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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 provide us with a time complexity of O(N*Log N)?
Patience Sorting uses binary search to find the appropriate pile to add an element to, and binary search takes O(Log N) time. Since we need to do this for all N elements, the total time taken is O(N*Log N).