Questions tagged [matrix]

This tag is for challenges involving matrices. A matrix, also known as a 2D array, is a list of numbers arranged in a rectangle with rows and columns.

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19 votes
15 answers
1k views

Spot all (anti)diagonals with duplicated values

Challenge: Given a matrix input, determine the amount of diagonals and anti-diagonals with duplicated numbers. So if we have a matrix like this: ...
14 votes
6 answers
805 views

Binary self-rotation

Given a binary 3D array, for each layer, cyclically rotate up each of its columns as many steps as indicated by the binary encoding of the columns of the layer above it, and then cyclically rotate ...
  • 28.3k
14 votes
3 answers
512 views

Matrix rotation sort

Lets define a non-empty, unsorted and finite matrix with unique numbers as follow: $$N = \begin{Bmatrix} 4&5&7\\1&3&6 \end{Bmatrix}$$ Lets define 4 matrix moves as: ↑* (up): Moves a ...
61 votes
20 answers
6k views

Dig a border trench

Background: Too many illegal immigrants from Blandia are crossing the border to Astan. The emperor of Astan has tasked you with digging a trench to keep them out, and Blandia must pay for the expenses....
  • 28.3k
25 votes
15 answers
3k views

Matrix Jigsaw Puzzles

Input: An integer n Two equal-sized square matrices (with their width/height being a multiple of n) Output: One of two ...
10 votes
15 answers
397 views

Matrix Jigsaw Puzzle Pieces

(Randomly inspired by https://codegolf.meta.stackexchange.com/a/17272/42963) Given a rectangular matrix of digits (i.e., 0 - 9), output the "pieces" of the matrix ...
  • 42.9k
19 votes
21 answers
911 views

Most contributing rows

Given a non-empty matrix of non-negative integers, answer which unique rows contribute most to the sum total of elements in the matrix. Answer by any reasonable indication, for example a mask of the ...
  • 28.3k
13 votes
13 answers
629 views

Count the contiguous submatrices

Migrated from chat Given two non-empty non-negative integer matrices A and B, answer the number of times A occurs as a contiguous, possibly overlapping, submatrix in B. Examples/Rules 0. There may not ...
  • 28.3k
7 votes
5 answers
206 views

Find equally-weighted complete graphs

Graph theory is used to study the relations between objects. A graph is composed of vertices and edges in a diagram such as this: ...
  • 7,259
97 votes
27 answers
6k views

The Hungry Mouse

Sixteen piles of cheese are put on a 4x4 square. They're labeled from \$1\$ to \$16\$. The smallest pile is \$1\$ and the biggest one is \$16\$. The Hungry Mouse is so hungry that it always goes ...
  • 171k
13 votes
16 answers
2k views

Trim that distracting background off!

Isn't it annoying when you're taking a picture, but the background detracts from the actual substance of the image? I'd say it is. I need to know how much I should crop so that I get rid of this ...
  • 41.6k
15 votes
15 answers
3k views

Output the anti-clockwise inward spiral of a 2D array

From this stackoverflow question Given a 2D array of size \$ M \times N \$, output the values in a anti-clockwise fashion. The output must start from the outside to the inside and the initial point ...
19 votes
12 answers
2k views

Is the Matrix Positive-Definite?

Introduction Today we're gonna take care of the bane of first-year linear algebra students: matrix definiteness! Apparently this doesn't yet have a challenge so here we go: Input A \$n\times n\$ ...
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7 votes
4 answers
642 views

Ordinary Least Squares Regression

I am quite surprised that a variant of linear regression has been proposed for a challenge, whereas an estimation via ordinary least squares regression has not, despite the fact the this is arguably ...
10 votes
7 answers
702 views

Whose neighbours are hostile?

Introduction For the purposes of this challenge, we will define the neighbours of an element \$E\$ in a square matrix \$A\$ (such that \$E=A_{i,j}\$) as all the entries of \$A\$ that are immediately ...
  • 41.6k
21 votes
14 answers
2k views

Chop off the matrix to get the desired sum

Definition Given a matrix \$M\$ of non-negative integers and a non-negative integer \$k\$, we define \$F_k\$ as the "chop-off" function that removes all rows and all columns in \$M\$ that ...
  • 171k
19 votes
14 answers
1k views

Square-Random-Symmetrical

Challenge Write a program or a function that returns or prints a square-random-symmetrical matrix. Input N: The size of the matrix i.e 6 x 6 Output The matrix. ...
  • 957
21 votes
11 answers
2k views

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 votes
5 answers
363 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 ...
15 votes
16 answers
5k views

Is the bus load legal?

I was in the bus today, and noticed this sign: ...
  • 28.3k
26 votes
16 answers
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 ...
27 votes
16 answers
3k views

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 ...
41 votes
32 answers
4k views

Remove surrounding zeroes of a 2d array

This is a 2-dimensional version of this question. Given a non-empty 2-dimensional array/matrix containing only non-negative integers: $$ \begin{bmatrix} {\color{Red}0} & {\color{Red}0} & {\...
  • 37.4k
19 votes
21 answers
2k 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 ...
24 votes
16 answers
4k 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&...
  • 22.8k
21 votes
15 answers
2k views

Find the Cell's Neighbours

...or Toroidal Moore Neighbourhoods Given positive integers h, w and a non-negative integer ...
  • 22.6k
37 votes
28 answers
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] \...
  • 41.6k
5 votes
16 answers
2k 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] [1,0] [1,...
10 votes
5 answers
699 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 ...
  • 14.9k
12 votes
11 answers
2k views

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 ...
  • 877
16 votes
8 answers
695 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 ...
  • 41.6k
2 votes
1 answer
120 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: ...
  • 4,274
18 votes
2 answers
416 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 ...
  • 4,274
0 votes
13 answers
627 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....
11 votes
15 answers
922 views

Sum of replicated matrices

Given a list of numbers \$[a_1, a_2, ... a_n]\$, compute the sum of all the matrices \$A_i\$ where \$A_i\$ is defined as follows (\$m\$ is the maximum of all \$a_i\$): $$ \begin{array}{c|cc} &...
  • 16.5k
15 votes
3 answers
343 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 ...
  • 40.3k
17 votes
16 answers
774 views

Progression of Matrix Columns

Consider the infinite matrix: ...
  • 42.9k
25 votes
56 answers
3k views

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 ...
  • 3,336
26 votes
12 answers
2k views

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 ...
  • 41.6k
9 votes
15 answers
871 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 ...
-2 votes
11 answers
2k 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 ...
23 votes
23 answers
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 ...
53 votes
12 answers
7k views

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 ...
  • 14.9k
23 votes
17 answers
3k views

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 ...
10 votes
2 answers
417 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 ...
27 votes
3 answers
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 ...
13 votes
5 answers
331 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 ...
10 votes
7 answers
2k views

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 new-...
10 votes
9 answers
1k views

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 ...
  • 40.3k
29 votes
7 answers
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-...