All these data structures are used for solving different problems: Segment tree stores intervals, and optimized for “which of these intervals contains a given point” queries. Interval tree stores intervals as well, but optimized for “which of these intervals overlap with a given interval” queries. It can also be used for point queries – similar … Read more
OK, I will describe first the simplest solution which is O(N^2), where N is the size of the collection. There also exists a O(N log N) solution, which I will describe also. Look here for it at the section Efficient algorithms. I will assume the indices of the array are from 0 to N – … Read more
You can do it in O(n) (where n is the number of digits) like this: Starting from the right, you find the first pair-of-digits such that the left-digit is smaller than the right-digit. Let’s refer to the left-digit by “digit-x”. Find the smallest number larger than digit-x to the right of digit-x, and place it … Read more
Use Prim’s algorithm when you have a graph with lots of edges. For a graph with V vertices E edges, Kruskal’s algorithm runs in O(E log V) time and Prim’s algorithm can run in O(E + V log V) amortized time, if you use a Fibonacci Heap. Prim’s algorithm is significantly faster in the limit … Read more
The parametric equation for a circle is x = cx + r * cos(a) y = cy + r * sin(a) Where r is the radius, cx,cy the origin, and a the angle. That’s pretty easy to adapt into any language with basic trig functions. Note that most languages will use radians for the angle … Read more
There are a number of different solutions for finding running median from streamed data, I will briefly talk about them at the very end of the answer. The question is about the details of the a specific solution (max heap/min heap solution), and how heap based solution works is explained below: For the first two … Read more
There can be many reasons to prefer an algorithm with higher big O time complexity over the lower one: most of the time, lower big-O complexity is harder to achieve and requires skilled implementation, a lot of knowledge and a lot of testing. big-O hides the details about a constant: algorithm that performs in 10^5 … Read more
There are many ways to do just this, provided you are not concerned about reliance on the original decimal data. The first and perhaps most popular method would be the Largest Remainder Method Which is basically: Rounding everything down Getting the difference in sum and 100 Distributing the difference by adding 1 to items in … Read more
Skip lists are more amenable to concurrent access/modification. Herb Sutter wrote an article about data structure in concurrent environments. It has more indepth information. The most frequently used implementation of a binary search tree is a red-black tree. The concurrent problems come in when the tree is modified it often needs to rebalance. The rebalance … Read more
Remember that log(n!) = log(1) + log(2) + … + log(n-1) + log(n) You can get the upper bound by log(1) + log(2) + … + log(n) <= log(n) + log(n) + … + log(n) = n*log(n) And you can get the lower bound by doing a similar thing after throwing away the first half … Read more