快速排序：迭代或递归 [英] Quicksort : Iterative or Recursive

问题描述

我了解快速排序，以及它如何在这两个递归与迭代的方法来实现。
在迭代的方法：

I learnt about quick sort and how it can be implemented in both Recursive and Iterative method.
In Iterative method :

1. 按范围（0 ... n）的入堆栈
2. 在分区中的给定阵列枢轴
3. 在弹出的顶级元素。
4. 推分区（指数范围）堆叠成如果范围包含多个元素
5. 请在上述3个步骤，直到堆栈为空

和递归版本是正常的维基定义。

And the recursive version is the normal one defined in wiki.

我了解到，递归算法总是比自己的迭代对手慢。
所以，这是方法pferred的时间复杂度（内存是不是一个问题）$ P $？
哪一个是速度不够快编程大赛使用？
是C ++ STL的sort（）使用递归的方法呢？

I learnt that recursive algorithms are always slower than their Iterative counterpart.
So, Which is method is preferred in terms of time complexity ( memory is not a concern )?
Which one is fast enough to use in Programming contest?
Is c++ STL sort() uses recursive approach?

推荐答案

在（渐进）的时间复杂度 - 他们都是同一个

递归是慢然后反复 - 理性的这句话背后是因为递归栈（保存和恢复调用之间的环境）的开销。
然而 - 这些都是老年退休金计划的常数，而不是改变迭代。

"Recursive is slower then iterative" - the rational behind this statement is because of the overhead of the recursive stack (saving and restoring the environment between calls).
However -these are constant number of ops, while not changing the number of "iterations".

这两个递归和迭代快速排序是 O（nlogn）的一般情况下和为O（n ^ 2）的最坏的情况下的。

Both recursive and iterative quicksort are O(nlogn) average case and O(n^2) worst case.

编辑：

只是为了好玩，我跑的（JAVA）code attahced到后一个标杆，然后我跑的秩统计检验，要检查什么的概率是运行时间的确是不同的。

just for the fun of it I ran a benchmark with the (java) code attahced to the post , and then I ran wilcoxon statistic test, to check what is the probability that the running times are indeed distinct

的结果是结论性的（P_VALUE = 2.6E-34，这意味着，它们是相同的概率是2.6 * 10 ^ -34 - 非常不可能）。但答案是不是你所期望的。
迭代求解的平均值为408.86毫秒递归，同时为236.81毫秒

The results are conclusive (P_VALUE=2.6e-34, that means that the probability they are the same is 2.6*10^-34 - very not probable). But the answer is not what you expected.
The average of the iterative solution was 408.86 ms while of recursive was 236.81 ms

（注意 - 我用整数，而不是 INT 作为参数传递给 recursiveQsort（） - 否则递归会取得更好的，因为它没有框许多整数，这也是耗费时间 - 我这样做是因为迭代求解别无选择，只能这样做。

(Note - I used Integer and not int as argument to recursiveQsort() - otherwise the recursive would have achieved much better, because it doesn't have to box a lot of integers, which is also time consuming - I did it because the iterative solution has no choice but doing so.

这样 - 你的假设是不正确的，递归的解决方案是更快（我的机器和java的最起码的），那么迭代之一，P_VALUE = 2.6E-34

Thus - your assumption is not true, the recursive solution is faster (for my machine and java for the very least) then the iterative one with P_VALUE=2.6e-34.

public static void recursvieQsort(int[] arr,Integer start, Integer end) { 
    if (end - start < 2) return; //stop clause
    int p = start + ((end-start)/2);
    p = partition(arr,p,start,end);
    recursvieQsort(arr, start, p);
    recursvieQsort(arr, p+1, end);

}

public static void iterativeQsort(int[] arr) { 
    Stack<Integer> stack = new Stack<Integer>();
    stack.push(0);
    stack.push(arr.length);
    while (!stack.isEmpty()) {
        int end = stack.pop();
        int start = stack.pop();
        if (end - start < 2) continue;
        int p = start + ((end-start)/2);
        p = partition(arr,p,start,end);

        stack.push(p+1);
        stack.push(end);

        stack.push(start);
        stack.push(p);

    }
}

private static int partition(int[] arr, int p, int start, int end) {
    int l = start;
    int h = end - 2;
    int piv = arr[p];
    swap(arr,p,end-1);

    while (l < h) {
        if (arr[l] < piv) {
            l++;
        } else if (arr[h] >= piv) { 
            h--;
        } else { 
            swap(arr,l,h);
        }
    }
    int idx = h;
    if (arr[h] < piv) idx++;
    swap(arr,end-1,idx);
    return idx;
}
private static void swap(int[] arr, int i, int j) { 
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}

public static void main(String... args) throws Exception {
    Random r = new Random(1);
    int SIZE = 1000000;
    int N = 100;
    int[] arr = new int[SIZE];
    int[] millisRecursive = new int[N];
    int[] millisIterative = new int[N];
    for (int t = 0; t < N; t++) { 
        for (int i = 0; i < SIZE; i++) { 
            arr[i] = r.nextInt(SIZE);
        }
        int[] tempArr = Arrays.copyOf(arr, arr.length);

        long start = System.currentTimeMillis();
        iterativeQsort(tempArr);
        millisIterative[t] = (int)(System.currentTimeMillis()-start);

        tempArr = Arrays.copyOf(arr, arr.length);

        start = System.currentTimeMillis();
        recursvieQsort(tempArr,0,arr.length);
        millisRecursive[t] = (int)(System.currentTimeMillis()-start);
    }
    int sum = 0;
    for (int x : millisRecursive) {
        System.out.println(x);
        sum += x;
    }
    System.out.println("end of recursive. AVG = " + ((double)sum)/millisRecursive.length);
    sum = 0;
    for (int x : millisIterative) {
        System.out.println(x);
        sum += x;
    }
    System.out.println("end of iterative. AVG = " + ((double)sum)/millisIterative.length);
}

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