A linked list contains a cycle if, starting from some node p , following a sufficient number of next links brings us back to node p . p does not have to be the first node in the list. Assume that you are given a linked list that contains N nodes. However, the value of N is unknown. Design an O (N ) algorithm to determine if the list contains a cycle. You may use O (N ) extra space. Repeat part (a), but use only O (1) extra space. (Hint: Use two iterators that are initially at the start of the list, but advance at different speeds.)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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A linked list contains a cycle if, starting from some node p , following a sufficient number of next links brings us back to node p . p does not have to be the first node in the list. Assume that you are given a linked list that contains N nodes. However, the value of N is unknown.

  1. Design an O (N ) algorithm to determine if the list contains a cycle. You may use O (N ) extra space.
  2. Repeat part (a), but use only O (1) extra space. (Hint: Use two iterators that are initially at the start of the list, but advance at different speeds.)
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