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.
298
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Is this a Hadamard matrix?
Hadamard matrices is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal.
In other words, it means that each pair of rows has matching entries in exactly half of ...
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9-16-25 2D Matrix
Given three grids and the sum of rows and columns of each grid, your task is:
Grid \$3×3\$: Fill the grid from \$1\$ to \$9\$, ensure no repeats within the grid.
Grid \$4×4\$: Fill the grid from \$1\...
user123147
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Contract a tensor
Introduction
Tensor contraction is an operation that can be performed on a tensor. It is a generalization of the idea of the trace of a matrix. For example, if we have a rank-2 tensor (a matrix) and ...
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Which line is best?
Consider an \$n \times n\$ grid of integers. The task is to draw a straight line across the grid so that the part that includes the top left corner sums to the largest number possible. Here is a ...
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Compute the logarithm of a matrix
There have already been challenges about computing the exponential of a matrix , as well as computing the natural logarithm
of a number. This challenge is about finding the (natural) logarithm of ...
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22
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Compute this fractal matrix
The unique-disjointness matrix ( UDISJ(n) ) is a matrix on all pairs of subsets of {1...,n} with entries $$ U_{(A,B)}=\begin{cases}
0, ~ if ~ |A\cap B|=1\\
1, ~ ...
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answers
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Diagonalize a vector
Diagonalize a vector into a matrix.
Input
A vector, list, array, etc. of integers \$\mathbf{v}\$ of length \$n\$.
Output
A \$n \times n\$ matrix, 2D array, etc. \$A\$ such that for each element \$a_i \...
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Bunny Shakespeare poetry [closed]
Suppose you have a grid of cells that is 6 wide and arbitrarily tall. In each cell is a word. Let the bottom row, which is row #1, be the last 6 words of sample.txt in order. Let the second to last ...
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Print all semimagic squares [closed]
I am working on a code to print all semimagic squares [1] of a given size. I am working with the following definition:
An \$n\times n\$ consists of numbers \$1,2,\cdots, n^2\$.
All numbers must be ...
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Borders of a Rectangular Matrix
Although it's done a few times as sub-challenge of a larger challenge, and we also have a challenge to remove the borders of a square matrix, I couldn't find a challenge to output the borders of a ...
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Calculate the Smith normal form of an integer matrix
Given an \$m \times n\$ matrix of integers A, there exist a \$m \times m\$ matrix P, an \$m \times n\$ matrix D, and an \$n \times n\$ matrix Q such that:
\$A = P D Q\$.
P and Q are unimodular ...
- 1,391
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13
answers
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Make a Custom Bayer Matrix
A Bayer matrix is a threshold map used for ordered dithering that gives the illusion of having more shades of color than actually present by using a crosshatch-like pattern.
Bayer matrices are square ...
- 4,060
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votes
1
answer
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4D rotation matrix to quaternions
It is well-known that a 3D rotation can always be represented by a quaternion. It is less well-known that a 4D rotation can always be represented by two quaternions, sending a point \$p=(a,b,c,d)^T\$ ...
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3D rotation matrix to quaternion
There are multiple ways to represent a 3D rotation. The most intuitive way is the rotation matrix –
$$A=\begin{bmatrix}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&...
- 3,935
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9
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Find Sub-matrix with matched cell 1
You are given a matrix of size m x n where each cell can contain either 1 or 0. You need to find the largest square submatrix that contains only 1's. The output should be the area of the largest ...
user116868
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answers
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Painting with Line Filler
Given a matrix of positive integers, output whether it's possible to generate it by starting with an empty1 matrix of the same dimensions and repeatedly filling a whole row or a whole column with the ...
- 26k
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Is this a shift matrix?
A Shift matrix is a binary matrix with one superdiagonal or subdiagonal formed by only ones, everything else is a zero.
A superdiagonal/subdiagonal is a diagonal parallel to the main diagonal, which ...
- 9,438
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votes
1
answer
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Implement Strassen's algorithm [closed]
Strassen's algorithm was the first method of matrix multiplication in subcubic time complexity, namely O(n**log2(7)) for a pair of ...
- 97
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8
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Find the representative submatrix
Note: This is a more limited version of a challenge from 2014 that only received one answer. That challenge required participants write two programs; this challenge is essentially one half of that. ...
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Find the box by its corners
Given a matrix of integers \$M\$ and a list of four integers \$L\$, find the sub-matrix \$N\$ whose corners are given by \$L\$ and return the sum of its elements.
Suppose you're given the list \$L = [...
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Make the cheapest cut
“Cut” a matrix of integers on the line where the sum of the absolute differences of “severed” neighbors is the least.
Example
Consider this matrix:
...
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Minimum rotation to get the maximum value
I recently solved a coding challenge in one of the challenge papers that my IT teacher gave to us. It was a seemingly simple, but fun challenge, so I thought it will make fun golfing.
The task
Given ...
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Box blur the string
Box blur is a simple operation for blurring images. To apply box blur, simply replace each pixel with the average of its and the surrounding 8 pixels' values. Consider, for example, the following ...
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Find a matrix whose sliding sum is the input
Given a matrix like this:
1 1 3 -2
3 -4 1 -1
1 1 1 0
0 -1 0 0
By taking a 2×2 "sliding sum", where the sum of every 2×2 region of the matrix is ...
- 18.9k
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17
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Reconstruct Matrix from its diagonals
Given the diagonals of a matrix, reconstruct the original matrix.
