Questions tagged [square-grid]
The square-grid tag has no usage guidance.
31
questions
3
votes
0answers
17 views
Algorithm to find equivalent classes of homotopic pathes on a grid with obstacles
Given a $n \times n$ grid with some walls and two cells $a$ and $b$, I want to compute the non-homotopics paths from $a$ to $b$ on this grid. A path is a sequence of adjacent cells (diagonal does not ...
0
votes
1answer
133 views
Maximum flow on a n ×n grid
I am currently dealing with a network flow problem and I am trying to find some similar solved problems to help me formulate my solution.
The text is:
You are the owner of a large chain of franchise ...
1
vote
1answer
45 views
Algorithm to find the path with minimum bending points on a square grid board
Let's suppose we have a square grid board like the one shown in the picture below:
I'm wondering how I can find the path with minimum number of "bending" points (like the ones shown in red) ...
1
vote
1answer
57 views
SAT formula for connected graphs on the grid
In the answer to an earlier question "SAT algorithm for determining if a graph is disjoint" a formula is constructed that is satisfiable iff a given graph is connected.
The formula uses a ...
1
vote
0answers
26 views
0
votes
0answers
25 views
find maximum number of sections that satisfies the condition in a grid
Here is the description of a problem
Given an array of strings representing an $N$x$N$ grid of $red$ and $blue$ cells and a target color $r$ or $b$, partition the grid into $N$ sections of $N$ ...
1
vote
1answer
43 views
How to mathematically determine row, column, and sub-square of cell in nxn array where n is a perfect square?
Given an one dimensional array of size nxn, where n is a perfect square
How can one mathematically determine the row, column, and/or sub-square the cell resides in? Additionally, is there a ...
1
vote
2answers
210 views
Grid Puzzle Split Algorithm
I want to generate a random partition of an $N\times N$ grid into $N$ connected groups having $N$ tiles each. How would I do this? Max grid size will be 10x10. Below is an example for a 5x5 grid.
2
votes
1answer
77 views
Algorithm to find player position in a 2D grid when all you know is the directional steps he has taken
Given the 2D grid shown below, where blue tiles can be visited and island tiles cannot.
Given that we do not know the starting position of a player on this grid.
Given that the player can move 1 ...
3
votes
2answers
52 views
Finding a hamiltonianISH path in a graph
Problem statement
Given a graph of all the blue squares in the following image where each blue square is connected to other blue squares in all 4 cardinal directions.
Given any starting node.
What ...
6
votes
1answer
2k views
Can someone explain this formula for calculating Manhattan distance?
This is from a Kickstart problem:
Note: The Manhattan distance between two squares (r1,c1) and (r2,c2)
is defined as |r1 - r2| + |c1 - c2|, where |*| operator denotes the
absolute value.
Then ...
0
votes
1answer
147 views
Grid Based DP: How do we tweak the Travelling Salesman Problem to work with Grids
The question is:
There is a n x n grid (Maze) which has either 0, 1 or 2. 0 means a path
exists, 1 means the cell is blocked and 2 means there exists gold in
that cell. Task is to start from 0,...
1
vote
0answers
24 views
Grid treaversal with forbidden coordinates
What alorithm/heuristic can be applied to get a shortest path to all the blue coordinates below without going through red coordinates? starting and ending in bottom left(0,0).
I have list of all the ...
2
votes
2answers
149 views
3
votes
1answer
505 views
Find smallest enclosing circle
On a 2d plane, there is a large circle centered at $(0, 0)$ with a radius of $R_{{o}}$. It encloses $\sim 100$ or so smaller circles distributed randomly across the parent circle otherwise with known ...
2
votes
1answer
100 views
Finding the best poker hand in a connected grid structure where order matters
I am trying to find the best poker hand in a connected grid, where order matters. An illustration is the best way of explaining the situation.
This grid has 12 random cards, in random positions. Each ...
