How to get the shortest route in the maze?

Question

I want to make a code that gives the shortest route when a maze is presented as a matrix.

In this case, the matrix representation of this maze is as follows.

## [,1] [,2] [,3] [,4]
## [1,] 2 0 0 0
## [2,] 1 1 0 1
## [3,] 0 1 0 0
## [4,] 1 1 1 3
 , where  0 denotes inaccessible points, 1 denotes accessible points.
          2 denotes the starting point, and 3 denotes the destination.

And, the desired result is: c(4,1,4,4,1,1)where 1 is East, 2 is North, 3 is West, and 4 is South.

I suppose that one possible code could be a function giving the shortest route as a vector when it is given a matrix representation of the maze.

, , , . , , n m, 4-4 . , , , .

Answer 1

:

# Construct nodes and edges from matrix
(nodes <- which(m == 1 | m == 2 | m == 3, arr.ind=TRUE))
#       row col
#  [1,]   1   1
#  [2,]   2   1
#  [3,]   4   1
#  [4,]   2   2
#  [5,]   3   2
#  [6,]   4   2
#  [7,]   4   3
#  [8,]   2   4
#  [9,]   4   4
edges <- which(outer(seq_len(nrow(nodes)),seq_len(nrow(nodes)), function(x, y) abs(nodes[x,"row"] - nodes[y,"row"]) + abs(nodes[x,"col"] - nodes[y,"col"]) == 1), arr.ind=T)
(edges <- edges[edges[,"col"] > edges[,"row"],])
#      row col
# [1,]   1   2
# [2,]   2   4
# [3,]   4   5
# [4,]   3   6
# [5,]   5   6
# [6,]   6   7
# [7,]   7   9

library(igraph)
g <- graph.data.frame(edges, directed=FALSE, vertices=seq_len(nrow(nodes)))

:

start.pos <- which(m == 2, arr.ind=TRUE)
start.node <- which(paste(nodes[,"row"], nodes[,"col"]) == paste(start.pos[,"row"], start.pos[,"col"]))
end.pos <- which(m == 3, arr.ind=TRUE)
end.node <- which(paste(nodes[,"row"], nodes[,"col"]) == paste(end.pos[,"row"], end.pos[,"col"]))
(sp <- nodes[get.shortest.paths(g, start.node, end.node)$vpath[[1]],])
#      row col
# [1,]   1   1
# [2,]   2   1
# [3,]   2   2
# [4,]   3   2
# [5,]   4   2
# [6,]   4   3
# [7,]   4   4

, (1: , 2: , 3: , 4: ), :

dx <- diff(sp[,"col"])
dy <- -diff(sp[,"row"])
(dirs <- ifelse(dx == 1, 1, ifelse(dy == 1, 2, ifelse(dx == -1, 3, 4))))
# [1] 4 1 4 4 1 1

.

:

(m <- matrix(c(2, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 3), nrow=4))
#      [,1] [,2] [,3] [,4]
# [1,]    2    0    0    0
# [2,]    1    1    0    1
# [3,]    0    1    0    0
# [4,]    1    1    1    3

Answer 2

, , gdistance, :

library(gdistance) ## A package to "calculate distances and routes on geographic grids"

## Convert sample matrix to a spatial raster
m = matrix(c(2, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 3), nrow=4)
R <- raster(m)

## Convert start & end points to SpatialPoints objects
startPt <- SpatialPoints(xyFromCell(R, Which(R==2, cells=TRUE)))
endPt   <- SpatialPoints(xyFromCell(R, Which(R==3, cells=TRUE)))

## Find the shortest path between them
## (Note: gdistance requires that you 1st prepare a sparse "transition matrix"
##  whose values give the "conductance" of movement between pairs of cells)
tr1 <- transition(R, transitionFunction=mean, directions=4)
SPath <- shortestPath(tr1, startPt, endPt, output="SpatialLines")

## Extract your direction codes from the steps taken in getting from 
## one point to the other. 
## (Obfuscated, but it works. Use some other method if you prefer.)
steps <- sign(diff(coordinates(SPath)[[1]][[1]]))
(t(-steps)+c(2,3))[t(steps!=0)]
## [1] 4 1 4 4 1 1

## Graphical check that this works
plot(R>0)
plot(rBind(startPt, endPt), col=c("yellow", "orange"), pch=16, cex=2, add=TRUE)
plot(SPath, col="red", lwd=2, add=TRUE)

Answer 3

, 1 0,9 . , .

, .

, , " " . .

, :

     [,1]  [,2]  [,3] [,4]
[1,] 0.53  0.00  0.0  0.00
[2,] 0.59  0.66  0.0  0.81
[3,] 0.00  0.73  0.0  0.00
[4,] 0.73  0.81  0.9  1.00

:

• , , .
• , 1

, [2,4] - . .