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

问题描述

我学习了快速排序以及如何在递归和迭代方法中实现它。

在迭代方法中：

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

1. 将范围（0 ... n）推入堆栈


2. 使用数据透视表对给定数组进行分区


3. 弹出顶部元素。


4. 如果范围有多个元素，则将分区（索引范围）推入堆栈


5. 执行上述3个步骤，直到堆栈是空的

1. Push the range (0...n) into the stack
2. Partition the given array with a pivot
3. Pop the top element.
4. Push the partitions (index range) onto a stack if the range has more than one element
5. Do the above 3 steps, till the stack is empty

递归版本是wiki中定义的正常版本。

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

我了解到递归算法总是慢于它们的迭代算法。

那么，就时间复杂度而言，哪种方法更受欢迎（内存不是问题）？

在编程竞赛中哪一个足够快？

使用递归方法c ++ STL sort（）？

I learnt that recursive algorithms are always slower than their iterative counterpart.
So, Which 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() using a recursive approach?

推荐答案

就（渐近）时间复杂度而言 - 它们都是相同的。

递归慢于迭代 - 这个语句背后的理性是由于递归堆栈的开销（在调用之间保存和恢复环境）。

但是 - 这些是操作的常数，而不是改变迭代次数。

"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".

递归和迭代快速排序都是 O（nlogn） 平均情况和 O（n ^ 2） 最坏情况。

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

编辑：

只是为了它的乐趣我运行了附加到帖子的（java）代码的基准测试，然后我运行了 wilcoxon统计测试，检查运行时间确实不同的概率

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

结果是确定的（P_VALUE = 2.6 e-34，这意味着它们相同的概率是2.6 * 10 ^ -34 - 非常不可能）。但答案不是你所期望的。

迭代解的平均值是408.86 ms，而递归的平均值是236.81 ms

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 作为的参数recursiveQsort（） - 否则递归会更好，因为它不需要包含很多整数，这也很耗时 - 我这样做是因为迭代解决方案别无选择，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.

因此 - 你的假设不正确，递归解决方案更快（对于我的机器和java至少）然后是迭代的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 recursiveQsort(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);
    recursiveQsort(arr, start, p);
    recursiveQsort(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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