Package smile.sort

Class QuickSort


  • public class QuickSort
    extends java.lang.Object
    Quicksort is a well-known sorting algorithm that, on average, makes O(n log n) comparisons to sort n items. For large n (say > 1000), Quicksort is faster, on most machines, by a factor of 1.5 or 2 than other O(n log n) algorithms. However, in the worst case, it makes O(n2) comparisons. Quicksort requires a bit of extra memory.

    Quicksort is a comparison sort. A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator) that determines which of two elements should occur first in the final sorted list. The only requirement is that the operator obey the three defining properties of a total order:

    • if a ≤ b and b ≤ a then a = b (antisymmetry)
    • if a ≤ b and b ≤ c then a ≤ c (transitivity)
    • a ≤ b or b ≤ a (totalness or trichotomy)

    Quicksort, however, is not a stable sort in efficient implementations. Stable sorting algorithms maintain the relative order of records with equal keys. If all keys are different then this distinction is not necessary. But if there are equal keys, then a sorting algorithm is stable if whenever there are two records(let's say R and S) with the same key, and R appears before S in the original list, then R will always appear before S in the sorted list.

    For speed of execution, we implement it without recursion. Instead, we requires an auxiliary array (stack) of storage, of length 2 log2 n. When a subarray has gotten down to size 7, we sort it by straight insertion.

    Author:
    Haifeng Li
    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static int[] sort​(double[] arr)
      Sorts the specified array into ascending numerical order.
      static void sort​(double[] arr, double[] brr)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static void sort​(double[] arr, double[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static void sort​(double[] arr, int[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static void sort​(double[] arr, int[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static void sort​(double[] arr, java.lang.Object[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static void sort​(double[] arr, java.lang.Object[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static int[] sort​(float[] arr)
      Sorts the specified array into ascending numerical order.
      static void sort​(float[] arr, float[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static void sort​(float[] arr, float[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static void sort​(float[] arr, int[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static void sort​(float[] arr, int[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static void sort​(float[] arr, java.lang.Object[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static void sort​(float[] arr, java.lang.Object[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static int[] sort​(int[] arr)
      Sorts the specified array into ascending numerical order.
      static void sort​(int[] arr, int[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static void sort​(int[] arr, int[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static void sort​(int[] arr, java.lang.Object[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static void sort​(int[] arr, java.lang.Object[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static <T extends java.lang.Comparable<? super T>>
      int[]
      sort​(T[] arr)
      Sorts the specified array into ascending order.
      static <T extends java.lang.Comparable<? super T>>
      void
      sort​(T[] arr, int[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static <T extends java.lang.Comparable<? super T>>
      void
      sort​(T[] arr, int[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static <T> void sort​(T[] arr, int[] brr, int n, java.util.Comparator<T> comparator)
      This is an effecient implementation Quick Sort algorithm without recursive.
      static <T extends java.lang.Comparable<? super T>>
      void
      sort​(T[] arr, java.lang.Object[] brr)
      Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      static <T extends java.lang.Comparable<? super T>>
      void
      sort​(T[] arr, java.lang.Object[] brr, int n)
      This is an effecient implementation Quick Sort algorithm without recursive.
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Method Detail

      • sort

        public static int[] sort​(int[] arr)
        Sorts the specified array into ascending numerical order.
        Returns:
        the original index of elements after sorting in range [0, n).
      • sort

        public static void sort​(int[] arr,
                                int[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(int[] arr,
                                int[] brr,
                                int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(int[] arr,
                                java.lang.Object[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(int[] arr,
                                java.lang.Object[] brr,
                                int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static int[] sort​(float[] arr)
        Sorts the specified array into ascending numerical order.
        Returns:
        the original index of elements after sorting in range [0, n).
      • sort

        public static void sort​(float[] arr,
                                int[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(float[] arr,
                                int[] brr,
                                int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(float[] arr,
                                float[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(float[] arr,
                                float[] brr,
                                int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(float[] arr,
                                java.lang.Object[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(float[] arr,
                                java.lang.Object[] brr,
                                int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static int[] sort​(double[] arr)
        Sorts the specified array into ascending numerical order.
        Returns:
        the original index of elements after sorting in range [0, n).
      • sort

        public static void sort​(double[] arr,
                                int[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(double[] arr,
                                int[] brr,
                                int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(double[] arr,
                                double[] brr)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(double[] arr,
                                double[] brr,
                                int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(double[] arr,
                                java.lang.Object[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static void sort​(double[] arr,
                                java.lang.Object[] brr,
                                int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static <T extends java.lang.Comparable<? super T>> int[] sort​(T[] arr)
        Sorts the specified array into ascending order.
        Returns:
        the original index of elements after sorting in range [0, n).
      • sort

        public static <T extends java.lang.Comparable<? super T>> void sort​(T[] arr,
                                                                            int[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static <T extends java.lang.Comparable<? super T>> void sort​(T[] arr,
                                                                            int[] brr,
                                                                            int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static <T> void sort​(T[] arr,
                                    int[] brr,
                                    int n,
                                    java.util.Comparator<T> comparator)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.
      • sort

        public static <T extends java.lang.Comparable<? super T>> void sort​(T[] arr,
                                                                            java.lang.Object[] brr)
        Besides sorting the array arr, the array brr will be also rearranged as the same order of arr.
      • sort

        public static <T extends java.lang.Comparable<? super T>> void sort​(T[] arr,
                                                                            java.lang.Object[] brr,
                                                                            int n)
        This is an effecient implementation Quick Sort algorithm without recursive. Besides sorting the first n elements of array arr, the first n elements of array brr will be also rearranged as the same order of arr.