#Algorithm

Write a function to determine if a linked list has a cycle in it. If there is a cycle, return the node where the cycle begins. Discuss the approach and the time complexity of your solution.

Given a linked list, remove the Nth node from the end of the list. The solution should maintain a linear time complexity and constant space complexity. Provide the implementation details and discuss edge cases.

Explain a problem that can be effectively solved using heaps. Provide an algorithm or approach that utilizes a heap data structure for the solution.

Given an array, find all unique quadruplets (a, b, c, d) such that a * b = c * d. Please ensure to handle duplicates and return the unique sets.

Solve a tricky binary search problem that goes beyond the typical element-finding tasks. You will need to apply binary search with insight into the specific problem constraints.