4
votes
1answer
203 views
Maximizing number of selected squares in a grid
We have an $n\times n$ grid of squares, each square has a non-negative integer. Two distinct squares are neighbours if they share a row or column. A selection of squares is good if every selected ...
2
votes
2answers
1k views
Efficient algorithm to find minimum steps to cover all the given points in infinite 2D grid?
Problem statement: You are in an infinite 2D grid where you can move in any of the 8 directions :
...
3
votes
0answers
511 views
Algorithm to traverse all unblocked $1*1$ squares in a $n*m$ grid
Given a $n*m$ grid, some $1*1$ squares are blocked(can't be entered) and some are unblocked(can be entered).
What is the algorithm which prints the shortest path, such that the path covers all ...
0
votes
0answers
58 views
Using counting to build a grid world
For this question, I have tried everything that I can think of, but cannot solve it. What I want to do is iterate over all possible values of $z_1$, but every method I use, it requires me to know ...
4
votes
1answer
259 views
Find a simple cycle in an undirected subgraph of a grid graph that encloses the most faces
Imagine a finite $n*n$ grid graph $G(V,E)$, much like a chessboard. Imagine further an undirected subgraph $H(V',E')$ of $G$. Let us call the squares of chessboard $G$ "faces". A DFS algorithm can ...
10
votes
1answer
2k views
Treewidth of k x k square grid graphs
According to some slides I found on google, the treewidth of any $k \times k$ square grid graph $G$ is $tw(G) = k$. I just started researching about treewidth and tree decomposition, and for the most ...
-2
votes
3answers
10k views
Draw a 5 × 5 grid graph. How many edges does the n × n grid graph have?
just confuse with this problem. What is n × n grid graph and how many edges it has?
1
vote
1answer
2k views
Square sub-grid with maximum sum
Given $N$ points in a grid having some weight, I have to find the side length of a square sub-grid with maximum sum of weight of points contained in that square sub-grid. Also square sub-grid must ...
5
votes
0answers
193 views
Upper bound on the number of hamiltonian cycles on a $n \times n $ grid graph
What is the best upper bound that is known for the number of hamiltonian cycles on a $n \times n $ grid graph?
I did some searching and found that the number of hamiltonian cycles on a planar graph ...
3
votes
0answers
252 views
Approximation ratio of a greedy grid-cover algorithm
We're given a $N\times M$ grid, and we want to cover all coordinates in the greedy by rectangles of size $\le k$.
Consider the following greedy algorithm. At each iteration, it chooses a rectangle ...
15
votes
1answer
3k views
Are "Flow Free" puzzles NP-hard?
A "Flow Free" puzzle consists of a positive integer $n$ and a set of (unordered) pairs of distinct vertices in the $n \times n$ grid graph such that each vertex is in at most one pair. A solution to ...
4
votes
2answers
519 views
Largest N squares that fit in a rectangle
I was working on a project and I needed to display N squares inside a rectangle area and I want them to be as large as possible, no rotations. More formally:
Problem: Given N equal-sized squares and ...
1
vote
1answer
944 views
Shortest path from starting cell to all cells in the grid
I found an algorithm for finding the shortest path on grid between selected cell, to all cells on the grid, with $O(KN)$ where $K$ is the number of neighbor cells and $N$ is the number of cells.
How ...
0
votes
1answer
209 views
Find a continuous path filling whole 3xN grid going through certain points in given order
I've got a grid consisting of squares that is 3 squares high and N squares long.
Some of the squares are filled with numbers that are not greater than 3*N. You can move only to squares that are below,...
6
votes
1answer
694 views
Route on a square grid with only (x,y) → (x,x+y) and (x,y) → (x+y,y) moves
This problem is about finding a route on a square grid.
The starting point is $(1,1)$ and the target point $(n,m)$.
I can move each step from my current point $(x,y)$ either to $(x+y,y)$ or $(x,y+x)$.
...
