# Questions tagged [mathematical-programming]

Using a computer to implement mathematics. For questions about (mathematical) optimization, (also) use the optimization tag.

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56 views

### Using recursion to find rotation matrices of higher dimensions

I am looking to find a way to calculate a rotation matrix of $m$ x $m$ dimensions.I was thinking since it is almost impossible to find analytically , maybe we can use recursion to solve much simpler ...
36 views

### Which algorithms could be suitable for solving my disjunctive programming problem?

Following a previous post on the cs stack exchange (link to question), I have been searching to no avail for an implementation of a disjunctive programming solver in C# (or wrapped in C#). In this ...
19 views

### Bundle diameter calculation algorithm with different wire sizes accounting for twisted pairs?

Based on the same question asked here: Bundle diameter calculation algorithm with different wire sizes? Best answer was this: https://scipython.com/blog/packing-circles-in-a-circle/ However, there are ...
12 views

### Existence of a Path from Initial to Accepting Configuration in Turing Machine Runs: A Reduction-Based Proof

Is it possible to show, by reduction(Reduction in the length of the path and the running time), that for a Turing machine M and an input X, there exists a run in which M accepts X if and only if there ...
27 views

### How to calculate transition areas of biomes in an image

I'm generating biomes for my game and I would like to store them in a single RGB image like the one below. A color hue can then be mapped to an ID through a table lookup. The problem I face is that I ...
1 vote
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### Approximate euclidean graph from distance matrix?

In a personal project of mine, I have been faced with the following problem. I have an $n \times n$ matrix $T$ where an entry $t_{ij} \geq 0$ denotes an arbitrary metric between two points $i$ and $j$ ...
68 views

### What is the fastest algorithm for division of crazy large integers?

I need to divide numbers represented as digits in byte arrays with non standard amount of bytes. It maybe 5 bytes or 1 GB or more. Division should be done with numbers represented as byte arrays, ...
123 views

### how to get the high 32-bit of the answer of two 32-bit integer multiple?

Recently, I study the instruction set of riscv32 and face a order as "mulh" which tends to multiply two 32-bits signed integers and store the high 32 value into the register. And here comes ...
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### Efficiently remove intersections among a set of spheres

I have a 3D space where N spheres of identical size, identified by the location of their centers, are continually inserted. When a new sphere is inserted, I have the ability to efficiently query the ...
98 views

### Find the largest possible number not larger than some integer N and is the product of K consecutive primes

Source: Hanoi student competition of unknown year (Kì thi học sinh giỏi thành phố) Additional conditions: N is a positive integer in range [1, 2^64 - 1] K is a positive integer in range [3, 10] ...
167 views

### Finding Sum(F(i)) where F(i) = min(⌈ Ai / B1 ⌉ * C1, ⌈ Ai / B2 ⌉ * C2, ⌈ Ai / B3 ⌉ * C3, .... ,⌈ Ai / Bm ⌉ * Cm)

Given three arrays A, B, and C of size n, m, and m respectively (1-based indexed). A function F(i) is defined as - F(i) = minimum_of(⌈ Ai / B1 ⌉ * C1 , ⌈ Ai / B2 ⌉ * C2 , ⌈ Ai / B3 ⌉ * C3 , .... , ⌈ ...
1 vote
673 views

### If greater than or equal to zero then binary variable equals 1: integer linear program

I have a variable $d_{i} \in \mathbb{Z}$ with an upper and lower bound. I also have a binary variable $v_{i}$ which I want to $=1$ if $d_{i} \geq 0$; else $v_{i} = 0$. How do I enforce this as a ...
1 vote
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### Beginning Algorithm Design and Proving

I know this is a general question, so you can address this by giving some examples that are specific to your field. I want to start learning algorithm design and consequently prove its convergence. ...
31 views

### When do I use inversions in an array?

In problems like the 15 Tile Problem or Larry's Array problem, we use inversions in the array as a method to solve. But what's the principle behind this method and how do I know when to use inversions?...
1 vote
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### Number of operands to take when evaluating postfix notation?

All sources I have seen list taking two operands from the stack once we encounter an operator. Why? What if not all of my operators are binary (taking two arguments)? What if I have custom unary and ...
25 views

### Is computing subgradients an open research area in Authomatic Differentiation

Large portions of the possible research areas in Automatic Differentiation have broadly defined known solutions; most of which were derived in the 80s and 90s. Compute vector jacobian products: use ...
156 views

### Algorithm to find largest intersection of sets

This is a cross-posting from here, on the mathematics Stack Exchange. I thought this might be a more appropriate venue. The problem is this: I have a list of sets $$S_1, S_2,... S_N$$ where each set ...
414 views

### How does Wolfram Alpha solve functional equations?

Wolfram Alpha is able to solve a few basic functional equations. For example, it knows how to solve equations like this. My question is: how does it do this? I am planning on creating a program to ...
1 vote
340 views

