最近在學習排序演算法，實現後比較了花費時間情況，現在總結一下

插入排序的時間複雜度是O(n²)，是一種很直觀的排序方式。歸併排序為O（nlogn），實現起來也比較簡單。快速排序平均時間複雜度也是O(nlogn），實現起來比歸併複雜一些。經過比較發現快速排序比歸併排序要快一些，大概一倍的時間，資料越大，效果越明顯。我嘗試用5000萬長度的隨機陣列成的陣列進行排序，歸併排序大概用了50s左右，期間出現過oom，比較消耗堆疊的空間，而快速排序則很穩定，實現的時候的不會額外建立陣列，全是在原陣列之上的操作，主要是swap操作，多次測試大概只用了20s左右的時間，也是5000萬長度的資料。然後做了簡單的二分查詢，實現了對排序陣列的指定的相等元素全部查找出來。

這是歸併排序花費的時間：

這是快速排序花費的時間

下面是具體程式碼實現：

import java.util.ArrayList;
import java.util.List;
import java.util.Random;

public class MergeSort {

    private static <T extends Comparable<? super T>> void mergeSort(T [] arr){

       // T [] tempArr= (T []) new Comparable[arr.length];

        mergeSort(arr, 0, arr.length - 1);

    }

    private static <T extends Comparable<? super T>> void mergeSort(T[] arr, int left, int right) {

        if (left < right){
            int mid = (left + right) / 2;
            mergeSort(arr, left, mid);
            mergeSort(arr, mid + 1, right);
            merge(arr, left, mid, right);
        }




    }

    private static <T extends Comparable<? super T>> void merge(T[] arr, int left, int mid, int rightEnd) {

        T [] temp = (T []) new Comparable[rightEnd - left + 1];
      //  System.out.println(temp);

        int leftEnd = mid;
        int right = mid + 1;
        int tempPos = 0;
        int numOfObj = rightEnd - left + 1;

        while(left <= leftEnd && right <= rightEnd){
            if (arr[left].compareTo(arr[right]) <= 0){
                temp[tempPos ++] = arr[left ++];
            }else {
                temp[tempPos ++] = arr[right ++];
            }
        }

        while (left <= leftEnd) {
            temp[tempPos++] = arr[left++];
        }

        while (right <= rightEnd) {
            temp[tempPos++] = arr[right++];
        }
       for (int i = numOfObj - 1; i >= 0;){
            arr[rightEnd--] = temp[i--];
        }
    }


    private static <T extends  Comparable<? super T>> void quickSort(T [] arr){
        quickSort(arr, 0, arr.length - 1);
    }

    private static <T extends  Comparable<? super T>> void quickSort(T[] arr, int start, int end) {
        if (end - start < 8) {
            insertSort(arr, start, end);
        } else {

            T key = prepQuickSort(arr, start, end);
            int leftIndex = start;
            int rightIndex = end - 1;
            for ( ; ;) {
                while (arr[++leftIndex].compareTo(key) < 0) { }
                while (arr[--rightIndex].compareTo(key) > 0) { }

                if (leftIndex > rightIndex) {
                    break;
                } else {
                    swapByReference(arr, leftIndex, rightIndex);
                }
            }
            swapByReference(arr, leftIndex, end - 1);

            quickSort(arr, start, leftIndex - 1);
            quickSort(arr, leftIndex + 1, end);
        }
    }

    private static <T extends  Comparable<? super T>> T prepQuickSort(T[] arr, int left, int right) {

        int mid = (left + right) / 2;
        if (arr[left].compareTo(arr[mid]) > 0)
            swapByReference(arr, left, mid);
        if (arr[left].compareTo(arr[right]) > 0)
            swapByReference(arr, left, right);
        if (arr[mid].compareTo(arr[right]) > 0)
            swapByReference(arr, mid, right);

        swapByReference(arr, mid, right - 1);
        return arr[right -1];
    }

    private static  <T extends  Comparable<? super T>> void insertSort(T[] arr) {
        insertSort(arr, 0, arr.length);
    }

    private static <T extends  Comparable<? super T>> void insertSort(T[] arr, int start, int end) {
        T min;
        int index;
        for (int i = start; i < end -1; i ++){
            min = arr[i];
            index = i;
            for (int j = i + 1; j < end; j++){
                if (min.compareTo(arr[j]) > 0){
                    min = arr[j];
                    index = j;
                }
            }
            swapByReference(arr, i, index);
        }

    }

    private static <T extends  Comparable<? super T>> void swapByReference(T[] arr, int before, int after) {
        if (before == after)
            return;
        else {
            T tmp;
            tmp = arr[before];
            arr[before] = arr[after];
            arr[after] = tmp;
        }

    }

    public static <T extends Comparable<? super T>> List binarySearch(T [] arr, T goal){

        if (arr == null || arr.length < 1 )
            return null;

        int left = 0;
        int right = arr.length -1;
        if (arr[left].compareTo(goal) > 0 || arr[right].compareTo(goal) < 0)
            return null;
        int mid = right / 2;

        while(left < right){
            if (arr[mid].compareTo(goal) == 0){
                List list = new ArrayList<Integer>();

                int eqLeft = getEqualsBound(arr, mid, false);
                int eqRight = getEqualsBound(arr, mid, true);

                for (int index = eqLeft; index <= eqRight; index ++){
                    list.add(index);
                }
                return list;

            } else if (arr[mid].compareTo(goal) > 0)
                right = mid - 1;
            else
                left = mid + 1;
            mid = (left + right) / 2;
        }
        return  null;
    }

    private static <T extends Comparable<? super T>> int getEqualsBound(T[] arr, int location, boolean sequence) {
        int result = location;
        if (sequence){
            while(arr[location].compareTo(arr[++result]) == 0){ }
            return result - 1;
        }else {
            while(arr[location].compareTo(arr[--result]) == 0){ }
            return result + 1;
        }
    }


    public static void main(String[] args) {

        Integer[] arr = {16,2,4,3,1,5,6,0,2,4,3,11,14,16,12,9,8,11,13,15,18,20,19,11,22,23,9,6,3,4,5,1,1,0,7,4,3,4,5,1,14,16};
        Integer[] arr1 = {2,2,2,2,2,2,2,2,2,2};

        List<Integer> list = new ArrayList<Integer>();
        Random random = new Random();
        for (int i= 0; i< 50000000; i++){
            list.add(random.nextInt(10000000));
        }
        Integer [] mkArr = list.toArray(new Integer[0]);

        long startTime = System.currentTimeMillis();
        System.out.println("start time is " + startTime + " ms");

        quickSort(mkArr);
        System.out.println("first node is " + mkArr[0] + " , mid node is " + mkArr[mkArr.length/2] + " , last node is " + mkArr[mkArr.length -1]);
        System.out.println(binarySearch(mkArr, 4000000));
        long stopTime = System.currentTimeMillis();
        System.out.println("end time is " + stopTime + " ms");
        System.out.println("cost time is " + (stopTime - startTime) + " ms");

    }