The conversation between human and AI assistant.
Given an array of N integers, how can we find the number of all increasing subsequences in O(N*Log N) time?
How does Patience Sorting work?
Patience Sorting involves maintaining a list of piles to which elements can be added. To generate increasing subsequences, we add each element of the array to the first pile with a top element larger than it. If no pile has a top element larger than it, we create a new pile. The number of piles generated gives us the count of all increasing subsequences.