the worst case, but often performs
+ * better on partially sorted arrays or arrays with certain predictable patterns.
+ * The exact number of comparisons depends on the structure of the input data.
+ * </p>
+ * <p>
+ * TimSort is stable and uses &Theta;(<em>n</em>) extra memory (not including the
+ * input array). It is well-suited for large datasets and is used in the Java standard
+ * library for sorting objects.
+ * </p>
+ * <p>
+ * For additional documentation on the algorithm, see
+ * <a href="https://en.wikipedia.org/wiki/Timsort">Timsort on Wikipedia</a>.
+ * </p>
+ *
+ * @author Max Loshak
+ */
+public class TimSort {
+    static int MIN_RUN = 32;  // default minimum size of a run
+
+    // This class should not be instantiated.
+    private TimSort() { }
+
+    /**
+     * Computes the minimum length of a run to be sorted using insertion sort in Timsort.
+     *
+     * @param n The length of the array or subarray to be sorted.
+     * @return The minimum run length. Runs shorter than this length will be sorted using insertion sort.
+     *
+     * <p>The method calculates the minimum run length by considering the bit representation of the array
+     * length (n). It repeatedly right-shifts n by 1 until n is less than {@code MIN_MERGE}. During each
+     * shift, if the least significant bit of n is 1, it is 'or-ed' into the result (r). The method returns
+     * the sum of the remaining value of n and r. This approach ensures a balance between the number of runs
+     * and their size, optimizing the performance of Timsort.</p>
+     *
+     * <p>Time Complexity: O(log n), where n is the length of the array or subarray to be sorted.</p>
+     */
+    public static int runLength(int n)
+    {
+        assert n >= 0;
+        int r = 0;
+        while (n >= MIN_RUN) {
+            r |= (n & 1);
+            n >>= 1;
+        }
+        return n + r;
+    }
+
+    /**
+     * Merges two sorted subarrays of {@code arr}.
+     * The first subarray is {@code arr[l..m]} and the second subarray is {@code arr[m+1..r]}.
+     * After the merge, the subarray {@code arr[l..r]} is sorted.
+     *
+     * @param arr The array of Comparable elements to be merged.
+     * @param l   The starting index of the first subarray to be merged.
+     * @param m   The ending index of the first subarray. This also separates the
+     *            two subarrays to be merged, with the second subarray starting at {@code m + 1}.
+     * @param r   The ending index of the second subarray to be merged.
+     *
+     * <p>This method performs the merge operation in the merge sort algorithm. It
+     * combines two contiguous, sorted subarrays within the larger array into a single
+     * sorted subarray. This is achieved by comparing the elements of the subarrays
+     * and copying them back into the original array in sorted order. Additional
+     * arrays are used to hold the elements of the subarrays during the merge process.</p>
+     *
+     * <p>Time Complexity: O(n), where n is the number of elements in the merged subarray.</p>
+     */
+    public static void merge(Comparable[] arr, int l, int m, int r)
+    {
+        int size1 = m - l + 1, size2 = r - m;
+        Comparable[] left = new Comparable[size1];
+        Comparable[] right = new Comparable[size2];
+        System.arraycopy(arr, l, left, 0, size1);
+        for (int x = 0; x < size2; x++) {
+            right[x] = arr[m + 1 + x];
+        }
+        int i = 0;
+        int j = 0;
+        int k = l;
+
+        // merging into larger subarray after comparing
+        while (i < size1 && j < size2) {
+            if (!less(right[j],left[i])) {
+                arr[k] = left[i];
+                i++;
+            }
+            else {
+                arr[k] = right[j];
+                j++;
+            }
+            k++;
+        }
+        // Copy remaining elements of left and right, if any
+        while (i < size1) {
+            arr[k] = left[i];
+            k++;
+            i++;
+        }
+        while (j < size2) {
+            arr[k] = right[j];
+            k++;
+            j++;
+        }
+    }
+
+    /**
+     * Rearranges the full array in ascending order, using the natural order.