### Understanding Time Complexity

I am sorry if these are such stupid noob questions. I am just getting into CS. I read a passage in a book that says: Time complexity is written T(n). It gives the number of operations the algorithm ...
240 views

### What algorithm is prefered to do a x b mod P with big numbers (256 bits)

I'm trying to implement multiple precision arithmetic operations modulo P, with P < 2^256. More specifically, ...
131 views

### Precise algorithm for finding higher order derivatives

I'm trying to make an algorithm that finds the first 10 or so terms of a function's Taylor series, which requires finding the nth derivative of the function for the nth term. It's easy to implement ...
224 views

### Count of different ways to express N as the sum of given numbers

I'm working on a case and I need some help :) I need to find number of ways and solutions itself to express N as the sum of given numbers. So, Sum (N) = 600 and the numbers from which I need to get ...
282 views

### Proof of Correctness : Arranging the sheep

I've come across a question in Codeforces contest 719(Div - 3). The problem goes like this : I was able to solve the problem by using another approach but had to use 4*n auxiliary space, where n is ...
1 vote
33 views

### How to create algebraic structures in code

I've been searching around google and this site and I haven't been able to find the answer to this. How are algebraic structures (like a set and its elements, groups, rings, etc.) defined in code (in ...
1 vote
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156 views

### How to get the calculate the binary logarithm of a fixed-point number with 18 decimals?

Suppose that: You're using a programming language that doesn't support fixed-point or floating-point numbers. The said programming language rounds down divisions, e.g. ...
1 vote
162 views

### Number of substrings with exactly k distinct characters

Given a string s and an int k, return an int representing the number of substrings (not unique) of s with exactly k distinct characters. If the given string doesn't have k distinct characters, return ...
1 vote
15 views

### Is this adjustment to an rms calculation valid?

I want to calculate the RMS AC value of a signal made up of several thousand readings every second. The processor that I am using doesn't have enough memory to store a whole second of data, so I want ...
103 views

### Competitive programming: Good Subsets problem

An array of length K is called good if for each subarray of the array, the sum of the subarray is not divisible by K+1. You are given an array A of length N. Find the number of subsequences of length ...
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### Random numbers with condition in matlab

I need ’n’ random numbers that: each one is bigger than ‘a’ their sum is smaller than ‘b’ How can I have that in Matlab?
244 views

### Adapt a one-tape turing machine's algorithm that find the center of a string in O(nlog(n)) to find the first third

I have found this answer that finds the center of an input string in nlog(n) complexity. I have tried to use it as a starting point to find an algorithm that finds the character(s) that separate the ...
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### Which topics of mathematics should I need to learn to be a good app developer?

I'm 29 years old. I couldn't continue my studies after grade 10 due to some financial issues and I didn't have time to practice mathematics. It's been more than 11 years since I left studies. Now I ...
40 views

### Optimal partitioning of n-arrays

You're given N integer arrays. Each array can have different size and contains unique values. However same integers can be found in different arrays. The goal is to partition those arrays into K ...
39 views

### Is there a way to map a multi-variable structure onto a single range?

I want to categorise variants of a structure made up of some number of variable components by mapping it to a unique range. Assume that the individual components all fall within the same base range. I'...
115 views

### Is there a way to combine linear equation and inequalities into same equation in order to optimise software calculations?

I’m programming web application which has some tricky calculations and I would need some help with mathematical calculations. What I'm trying to calculate: I have number of items. Lets call items a1, ...
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1 vote
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### Accessible CS Math Job [closed]

I am a CS undergrad and a huge enthusiast of pure math. I have been doing competitive programming and proofs for a while. My ambition is to become an academic in theoretical computer science. The ...
23 views

### If there is any research on Goal Based Programming (GBP)?

The more I think about programming and optimization, the more I think "why not just specify a goal and have the program figure out the optimal solution to it". I am familiar with basic "optimization ...
39 views

### Intersection algorithim for finding the intersection points of two arbitrary mathematical curves

I'm looking for an intersection algorithm for finding the intersection points of two arbitrary mathematical curves. Websites like Desmos, GeoGebra, and WolframAlpha allow you to graph and/or input two(...
798 views

### Given a set of points in the plane all laying on the axis, find the number of right angled triangles

My approach:- I separated the x coordinates and y coordinates in 2 separate arrays..then i used the idea of pythagoras theorem by selecting three vertices(1 from x axis and 2 from yaxis and vice versa)...
158 views

### Being stuck and frustrated with my masters project

I'm doing a masters in CS that requires me to implement from scratch most of the neural network models and because python libraries aren't applicable to what i want. The problem is that i don't feel ...
86 views

### Counting triplets from three arrays satisfying the equation x^2 = yz

Let's say I have three arrays of positive integers X, Y and Z. You can assume that each of ...