Questions tagged [mathematics]

For code that aims to solve problems in all branches of mathematics. (Please do NOT use this tag for incidental trivial use of arithmetic. A simple test to apply is: would an amateur or professional mathematician take an interest in the question?)

5
votes
2answers
66 views

Check if an integer equals the sum of its digits to the fifth power

I can do this in one line in Python: sum([i for i in range(9,9999999) if i == sum([int(x)**5 for x in str(i)])]) Not very fast, but works nicely. I thought it ...
-1
votes
0answers
17 views

Differential equation slope field and cauchy solution [closed]

Given the differential equation \$2y'=\frac{yx}{x^2+4}+\frac{x}{y}\$ I have to draw the slope field in a rectangle called \$P\$, containing the point (2, 1). ...
11
votes
1answer
55 views

Visualization of the Pythagorean theorem

Background The Pythagorean theorem asserts that for a right triangle with hypotenuse \$c\$ and other sides \$a\$ and \$b\$, the area of the square placed upon \$c\$ is equal to the sum of the areas ...
3
votes
1answer
41 views

Stern's diatomic series fusc: replacing #define functions with two return values

I have a function to review which implements Stern's diatomic series fusc for a single word (ulong = unsigned long) in place, as ...
3
votes
2answers
63 views

Gram-Schmidt process in Java for computing independent bases in linear spaces

Given a set of \$k\$ \$n\$-vectors \$\vec{x_1}, \dots, \vec{x_k}\$, Gram-Schmidt process computes a basis \$\vec{y_1}, \dots, \vec{y_m}\$ (\$m \leq k\$) the vectors of which span the same space as \$\...
0
votes
1answer
30 views

Modular multiplicative inverse in Ruby

I implemented an algorithm to find the modular multiplicative inverse of an integer. The code works, but it is too slow and I don't know why. I compared it with an algorithm I found in Rosetta Code, ...
1
vote
1answer
79 views

Sum of number's quotients when divided by exact powers of 2

Problem I have written code to solve this challenge: Given a formula: GCD(x,y) means the GCD (Greatest Common Divisor) of x and y. For example: if N=2, then: f(2) = 1/GCD(1,...
3
votes
2answers
183 views

Reverse int within the 32-bit signed integer range: \$[−2^{31}, 2^{31} − 1]\$ Optimized

LeetCode Problem Reverse digits of a 32-bit signed integer. When the reversed integer overflows return 0. Feedback Optimized from beta code in the original question here. Based on this LeetCode ...
2
votes
0answers
90 views

Shutting down all lamps with minimum number of switch presses

I found an optimization problem written in Finnish but I will translate it into English. The following is an example case. I have \$n=120\$ lamps in a circle, and enumerated by \$L_1,…,L_{120}\$. ...
3
votes
0answers
58 views

Optimising multiplication of matrix rows with matrix slice/page

I've recently vectorized most of the code for an optimization problem but this one still eludes me. As the procedure and not the actual values are important here, I have replaced the original matrices ...
2
votes
0answers
57 views

Python RSA/DSA File Cryptography, Key Generation, Key Protection

I have forked a previous version of my script, critiqued here: Generate public/private keys, encrypt, decrypt, sign, verify This program allows you to encrypt and decrypt raw files using RSA keys ...
2
votes
2answers
75 views

Project Euler, Problem 273: finding perfect-square partitions

Problem: Consider equations of the form: \$a^2 + b^2 = N; 0 \leq a \leq b; a, b, N \in \mathbb{N}\$. For \$N=65\$ there are two solutions: \$a=1, b=8\$ and \$a=4, b=7\$. We call \$S(...
2
votes
2answers
105 views

PHP find cheapest permutation

I have multiple products that all have sizes and I need to find the cheapest configuration that meets the minimum required size. For example, John needs a minimum of 10 litres of storage - it can be ...
4
votes
0answers
83 views

Faster algorithm to tailor given mathematical expression

Is there a more optimized solution to solve the stated problem? Given an array 'arr' of 'N' elements and a number 'M', find the least index 'z' at which the equation gets satisfied. [ ] is ...
5
votes
5answers
114 views