+     * @param arr the array to be sorted
+     */
+    public static void sort(Comparable[] arr) {
+        int n = arr.length;
+        sort(arr, 0, n);
+        assert isSorted(arr);
+    }
+
+    /**
+     * Iterative Timsort function to sort the part of array [..,lo,...,hi,..] in ascending order.
+     * @param arr the array to be sorted
+     * @param lo left endpoint (inclusive)
+     * @param hi right endpoint (exclusive)
+     *
+     * <p>This method implements the Timsort algorithm, which is optimized for real-world data
+     * that often contains ordered subsequences. It first sorts small segments of the array
+     * using insertion sort and then efficiently merges these segments. The merging of segments
+     * is done in a manner that optimizes the number of comparisons and moves, making Timsort
+     * faster and more efficient than traditional mergesort on real-world data.</p>
+     *
+     * <p>Time Complexity: O(n log n), where n is the number of elements in the range [lo, hi).</p>
+     */
+    public static void sort(Comparable[] arr, int lo, int hi)
+    {
+        int minRun = runLength(MIN_RUN);
+
+        // Sort individual subarrays of size RUN
+        for (int i = lo; i < hi; i += minRun) {
+            Insertion.sort(
+                    arr, i,
+                    Math.min((i + MIN_RUN - 1), (hi)));
+        }
+
+        // Start merging from size RUN (32). It will merge to form size 64, 128 and so on
+        for (int size = minRun; size < hi; size = 2 * size) {
+
+            for (int left = 0; left < hi; left += 2 * size) {
+                int mid = left + size - 1;
+                int right = Math.min((left + 2 * size - 1),
+                        (hi - 1));
+
+                // Merge arr[left.....mid] and arr[mid+1....right]
+                if (mid < right)
+                    merge(arr, left, mid, right);
+            }
+        }
+
+        assert isSorted(arr, lo, hi - 1);
+    }
+
+
+    /***************************************************************************
+     *  Helper sorting functions.
+     ***************************************************************************/
+
+    // is v < w ?
+    private static boolean less(Comparable v, Comparable w) {
+        return v.compareTo(w) < 0;
+    }
+
+
+    /***************************************************************************
+     *  Check if array is sorted - useful for debugging.
+     ***************************************************************************/
+    private static boolean isSorted(Comparable[] a) {
+        return isSorted(a, 0, a.length - 1);
+    }
+
+    private static boolean isSorted(Comparable[] a, int lo, int hi) {
+        for (int i = lo + 1; i <= hi; i++)
+            if (less(a[i], a[i-1])) return false;
+        return true;
+    }
+
+
+    // print array to standard output
+    private static void show(Comparable[] a) {
+        for (int i = 0; i < a.length; i++) {
+            StdOut.println(a[i]);
+        }
+    }
+
+    /**
+     * Reads in a sequence of strings from standard input; heapsorts them;
+     * and prints them to standard output in ascending order.
+     *
+     * @param args the command-line arguments
+     */
+    public static void main(String[] args) {
+        String[] a = StdIn.readAllStrings();
+        TimSort.sort(a);
+        show(a);
+    }
+}
+
+/******************************************************************************
+ *  Copyright 2002-2022, Robert Sedgewick and Kevin Wayne.
+ *
+ *  This file is part of algs4.jar, which accompanies the textbook
+ *
+ *      Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
+ *      Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
+ *      http://algs4.cs.princeton.edu
+ *
+ *
+ *  algs4.jar is free software: you can redistribute it and/or modify
+ *  it under the terms of the GNU General Public License as published by
+ *  the Free Software Foundation, either version 3 of the License, or
+ *  (at your option) any later version.
+ *
+ *  algs4.jar is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License
+ *  along with algs4.jar.  If not, see http://www.gnu.org/licenses.
+ ******************************************************************************/