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Questions tagged [matrix]

A matrix is a list of numbers arranged in a rectangle with rows and columns. In programming, it is also known as a 2D array. Use this tag if your challenge is about manipulating matrices.

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A knight's graph on an N-by-N board

In chess, a knight can only move to the positions marked with X relative to its current position, marked with ♞: A Knight's Graph is a graph that represents all legal moves of the knight chess piece ...
11
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5answers
303 views

Minimal Centrosymmetrization

Topically related. Objective: Given a matrix of positive integers \$M\$, output the smallest centrosymmetric matrix which contains \$M\$ (this matrix may contain non-positive integers as well). A ...
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16answers
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Is the bus load legal?

I was in the bus today, and noticed this sign: ...
26
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16answers
4k views

Roman Army Shields

Sandbox post (deleted) The old roman army formations are very famous around the world. In these formations roman legionaries grouped in a geometric shape (usually a rectangle) protecting the flanks ...
26
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16answers
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Beware of the matrix tornado!

The matrix tornado is just like any other tornado: it consists of things rotating around a center. In this case, elements of the matrix instead of air. Here is an example of a matrix tornado: First ...
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20answers
1k views

Collapsing Matrices

Related: Let's design a digit mosaic, Print/Output the L-phabet. Sandbox post here Given 2 inputs C = columns and rows, S = starting point output a matrix as ...
22
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16answers
3k views

Find the inverse of a 3 by 3 matrix

Challenge Given nine numbers, a, b, c, d, e, f, g, h, i, as input which correspond to the square matrix: $$\mathbf{M} = \begin{pmatrix}a& b& c\\ d& e&...
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15answers
1k views

Find the Cell's Neighbours

...or Toroidal Moore Neighbourhoods Given positive integers h, w and a non-negative integer ...
37
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28answers
4k views

Is the matrix centrosymmetric… and so is the code?

Defintion A centrosymmetric matrix is a square matrix that is symmetric about its center. More rigorously, a matrix \$A\$ of size \$n \times n\$ is centrosymmetric if, for any \$i,\: j \in ([1, n] \...
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16answers
500 views

2D Array Middle Point

Given dimensions of a 2D array, except 1xn, that results in an odd number of elements, find the midpoint index. Example: Input is 3x5, representing the 2D array [0,0] [0,1] [0,2] [0,3] [0,4] [...
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3answers
372 views

Saddle points in a matrix

A matrix can be thought of as the altitudes of a surface in 3D space. Consider the 8 neighbours (orthogonal and diagonal) of a cell as a cyclic sequence in clockwise (or anticlockwise) order. Some ...
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11answers
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Find the Number With the Highest Sum of Neighbors

The Challenge Given a grid of numbers (10 <= N <= 99) Return number with the highest sum of the four numbers adjacent to it; that is the numbers above, below, right, and left of the number, but ...
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8answers
539 views

Classify a region by its slope

Definitions The kth ring of a square matrix of size N, where 1 ≤ k ≤ ceiling(N/2) is the list formed by the elements of the kth and (N-k+1)th rows and columns, but without the first and last k-1 ...
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1answer
92 views

Array-of-array string conversion to and from matrix [closed]

Matrix challenges are popular. There's an issue of how to provide test cases. A common method is the row-wise array-of-arrays representation, such as: ...
18
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2answers
313 views

Is this a Weyr matrix?

There's a type of n×n matrix W called the basic Weyr canonical form. Such a matrix is described by its blocks and has the following properties, using the following reference diagram: the main ...
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13answers
277 views

Beginners 10x10 multiplication matrix [duplicate]

I was looking for a very easy task to look how short of a code can be produced on a beginners exercise. The goal is to produce a simple table that looks like this common java/c# code is about 4 lines....
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12answers
818 views

Sum of replicated matrices

Given a list of numbers [ a1 a2 ... an ], compute the sum of all the matrices Aᵢ where Aᵢ is defined as follows (m is the maximum of all aᵢ): ...
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3answers
263 views

Are there mountain rings?

Challenge Given a matrix of positive integers, determine if there are any "rings" of mountains. The formal definition for this challenge is: given a matrix of positive integers, is there any positive ...
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16answers
727 views

Progression of Matrix Columns

Consider the infinite matrix: ...
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50answers
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Orthodiagonal steps

It's a common problem to navigate in a 2D matrix. We've seen it many times and will see again. So let's help future us and develop the shortest solutions to generate all eight possible steps in a 2D ...
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12answers
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Find arsonist's lullaby

Imagine an arsonist walking around the town and picking its victims according to a very specific pattern (Or, alternatively, Imagine a bee flying around the garden and picking its flowers to pollenize ...
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15answers
533 views

The biggest square

This question is similar to Biggest Square in a grid. Challenge Given a matrix of 1 and 0 in a string format ...
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11answers
886 views

Getting the Vowel Square

Challenge You will create a function which takes a matrix filled with letters from the alphabet and determine if a 2x2 square composed of vowels exists. If a 2x2 ...
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20answers
3k views

Matrix in “slash” order

Given two positive numbers N >= 2 and N <= 100 create a matrix which follows the following rules: First Number starts at ...
49
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10answers
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Seats in a Finnish cinema

You're given the map of a cinema theatre as a boolean matrix: 0 represents a free seat, 1 - occupied. Each Finn who walks in chooses the seat farthest away (Euclidean distance) from the nearest ...
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17answers
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Generate a Walsh Matrix