The diagonals parallel to the major diagonal (the main diagonals) will be given.
Diagonals: ...
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11
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Flood fill by distance
Say I have a grid with some obstacles:
----
| X |
| |
|XX |
| |
----
I can fill this with numbers, as distance from the top left corner. But, because ...
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Create Bernard from Desmos
Background
In the online graphing calculator Desmos, there is a certain shape that appears in the lower left portion of the graph in many high detail graphs, which the Desmos community has dubbed &...
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fastest matrix multiplication on x86
This challenge requires integration with C, so you can stop reading if you're not interested.
Matrix multiplication is a simple operation, but the performance depends a lot on how efficiently the code ...
- 2,375
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votes
15
answers
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center a matrix [closed]
The words "center a" probably give flashbacks to any decent HTML developer. Luckily, we are not working with divs, we are working with matrices.
Given a matrix where w=h, and given a "...
- 691
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Storing a band matrix
Related challenge
A band matrix is a matrix whose non-zero entries fall within a diagonal band, consisting of the main diagonal and zero or more diagonals on either side of it. (The main diagonal of a ...
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Convert J brackets back to 2-D list
Let's say we have a 2-D list, like the following one:
\$
\begin{bmatrix}
\color{red}{1} & \color{red}{2} & \color{red}{3} & \color{red}{4} \\
\color{blue}{5} & \color{blue}{6} & \...
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Simulate the ripple effect
Imagine throwing a rock into a pond. You get to see perfect circles of ripples spreading out over the pond, bouncing off of each other. Of course, nothing can be as serene as that in coding, but, we ...
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Recreate Minecraft's lighting
Minecraft has a fairly unique lighting system. Each block's light value is either one less than the brightest one surrounding it, or it is a light source itself. Your task is to write a method that ...
- 691
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votes
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Convert between graph representations
What?
Let's say I have this graph:
1
\
\
2 3
\ /
\ /
4
I can represent it in 2 ways:
A list of connected vertices. ...
- 1,655
12
votes
3
answers
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Line Islands in a Word Search
My third word search related challenge in a row. :)
Challenge:
Brief explanation of what a word search is:
In a word search you'll be given a grid of letters and a list of words. The idea is to cross ...
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votes
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Generate this string table [duplicate]
For the given string s, generate generate a table like below.
...
- 1,993
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answers
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NxM List Combination Closest to Target
Given a list of N lists, each containing M positive integers, and a separate list of M positive integers (target values), return a list of N scalars (integers with a value of 0 or more) that ...
- 757
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votes
3
answers
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Appease the Picky Eater
Your friend Jack is a picky eater. He only likes certain foods, and he only likes to eat a certain amount of them each day. Despite this, Jack has very strict calorie and macronutrient goals that he ...
- 757
3
votes
2
answers
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views
Resize the image
Given an \$n\times m\$ matrix \$A\$ and two integers \$w,h\$, output a matrix of \$w\times h\$ called \$B\$, such that $$B_{i,j} = \int_{i-1}^i\mathbb dx\int_{j-1}^j A_{\left\lceil \frac xw\cdot n\...
- 26k
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Bandwidth of a matrix
A band matrix is a matrix whose non-zero entries fall within a diagonal band, consisting of the main diagonal and zero or more diagonals on either side of it. (The main diagonal of a matrix consists ...
- 38.8k
8
votes
2
answers
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Count the ways to transform (2)
Your input is a matrix (2d array) of positive integers. For example:
\begin{matrix}
1 & 1 & 4 & 7\\
1 & 3 & 5 & 6\\
2 & 1 & 4 & 5 \\
\end{matrix}
A semi-continuous ...
- 7,918
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Knights Jam | Chess
The knight is a chess piece that, when placed on the o-marked square, can move to any of the x-marked squares (as long as they ...
- 5,097
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Simulating Bombs
More advanced version of this
The aim of this puzzle is to simulate the impact of the shock wave of bombs on a square grid. The grid initially contains cells labelled ...
- 5,097
22
votes
6
answers
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Check if a matrix is Zarankiewicz-maximal
My final-year project at the National University of Singapore is on Zarankiewicz's problem:
What is the maximum number of 1s in an \$m×n\$ binary matrix (\$m\$ rows and \$n\$ columns) with no \$a×b\$ ...
- 3,935
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answers
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Output the 12 Bar Blues
Note to those without experience in music: Through making an attempt to solve this problem, you may find that music and computer programming are similar in the ways that they implement rules and ...
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votes
14
answers
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SuperSquares NxN
Given an integer N from 1-9, you must print an NxN grid of NxN boxes that print alternating 1s and Ns, with each box having an alternating starting integer.
Examples
...
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votes
14
answers
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Ragged Matrix Indexing
A ragged matrix, is a matrix that has a different number of elements in each row. Your challenge is to write a program in any favorable language to find the indices of all occurrences of target in the ...
- 5,097
23
votes
18
answers
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Print a NxN integer involute
Given an integer \$N\$, you must print a \$N\times N\$ integer involute with the numbers increasing in a clockwise rotation. You can start with either 0 or 1 at the top left, increasing as you move ...
- 431
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votes
8
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Count the ways to transform
A rigid transformation of a square array is a mapping from square arrays of a certain size to square arrays of the same size, which rearranges the elements of the array such that the distance to each ...
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votes
7
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Cell Evolution Matrix
Your lab needed to simulate how a particular cell evolves over time in a 2D grid space. A sample 2D grid space below shows a single cell at the centre of the grid.
...
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