go

Hi there! Today I implemented Djikstra’s algorithm to find the minimum path between one source vertex and all the other vertices in the graph. This algorithm was devised in 1956 by the Dutch computer scientist Edsger W. Djikstra. It is quite fast having a complexity of $O(n\log n)$ when implemented with an auxiliary heap structure. To implement the heap in Go, I made use of the package heap. The package website also has an example of how to use and mine is basically a copy of it....

Hi there! Today’s program aims to solve the minimum cut problem. It is another one that I learned in Algorithms: Design and Analysis, Part 1 course from Coursera. A cut is partition of a graph and partitioning a graph means dividing it into two disjoint subsets of vertices. The minimum cut then would be such that the number of edges going from one partition to the other is minimal. Below is a simple example of a graph with 4 nodes....

Hi there! Today’s challenge is another algorithm that I learned more in detail in the Algorithms: Design and Analysis, Part 1 course from Coursera: QuickSort. This algorithm chooses a pivot and does a partial sort around that pivot, having all elements less than the pivot to its left and all greater to its right, considering we want the number in increasing order. The main function is qsort which calls the function to choose a pivot and another to partition around the pivot....

One of the big limitations of simple number data types is the maximum number they can hold. A 64 bit unsigned long can hold up to the number $2^{64}-1$. This is a pretty huge number, but if you try to compute the factorial of a number like $25!$, it is not enough. The good news is that there are software libraries that allow us to surpass this limitation. The bad is that the computations take longer....

Hi there! Today’s post is not from HackerRank. This was an assignment that I solved for the Algorithms: Design and Analysis, Part 1 course from Coursera. The goal is to implement an algorithm presented in the videos. It was explained in high level and not considering edge cases. I first tried to do it in C++ but it was taking me more time than I wanted to spend and then I switched to Go and it was blazing fast to code....

Hi there! Today’s problem is very similar to the last day, again using a binomial distribution. Question Given that 12% of the pistons of a manufacture are rejected because of incorrect sizing, what is the probability of batch of 10 pistons contain No more than two rejects? At least two rejects? Again, very similar. Now the probability of success for the Bernoulli trial is of the chance of the piston being reject, the same as being incorrectly sized....

Hi there! Today’s challenge from HackerRank was a little more involved. The challenge is Given the ratio $1.09 : 1$ of boys to girls for babies born in a certain country, what is the proportion of families with exactly 6 children that will have at least 3 boys?. Before actually solving that, it is important to understand a Bernoulli trial and also the Binomial Distribution. Bernoulli trial According to Wikipedia, a Bernoulli trial is a random experiment with exactly two possible outcomes, “success” and “failure”, in which the probability of success is the same every time the experiment is conducted....

Hi there! Today’s challenge was to compute standard deviation of an array of data given the formula $$\sigma = \sqrt{\frac{\sum_{i=0}^{N-1} (x_i - \mu)^2}{N}},$$ where $$\mu = \frac{\sum_{i=0}^{N-1} x_i}{N}.$$ The first input to the program is N and then N integers are fed to the program in sequence. My solution is given below. package main import ( "fmt" "math" ) func mean(a []int) float64 { n := float64(len(a)) sum := 0.0 for i := 0; i < len(a); i++ { sum += float64(a[i]) } return sum / n } func sigma(a []int) float64 { mu := mean(a) sum := 0....

Hi there! Today’s challenge is quite similar to the last one. Again, there are quartiles, but the input is a little different and the output is the interquartile range: $Q_3 - Q_1$. The first input is $n$ followed by an array $X$ of size $n$ with our data, but the frequencies of each point are included in another array of $n$ elements, $F$, that is the next input. After reading this we need to construct the actual data array $S$....

Hi there! The problem for today required me to find the quartiles of set of data values. The concept is actually new to me but, once I learned it, it resembled a lot the median of a data set. Actually, the second quartile $Q_2$ is the median itself, while the other two quartiles, $Q_1$ and $Q_2$, are basically medians of sub datasets divided around the second quartile. The three quartiles divide the data in four regions instead of two regions using only the median....