At a high level, the difference between LL parsing and LR parsing is that LL parsers begin at the start symbol and try to apply productions to arrive at the target string, whereas LR parsers begin at the target string and try to arrive back at the start symbol. An LL parse is a left-to-right, … Read more
Here is a very simplified explanation: Your web browser downloads the web server’s certificate, which contains the public key of the web server. This certificate is signed with the private key of a trusted certificate authority. Your web browser comes installed with the public keys of all of the major certificate authorities. It uses this … Read more
Cantor pairing function is really one of the better ones out there considering its simple, fast and space efficient, but there is something even better published at Wolfram by Matthew Szudzik, here. The limitation of Cantor pairing function (relatively) is that the range of encoded results doesn’t always stay within the limits of a 2N … Read more
Dynamic programming is when you use past knowledge to make solving a future problem easier. A good example is solving the Fibonacci sequence for n=1,000,002. This will be a very long process, but what if I give you the results for n=1,000,000 and n=1,000,001? Suddenly the problem just became more manageable. Dynamic programming is used … Read more
I encountered similar problem. I had to find a good method of selecting contrastive font color to display text labels on colorscales/heatmaps. It had to be universal method and generated color had to be “good looking”, which means that simple generating complementary color was not good solution – sometimes it generated strange, very intensive colors … Read more
See this page on the ARC project for a survey of solutions, there is a trade-off between implementation complexity/time and optimality, but there is a wide range of algorithms to choose from. Here’s an extract of the algorithms: First-Fit Decreasing Height (FFDH) algorithm FFDH packs the next item R (in non-increasing height) on the first … Read more
This problem can be solved with a recursive combinations of all possible sums filtering out those that reach the target. Here is the algorithm in Python: def subset_sum(numbers, target, partial=[]): s = sum(partial) # check if the partial sum is equals to target if s == target: print “sum(%s)=%s” % (partial, target) if s >= … Read more
I approximated the iTunes 11 color algorithm in Mathematica given the album cover as input: How I did it Through trial and error, I came up with an algorithm that works on ~80% of the albums with which I’ve tested it. Color Differences The bulk of the algorithm deals with finding the dominant color of … Read more
You can keep a priority queue of the 100 biggest numbers, iterate through the 1 billion numbers. Whenever you encounter a number greater than the smallest number in the queue (the head of the queue), remove the head of the queue and add the new number to the queue. A priority queue implemented with a … Read more
In simple words, a loop invariant is some predicate (condition) that holds for every iteration of the loop. For example, let’s look at a simple for loop that looks like this: int j = 9; for(int i=0; i<10; i++) j–; In this example it is true (for every iteration) that i + j == 9. … Read more