Floyd's Cycle-Finding Algorithm

最新推荐文章于 2024-05-30 20:56:49 发布

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最新推荐文章于 2024-05-30 20:56:49 发布

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本文链接：https://blog.youkuaiyun.com/sinat_27634503/article/details/79701817

本文介绍了一种通过快慢指针来检测链表中是否存在循环的方法，并进一步分析了如何找到循环开始的位置。通过数学推导解释了快慢指针相遇时距离起点与循环起始点之间的关系。

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s --a-- begin --x----meet point
        |                |
        |----------------|


1.fast goes two steps each time, while slow goes one step each time.

2.Supposing slow goes d, then fast goes 2*d. Considering the fast goes n loops, the distance of fast goes is d+ n*r, where r is the circle of loop. Then, 
2*d = d+ n*r
d = n*r

d = a + x = n * r = (n-1)*r + r
  = (n-1)*r + L-a               // L is the length of the list

a = (n-1)*r + L-a-x     
It means the distance from start point to the start of loop is equal to the distance from meet point moving to the start of loop.