Intersection problem of cyclic or acyclic linked lists

How to efficiently determine if two linked lists intersect, even if one or both have cycles?

There are several algorithms that can be used to determine if two linked lists intersect, even if one or both have cycles. One common approach is to use the Floyd's cycle-finding algorithm to detect the presence of cycles in each list. If either list has a cycle, the algorithm will return the cycle's starting point. If both lists have cycles, the algorithm will return the common cycle's starting point. Once the cycles have been detected, the intersection point can be found by traversing both lists simultaneously, starting from the cycle's starting point in each list. The intersection point is the first node that is common to both lists.

What are the time and space complexity implications of different algorithms for finding the intersection point in intersecting linked lists with cycles?

The time complexity of the Floyd's cycle-finding algorithm is O(n), where n is the total number of nodes in the two linked lists. The space complexity of the algorithm is O(1), as it does not require any additional space beyond the space that is already occupied by the linked lists.

Other algorithms for finding the intersection point in intersecting linked lists with cycles include the Tortoise and Hare algorithm and the Brent's algorithm. These algorithms have similar time and space complexity to the Floyd's cycle-finding algorithm.

How can we adapt existing algorithms for finding the intersection point in non-intersecting linked lists to account for the presence of cycles?

Existing algorithms for finding the intersection point in non-intersecting linked lists can be adapted to account for the presence of cycles by using the Floyd's cycle-finding algorithm to detect the presence of cycles in each list. If either list has a cycle, the algorithm can be used to return the cycle's starting point. If both lists have cycles, the algorithm can be used to return the common cycle's starting point. Once the cycles have been detected, the intersection point can be found by traversing both lists simultaneously, starting from the cycle's starting point in each list. The intersection point is the first node that is common to both lists.

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