测试链表是否有环的最佳算法 [英] Best algorithm to test if a linked list has a cycle

问题描述

确定链表中是否有环的最佳(停止)算法是什么?

What's the best (halting) algorithm for determining if a linked list has a cycle in it?

对时间和空间的渐近复杂性进行分析会很好，因此可以更好地比较答案.

Analysis of asymptotic complexity for both time and space would be sweet so answers can be compared better.

最初的问题不是解决出度 > 1 的节点，但有一些讨论.这个问题更像是检测有向图中循环的最佳算法".

Original question was not addressing nodes with outdegree > 1, but there's some talk about it. That question is more along the lines of "Best algorithm to detect cycles in a directed graph".

推荐答案

有两个指针遍历列表；让一个以两倍于另一个的速度迭代，并在每一步比较它们的位置.在我的头顶上，类似:

Have two pointers iterating through the list; make one iterate through at twice the speed of the other, and compare their positions at each step. Off the top of my head, something like:

node* tortoise(begin), * hare(begin);
while(hare = hare->next)
{
    if(hare == tortoise) { throw std::logic_error("There's a cycle"); }
    hare = hare->next;
    if(hare == tortoise) { throw std::logic_error("There's a cycle"); }
    tortoise = tortoise->next;
}

O(n)，这是你能得到的最好的.

O(n), which is as good as you can get.

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