complexity-theory

I have to store 500M two digit unicode character in memory (RAM). The data structure I use should have: Worst Case Space Complexity: O(n) Worst Case Time Complexity: O(1) <-- insertion, read, update, deletion I was thinking of choosing dict which is implementation of hash in python but then problem is it assures time complexity of O(1) for the required operations only in average cases than worst case. I heard that if number of entries is known, time complexity of O(1) can be achieved in worst case scenarios. How todo that? In case, thats not possible in python can I access memory addresses and

What is the difference in CPU cycles (or, in essence, in 'speed') between x /= y; and #include <cmath> x = sqrt(y); EDIT: I know the operations aren't equivalent, I'm just arbitrarily proposing x /= y as a benchmark for x = sqrt(y) osgx The answer to your question depends on your target platform. Assuming you are using most common x86 cpus, I can give you this link http://instlatx64.atw.hu/ This is a collection of measured instruction latency (How long will it take to CPU to get result after it has argument) and how they are pipelined for many x86 and x86_64 processors. If your target is not

To build a MAX heap tree, we can either siftDown or siftUp , by sifting down we start from the root and compare it to its two children, then we replace it with the larger element of the two children, if both children are smaller then we stop, otherwise we continue sifting that element down until we reach a leaf node (or of course again, until that element is larger that both of its children). Now we will only need to do that n/2 times, because the number of leaves is n/2 , and the leaves will satisfy the heap property when we finish heapifying the last element on the level before the last