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:
- 将范围（0 ... n）推入堆栈
- 使用数据透视表对给定数组进行分区
- 弹出顶部元素。
- 如果范围有多个元素，则将分区（索引范围）推入堆栈
- 执行上述3个步骤，直到堆栈是空的
- Push the range (0...n) into the stack
- Partition the given array with a pivot
- Pop the top element.
- Push the partitions (index range) onto a stack if the range has more than one element
- 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，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);
}
这篇关于Quicksort：迭代或递归的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！