From 925e1497aa57bb21ceac569cec381720c4642c56 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Wed, 28 Oct 2026 22:51:16 +0800 Subject: [PATCH] =?UTF-8?q?Update=2023.=20=E9=93=BE=E8=A1=A8=E4=B8=AD?= =?UTF-8?q?=E7=8E=AF=E7=9A=84=E5=85=A5=E5=8F=A3=E7=BB=93=E7=82=B9.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 重新绘制配图,第一人称改为客观陈述。 --- notes/23. 链表中环的入口结点.md | 8 ++++---- notes/pics/offer23-cycle-entry.png | Bin 0 -> 128269 bytes 2 files changed, 4 insertions(+), 4 deletions(-) create mode 100644 notes/pics/offer23-cycle-entry.png diff --git a/notes/23. 链表中环的入口结点.md b/notes/23. 链表中环的入口结点.md index 4e38045f..486a7e15 100644 --- a/notes/23. 链表中环的入口结点.md +++ b/notes/23. 链表中环的入口结点.md @@ -12,17 +12,17 @@ 假设环入口节点为 y1,相遇所在节点为 z1。 -假设快指针 fast 在圈内绕了 N 圈,则总路径长度为 x+Ny+(N-1)z。z 为 (N-1) 倍是因为快慢指针最后已经在 z1 节点相遇了,后面就不需要再走了。 +假设快指针 fast 在圈内绕了 N 圈,则总路径长度为 x+Ny+(N-1)z。z 为 (N-1) 倍是因为快慢指针最后已经在 z1 节点相遇了,后面就不需要再走了。 而慢指针 slow 总路径长度为 x+y。 因为快指针是慢指针的两倍,因此 x+Ny+(N-1)z = 2(x+y)。 -我们要找的是环入口节点 y1,也可以看成寻找长度 x 的值,因此我们先将上面的等值分解为和 x 有关:x=(N-2)y+(N-1)z。 +要找的是环入口节点 y1,也可以看成寻找长度 x 的值,因此先将上面的等式整理为和 x 有关:x=(N-2)y+(N-1)z。 -上面的等值没有很强的规律,但是我们可以发现 y+z 就是圆环的总长度,因此我们将上面的等式再分解:x=(N-2)(y+z)+z。这个等式左边是从起点x1 到环入口节点 y1 的长度,而右边是在圆环中走过 (N-2) 圈,再从相遇点 z1 再走过长度为 z 的长度。此时我们可以发现如果让两个指针同时从起点 x1 和相遇点 z1 开始,每次只走过一个距离,那么最后他们会在环入口节点相遇。 +上面的等式没有很强的规律,但是 y+z 就是圆环的总长度,因此将上面的等式再分解:x=(N-2)(y+z)+z。这个等式左边是从起点 x1 到环入口节点 y1 的长度,而右边是在圆环中走过 (N-2) 圈,再从相遇点 z1 再走过长度为 z 的长度。因此如果让两个指针同时从起点 x1 和相遇点 z1 开始,每次只走过一个距离,那么最后它们会在环入口节点相遇。 -

+

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