A Walsh matrix is a special kind of square matrix with applications in quantum computing (and probably elsewhere, but I only care about quantum computing). Properties of Walsh matrices The ...
11
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2answers
357 views

The Lonely Islands

Input: A 2D array containing two distinct (optional) values. I'll use 0 and 1 when explaining the rules. The input format is of course flexible. Challenge: Zeros are water, and ones are islands. In ...
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3answers
1k views

Golf A Free Lunch

Find a maximally profitable sequence of exchanges given an exchange rate table. As an example consider the currencies Ariary (your home currency), Baht, Cedi, and Denar where the rate from one to ...
12
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5answers
203 views

Matrix trace for any matrix through… Bresenham’s line rasterisation

Inspired by this. Agatha Stephendale, a sophomore who is really into raster graphics, has taken a course in linear algebra. Now she imagines matrices as rectangles, but in her artistic mind, she ...
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7answers
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There, I fixed it (with rope)

Related: Rather similar (but much easier) challenge horizontally: There I fixed it (with tape) Challenge: Given a string only containing upper- and/or lowercase letters (whichever you prefer) and ...
10
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9answers
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Convergence of a Markov Process

Challenge Given a left- or right-stochastic matrix where the limit as x approaches infinity of the matrix to the power of x approaches a matrix with all finite values, return the matrix to which the ...
29
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7answers
2k views

We ended up where we started!…

Challenge: Input: You take two inputs: - A string only containing printable ASCII (excluding spaces, tabs or new-lines) - A printable ASCII character Output: The first line will contain the string-...
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31answers
3k views

Rebuild a rectangular array from a corner

I once had a beautiful rectangular array. It was very symmetrical, but unfortunately it has fallen apart and now I only have the top left corner. Your task will be to rebuild the original array. Your ...
22
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13answers
2k views

Codegolf the Hafnian

The challenge is to write codegolf for the Hafnian of a matrix. The Hafnian of an 2n-by-2n symmetric matrix ...
18
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20answers
2k views

How to print the below format in the fewest bytes?

This challenge is inspired by this, now deleted question. Take a positive integer N as input, and output a matrix with the numbers 1 .. N2 that follows the pattern below: Fill in the first row with ...
16
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18answers
3k views

Hermitian matrix?

Note that this challenge requires no handling or understanding of complex numbers. Given a non-empty square matrix where every element is a two-element (Re,Im) integer list, determine (giving any ...
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10answers
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Minimally sort a list into a matrix

Given an unsorted list of unique strictly positive integers, minimally sort it into a 2D matrix. The input list is guaranteed to be of composite length, which means the output matrix is not ...
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14answers
818 views

Generate all square sub-matrices of a given size

You will be given a square matrix of integers M and another positive integer n, strictly smaller than the size of M. Your task is to generate all square sub-matrices of M of size n. For the purposes ...
8
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4answers
166 views

Flattened Spiral Permutation Index

Context Consider square matrices with n columns and rows containing the first n^2 (i.e. n ...
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13answers
4k views

Friar simulator

The brethren from the order of St Golfus the Concise have a tradition of reciting a short prayer whenever they see someone make the sign of the cross. Due to the high level of sin measured among ...
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34answers
2k views

Perfect Squares Without Borders

Given n=m^2, return a list of integers that do not border the m x m grid of integers from ...
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13answers
4k views

Fryer simulator

Your task is to model the effects of batter on pieces of food. Please add three layers of crust. ...
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13answers
2k views

Check if all non-zero elements in a matrix are connected

Input: A matrix containing integers in the range [0 - 9]. Challenge: Determine if all non-zero elements are connected to each other vertically and/or horizontally. Output: A truthy value if all ...
16
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0answers
161 views

Matrices Generated Using Rectangles

Input is an r by c matrix of non-negative integers (you may input r and c as other parameters if this helps with golf). This may be inputted as a 2D array or, if you prefer, a 1D array (though taking ...
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27answers
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Generalized matrix trace

Inspiration. Given (by any means): A two-argument (or single argument consisting of a two-element list) black box function, f: ℤ+ × ℤ+ → ℤ+ (input and output are ...
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29answers
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Rotation summation

Take a square matrix containing positive integers as input, and calculate the "rotated sum" of the matrix. Rotated sum: Take the sum of the original matrix and the same matrix rotated 90, 180 and ...
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20answers
1k views

Compute the Optimal Square Matrix

The optimal matrix (for the rather narrow scope of this challenge) is obtained by "zipping" the elements from the corresponding rows and columns of a square matrix and getting the maximum of each pair....
16
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7answers
608 views

Queue Our Decomposition

In this challenge I will ask you to find a QR decomposition of a square matrix. The QR decomposition of matrix A is two Matrices Q and R such that A = QR. In particular we are looking for Q to be an ...
3
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0answers
78 views

lexicographically sorted list of index [closed]

Given a drawing of the letter shoot system, where an existing piece of pipe is marked with a *, and an empty spot is marked with a ., your task is to compile a lexicographically sorted list of index ...
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40answers
3k views

Is my Matrix Arrowhead?

Definition An arrowhead matrix is a matrix that has all entries equal to 0, except the ones on the main diagonal, top row and leftmost column. In other words, the matrix should look like this: * * * ...