Get n-th perfect number

The task: A number is considered perfect if its digits sum up to exactly 10. Given a positive integer n, return the n-th perfect number. For example, given 1, you should return 19. Given ...
3
votes
2answers
74 views

Finding the number of integers between 1 and K, who's sum of the digits is a multiple of D

Good day. So, I need to find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo (10^9)+7: The sum of the digits in base ten is a multiple of D Here is my ...
4
votes
1answer
114 views

Automatic Differentiation with C++ Header-Only Library

Code review/feedback is requested and appreciated for the following open-source automatic differentiation C++ header-only library released under the Boost License. I am the author. https://github.com/...
7
votes
2answers
598 views

Balanced centrifuge configurations

Given an input N as the size of a centrifuge, I need to find out the number of balanced configurations. The full description is here. Centrifuge is a piece of ...
8
votes
1answer
206 views

Find “prime polynomials” for a user's given prime, bounds, and degree

Very amateur programmer and first-time poster here. The program I wrote asks the user for a prime number, a lower and upper bound, and a degree (all of these are integers). I want to generate a list ...
3
votes
2answers
68 views

Expressing positive integers as the sum of different charming numbers

In a practice academic interview of mine, we discussed question six, round one, of the United Kingdom Mathematics Trust's 2015 British Mathematical Olympiad. Which states: A positive integer is ...
4
votes
1answer
59 views

Hungarian algorithm to perform least-cost assignments

The Hungarian algorithm solves the assignment problem, and I'm looking for any suggestions regarding improvement on my implementation (also coding style). It is based on the wikipedia entry and ...
5
votes
1answer
769 views

Determinant using Gauss Elimination

We had a question in examination to compute determinant of general square matrix. Now I had made the normal program using Laplace Formula of determinant, ie, recursive solution. Now I was thinking of ...
2
votes
2answers
496 views

Generating all permutations of 1 digit, 2 equal letters and 2 different letters efficiently

I created a function that generates all the combinations of 1 digit, 2 equal letters and 2 different letters. I reduced the numbers and letters to make it more easy to calculate: ...
4
votes
2answers
458 views

Project Euler Problem 21 in Python: Summing amicable numbers

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b ...
5
votes
1answer
106 views

Generating all unlabeled trees with up to n nodes

I want to visualize all unlabeled trees with \$n\$ or fewer nodes, not just count them. First idea/attempt: Take a list of all \$n-1\$ node trees, then append a new leaf to every tree in every way to ...
0
votes
1answer
113 views

Project Euler problem 12 Python

I'm new to python and programming in general and I found Project Euler problems a good way to practice python. But my code is pretty slow. It seems to work, didn't wait long enough for the code to ...
8
votes
3answers
445 views

Draw sine wave going around a circle

I have used d3 to draw a sine wave going around a circle. This is the very first time I've used d3 or drawn a SVG and I'm fairly new to JS as well, so I don't know if I've overcomplicated it/if there ...
3
votes
1answer
76 views

Counting Divisors of a number with restrictions on the divisors

Given a fraction p/q, I want to count the number of unit fraction solutions $$\frac{p}{q} = \frac{1}{u} + \frac{1}{v}$$ with some contraints $$lower \le u \le upper$$ By manipulating the first ...
0
votes
0answers
23 views

Normal Distribution and K-means clustering demonstration

I have two classes, the 1st one aims to display the Normal Distribution, and the 2nd one aims to perform K-means clustering. The emphasis is to build classes of the mathematical methods as examples ...
4
votes
3answers
463 views

Find smallest number of squares that sum to a number

Leetcode problem 279 “Perfect Squares” is: Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, ...) I wrote the following solution: ...
1
vote
1answer
110 views

Scaling decimal numbers up within bounds of limit

This code is part of a simulation and inputs will be positive values less than one and inputs are constrained elsewhere. The goal of the algorithm is to scale the inputs up to much larger numbers, ...
2
votes
1answer
43 views

Grade of Service Probability Function Python

Consider the following typical probability scenario: I defined this function to handle that scenario, I'm curious if Python has a more efficient method to handle this, or if this is the best way: <...
6
votes
3answers
870 views

