Questions tagged [mathematical-programming]

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

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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] ...
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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 , .... , ⌈ ...
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Factor a number in the longest possible product of distinct numbers

I got stuck with quite a simple problem: Given a positive number $X$ find the largest number $k$, for which exists the positive distinct integers $Y_1,…,Y_k$ such that $(Y_1+1)(Y_2+1)⋯(Y_k+1)=X$ Any ...
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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 ...
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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. ...
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How to calculate 3D depth reconstruction of an image using a set of 3 similar images?

From a set of 2 similar images taken some small translation distance apart, we can calculate the depth of the a particular point, if we know the distance of a reference object in the frames. This is ...
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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?...
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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 ...
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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 ...
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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 ...
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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 ...
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2 answers
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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EM algorithm - What happens with the standard deviation?

What have you tried? So I watched this video. According to the video, we've to calculate the variance $\sigma^2$ as follows: $$ \sigma_{k}^{2} = \frac { p_{1} \left(x_{1} -...
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Four functions problem

This is not from online contest Hi guys, a friend of mine recently give me this problem that I couldn't figure out an effective way to solve it. Four functions You are given four functions $$ \begin{...
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1 answer
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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. ...
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1 vote
1 answer
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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 ...
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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 ...
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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?
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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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3 answers
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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 ...
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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 ...
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1 answer
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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'...
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1 answer
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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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How to cluster a dataset in which each data point is composed of a set of 2-dimensional coordinates

I have a dataset with totally $1000$ scenarios, each of which is composed of $5$ users' coordinates $(x_i,y_i), \forall i \in \{1,\dots,5\}$. Now, based on users' coordinates, I want to cluster these $...
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1 vote
1 answer
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What is the difference between a fraction and a float?

I understand any fraction to be a quotient of integers which isn't 0, but after coming across the term "float" in various programming languages (such as JavaScript) I misunderstand why it is ...
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3 answers
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Divide first n square numbers 1^2, 2^2, ....... n^2 into two groups such that absolute difference of the sum of the two groups is minimum [closed]

lets say Given input is n = 6 (n is as large as 100000) My task is to divide {1, 4, 9, 16, 25, 36} into two groups and PRINT these two groups Possible Solution 1: dividing groups as {1, 9, 36} and {4, ...
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5 votes
3 answers
297 views

Usefulness of Differential Geometry

I recently came across these books: Differential Geometry and Lie Groups: A Computational Perspective Differential Geometry and Lie Groups: A Second Course Their subject matter really intrigues me, ...
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1 answer
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Convert ((50^A)*((((50^B)(((50^C)+1)/(4)))+1)/(4)))/(4) to MathJax? [closed]

I need help coverting these two question to Math Jax ((50^A)*((((50^B)(((50^C)+1)/(4)))+1)/(4)))/(4) and (((50^A)(50^B)(50^C))/(4^2)) + (((50^A)(50^B))/(4^2))+((50^A)/(4))+(1/4) I don't know how to ...
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Stable matching with dynamic preference lists

I have a set $F$ of $n_1$ families, a set $C$ of $n_2$ children ($n_1<n_2$) and a set $M$ of feasible one-to-one matchings of the families with the children. All the children have the same ...
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1 vote
0 answers
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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 ...
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1 answer
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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 ...
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1 answer
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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(...
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0 votes
1 answer
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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)...
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2 votes
2 answers
124 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 ...
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2 votes
0 answers
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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 ...
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0 votes
1 answer
294 views

Why do we need/use operator precedence for Arithmetic operators?

Why do we use operator precedence rule for Arithmatic operators? Can't we simply just do the operation in a linear manner from left to right or vice-versa and deal with the operator that comes first. ...
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1 vote
0 answers
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Proof of Fundamental Lower Bound on Regret

Online Convex Optimization sees optimization as a continuous process in which the algorithm learns new aspects of the problem and improves upon. Every iteration consists of the player making a ...
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1 answer
623 views

Min-plus matrix multiplication implementation

I had a look at topological sorting where they mention a possible parallel algorithm that relies on matrix multiplication, but using min-plus matrix multiplication: One method for doing this is to ...
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5 votes
2 answers
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Fermat's last theorem: How to (partially) solve by programs

No three distinct positive integers $a, b, c$ can satisfy the equation : $a^n + b^n=c^n$, if $n$ is an integer greater than two. The above statement, known as the Fermat's last theorem is proven ...
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1 vote
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Find lines segment portions close together

I have two lines segment in 3D space. Lines segment are defined by 2 points each: $A_1$, $B_1$ and $A_2$, $B_2$ (see left part in the below schema). I would a like to find an algorithm to detect ...
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3 votes
3 answers
209 views

Are regular languages and their regular expressions part of computer science?

I am trying to understand if regular languages and their regular expressions are concepts of computer science in general and if these are discovered, or invented, by computer scientists, in particular....
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1 answer
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Do all the numbers belong to same slot in the Hashtable?

I was reading the CLRS. In the Hashing Chapter on page 262 a statement says: "For example, if we know that the keys are random real numbers $k$ independently and uniformly distributed in the range $0 \...
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Number of multiplications and additions in the given code

$N:=2^p$ Input: $f \in \mathbb C^N$ 1: $n=N/2$ 2: initialize vectors $f^{(1)}, f^{(2)} \in \mathbb C^n$ 3: $w_N^0=1$ 4: for $j=0,\ldots,n-1$ do 5: $\ \ \ \ \ f_j^{(1)}=f_j+f_{j+n}$ 6: $\ \ \ \ ...
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1 vote
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How can I calculate the exponential integral?

(I'm not sure this is the right forum.) I'm writing a program that uses the prime-counting function. Right now, I'm using x/log(x), but I want to switch to ...
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