Here’s a summary of Dimitris Andreou’s link. Remember sum of i-th powers, where i=1,2,..,k. This reduces the problem to solving the system of equations a1 + a2 + … + ak = b1 a12 + a22 + … + ak2 = b2 … a1k + a2k + … + akk = bk Using Newton’s identities, … Read more
The common approach to get a unique collection of items is to use a set. Sets are unordered collections of distinct objects. To create a set from any iterable, you can simply pass it to the built-in set() function. If you later need a real list again, you can similarly pass the set to the … Read more
I usually go with something like the implementation given in Josh Bloch’s fabulous Effective Java. It’s fast and creates a pretty good hash which is unlikely to cause collisions. Pick two different prime numbers, e.g. 17 and 23, and do: public override int GetHashCode() { unchecked // Overflow is fine, just wrap { int hash … Read more
An alternative approach would be to extract features (keypoints) using the scale-invariant feature transform (SIFT) or Speeded Up Robust Features (SURF). You can find a nice OpenCV code example in Java, C++, and Python on this page: Features2D + Homography to find a known object Both algorithms are invariant to scaling and rotation. Since they … Read more
Consider a simple function that adds the first N natural numbers. (e.g. sum(5) = 0 + 1 + 2 + 3 + 4 + 5 = 15). Here is a simple JavaScript implementation that uses recursion: function recsum(x) { if (x === 0) { return 0; } else { return x + recsum(x – 1); … Read more
I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve’s algorithm. The AI simply performs maximization over all possible moves, followed by expectation over all possible tile spawns (weighted by the probability of the tiles, i.e. 10% for a 4 and 90% for a 2). As far as I’m … Read more
I cannot understand how to identify a function with a log time. The most common attributes of logarithmic running-time function are that: the choice of the next element on which to perform some action is one of several possibilities, and only one will need to be chosen. or the elements on which the action is … Read more