Calculator of combinations without repetition

I am interested to find an absolute value (not an approximation) of "combination without repetition" for given \$n\$ and \$k\$, or \$\binom{n}{k}\$. The brute force solution would look like this <...
8
votes
1answer
422 views

Lagrange Interpolation over quadrilateral points

I've been working on a program which calculates, given a point and 4 surrounding points, the Lagrange polynomial, in order to interpolate a value. Consider that I'm not a mathematician and I better ...
1
vote
2answers
221 views

Find coprime numbers less than n

I get the coprime numbers less than n with the following algorithm: ...
3
votes
3answers
133 views

Return the product of the pythagorean triplet if a+b+c == 1000

I have found the answer to the problem I am trying to solve, but I am curious if there can be any improvements made to my code. ...
7
votes
2answers
826 views

Class Matrix implementation

Following the 18.06 Linear algebra course, I was curious to reinvent the matrix class and basic functionality, like \$PA=LU \$ decomposition, Gauss elimination, finding inverse matrix etc. Any ...
2
votes
2answers
326 views

Math Problem generator using switch statement ,Random method and arrays in Java

I m new in java and created a small project in which you have to solve random math problems there is three levels in it Easy, Medium , Hard, if you win or loss in game the message for three level will ...
24
votes
7answers
5k views

Python program to calculate GCD

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6
votes
4answers
493 views

Pascal Triangle calculation with BigIntegers

On a well known programming challenges website(CW) there is a Kyu2 eggs height problem that can be solved utilizing a variation of Pascals Triangles properties. The problem asks to solve ...
5
votes
1answer
105 views

Convert numbers from base X to base Y

I recently wrote a piece of code to convert between two bases of X, (Where 26 > X > 0). I was mighty proud that I did this. And then I started wondering, am I using modern coding conventions/practices?...
4
votes
1answer
214 views

Method to return center items in a 2D array

I wish to have code that returns the center items of a 2d grid. Because I need an average value. The code I came up with does what I want (see the unit tests beneath it). But I think the code is ugly ...
3
votes
1answer
556 views

Circle - Line segment collision

I wrote an implementation of circle - line segment collision detection algorithm. Here is quick demonstration how it works: And here is my implementation in Javascript using HTML canvas: index.html ...
0
votes
3answers
257 views

Project Euler #12 (Highly divisible triangular numbers) in Python 3.x

I'm a beginner to programming and just started python, I've been trying to work through Project Euler challenges. I wrote a program to solve Project Euler #12, which asks for the smallest number of ...
4
votes
1answer
144 views

Math Vector Header Library Templated on Data Type and Size

I have created a vector math header library where the size and data type stored are template values, and I'd like it peer-reviewed please. I have a few main questions: Will using my SizedVectorBase ...
1
vote
1answer
75 views

Find GCD of two numbers without using multiplication, division or modulus operators

If either a or b is 0 return the other number. If both even return gcd of a/2 and b/2. If either a or b is even divide it by 2 and return gcd of the pair. If a less than or equal to b, return the gcd ...
3
votes
1answer
112 views

Trigonometric Subplots with Matplotlib

The code consists of 4 functions that result in a figure with 3 subplots: a sine wave a cosine wave and the superposition of both (a bichromatic wave). I have shown in 4 ways, the first two are ...
4
votes
4answers
866 views

Power of two integers

Challenge: Given a positive integer which fits in a \$32\$ bit signed integer, find if it can be expressed as \$A^P\$ where \$P > 1\$ and \$A > 0\$. A and P both should be integers. ...
5
votes
1answer
305 views

Matrix implementation with Rank and Inverse calculation using Gaussian Elimination in Java

Disclaimer Some things that I must state: This is just for practice. I want to know the various algorithms in linear algebra in detail. I will not use this in a practical scenario. Except for ...
3
votes
1answer
95 views

Sum the remainders of ai%aj given an array “a”

Given an array of numbers, I am creating a table where, the cell at the intersection of row i and column j contains a number ai % aj. Numbers in the array can occur multiple times. Example: For ...