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.
283
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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 ...
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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 ...
- 6,366
3
votes
1
answer
168
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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 ...
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9
votes
8
answers
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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. ...
- 9,136
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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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4
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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 ...
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15
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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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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 ...
- 2,263
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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 "...
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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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12
votes
10
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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} & \...
- 12.5k
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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
12
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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. ...
- 1,954
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
5
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Generate this string table [duplicate]
For the given string s, generate generate a table like below.
...
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2
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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 ...
- 727
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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 ...
- 727
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votes
2
answers
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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\...
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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 ...
- 35.7k
7
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 ...
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votes
7
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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 ...
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5
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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 ...
- 4,887
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\$ ...
- 1,263
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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
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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
12
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 ...
- 4,887
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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 ...
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votes
8
answers
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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 ...
- 92.5k
10
votes
7
answers
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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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13
answers
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Mat Printing Matrix
A manufacturing company wants to print a design on mats of varying dimensions, and they hired you to program a robot to make these mats. The design consists of alternating rings of any 2 symbols on a ...
- 4,887
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votes
4
answers
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Simulate weathering of a rock
Inspired by my geography class, Sandboxed
Simulate weathering / erosion.
Input
Input will be given as a string of any 2 characters (or see below) you like in the shape of the rock (here i use spaces ...
- 1,954
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6
answers
763
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Is it an elementary matrix?
Consider a linear system of equations, in \$n\$ unknowns, expressed as
$$A \textbf x = \textbf b$$
where \$A \in M_{n,n}(\mathbb Z)\$ is an \$n \times n\$ matrix of integers, \$\textbf x\$ is a column ...
- 48.5k
19
votes
13
answers
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Compute matrix blockiness
Consider a non-empty binary matrix M and a natural number n. For the purposes of this challenge, M is said to have blockiness n if it can be built using adjacent square blocks of size n, where each ...
- 102k
16
votes
10
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Remove submatrices
Given two integer matrices a and b, your challenge is to replace any occurences of b in <...
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6
votes
1
answer
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Fast Matrix Multiplicator Evaluator
A triplet of real tensors \$(A,B,C)\$ of size \$\gamma \times \gamma \times \sigma\$ represents a matrix multiplication algorithm with \$\sigma\$ elementary multiplications iff the following function ...
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Bird's Algorithm for Computing Determinants
There is a division-free algorithm for computing determinants published by R.S.Bird in 2011 that uses only matrix multiplications. Given a \$n×n\$ matrix \$X\$, the matrix \$Y=μ(X)\$ is another \$n×n\$...
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Checkered grid with X mark
Challenge
Given two integer values \$a \ge 2\$ and \$0 \le b < a\$, generate a \$(2a-1) \times (2a-1)\$ matrix consisting of the integers 0, 1, and 2 as follows:
Create a checkerboard of 0s and 1s ...
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Double trace of a square matrix
Inspired by a question (now closed) at Stack Overflow.
Given a square matrix, let its double trace be defined as the sum of the entries from its main diagonal and its anti-diagonal. These are marked ...
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8
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Find the number of paths in a n×n grid
Information
Given a non-negative odd integer (let's call it \$n\$), find the number of all possible paths which covers all squares and get from the start to end on a grid.
The grid is of size \$n\$×\$...
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Drop down the numbers
This was inspired by Apply gravity to this matrix
Your challenge is to input a matrix with non-negative one-digit integers and drop down the 1's down 1 column, the 2's down 2 columns, the 3's down 3 ...
- 3,169
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25
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Apply gravity to this matrix
This was inspired by this question.
Given an \$m\times n\$ matrix of \$0\$'s and \$1\$'s, apply "gravity" to it. This means to drop down all the \$1\$'s as if they were affected by gravity.
...
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4
answers
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Calculate the integer square root of a matrix
Let \$A\$ be a square matrix that is at least \$2 \times 2\$ where each element is an integer. \$A^2 = A \times A\$ will then have the same dimensions as \$A\$, and will have integer elements. For ...
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Is this a Jordan matrix?
Background
A Jordan matrix is a block-diagonal matrix where each block on the diagonal has the structure of
$$
\begin{bmatrix}
\lambda & 1 & 0 & \cdots & 0 \\
0 &...
- 69.4k
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votes
26
answers
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Recursive Z-matrix
Originally from a CMC I proposed for the last BMG event
Challenge
Given a non-negative integer \$n\$, create a 2D array of size \$2^n × 2^n\$ which is generated in the following manner:
Divide the ...
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