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Knight-fill a grid

A knight fill is a flood fill using the connectivity of the knight chess piece. Specifically:

(0 is the initial point, 1s show the connected cells)

Challenge

Given a 2D grid of spaces and walls, and an initial location, perform a knight-fill on the grid. Shortest code wins.

Rules

You may take input and produce output in any format you like (image, string, array, whatever). You may take the initial location as part of the input grid or as a separate coordinate. For the purpose of this explanation, the following format will be used:
```
######## # = wall
######## x = initial location
## x ##
## ##
########
## ##
########
########
```
Output is a copy of the input grid with the knight-fill result added
Your fill must not be in the same "colour" as the space or walls, but can be the same as the initial location marker. For example given the image above, a valid output would be:
```
######## # = wall
######## @ = fill (could also have been x)
## @ @##
## @ @##
########
##@ @ ##
########
########
```
You may assume that the input grid will always contain a 2-cell wall on all sides
You may assume that the initial location will never be inside a wall
You may assume that the grid will never be larger than 1000x1000
Builtins are fine
Shortest code (in bytes) wins

Test Cases

In all test cases, # denotes a wall, denotes empty space, and x denotes the initial location of the fill. @ denotes the output fill.

Input 1:
########
########
## x ##
## ##
########
## ##
########
########
Output 1:
########
########
## @ @##
## @ @##
########
##@ @ ##
########
########
Input 2:
############
############
## ## x##
## ## ##
##### ##
## ##
############
############
Output 2:
############
############
## ##@@@@@##
##@##@@@@@##
#####@@@@@##
## @@@@@@@##
############
############
Input 3:
####################
####################
## ## ##
## ## ##
## ## ######## ##
## ## ######## ##
## ## ## ## ##
## ## ## ## ##
## ## ## ## ##
## ## ## ## ##
## ## ######## ##
## ## ######## ##
## ## ## ##
## ## x## ##
## ############ ##
## ############ ##
## ##
## ##
####################
####################
Output 3:
####################
####################
##@@##@@@@@@@@@@@@##
##@@##@@@@@@@@@@@@##
##@@##@@########@@##
##@@##@@########@@##
##@@##@@## ##@@##
##@@##@@## ##@@##
##@@##@@## ##@@##
##@@##@@## ##@@##
##@@##@@########@@##
##@@##@@########@@##
##@@##@@@@@@@@##@@##
##@@##@@@@@@@@##@@##
##@@############@@##
##@@############@@##
##@@@@@@@@@@@@@@@@##
##@@@@@@@@@@@@@@@@##
####################
####################
Input 4:
################
################
## ###
## x ###
## ####### ###
## ####### ###
## ## ## ###
## ## ## ###
## ## ## ###
## ######## ##
## ######## ##
## ## ##
## ## ##
################
################
Output 4:
################
################
## @ @ ###
## @ @ @ ###
## ####### ###
##@ ####### @###
## ## ## ###
## @## ##@ ###
## ## ## ###
##@ ########@ ##
## ######## ##
## @ @ ## @##
## @ @## ##
################
################
Input 5:
##############
##############
## ###
## ###
## ###
## ### ###
## #x# ###
## ### ###
## ###
## ###
## ###
##############
##############
Output 5:
##############
##############
##@@@@@@@@@###
##@@@@@@@@@###
##@@@@@@@@@###
##@@@###@@@###
##@@@#@#@@@###
##@@@###@@@###
##@@@@@@@@@###
##@@@@@@@@@###
##@@@@@@@@@###
##############
##############

Answer*

## Mathematica, 117 bytes

The usual story: powerful built-ins but long names…

 HighlightGraph[g,ConnectedComponents[h=Subgraph[g=KnightTourGraph@@Dimensions@#,Flatten@#~Position~1],#2]~Prepend~h]&

[Try it at the Wolfram sandbox!](https://sandbox.open.wolframcloud.com/)

It takes two inputs: first is the input grid as an array of `0`s (for the walls) and `1`s (for spaces), then a single integer for the starting position, found by numbering the grid along the rows from top to bottom, e.g.

 1 2 3 4 5
 6 7 8 9 10
 11 12 13 14 ...

You can call the function like `HighlightGraph[...~Prepend~h]&[{{0,0,...,0}, {0,0,...,0}, ..., {0,0,...,0}}, 20]`.

The `KnightTourGraph` function constructs a graph with vertices corresponding to positions in the grid and edges corresponding to valid knight moves, then we take the `Subgraph` of the vertices that aren't walls, and find the `ConnectedComponents` of the starting vertex. The output is a graph (shown rotated 90º anticlockwise) with the non-wall vertices highlighted red, and the filled vertices highlighted yellow. For example, for the first test case, the output looks like:

[![Output for test case 1: a graph with some areas highlighted][1]][1]


 [1]: https://i.sstatic.net/BdSTC.png

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one. Explanations of your answer make it more interesting to read and are very much encouraged.
…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).

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Edit Summary*

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\$\begingroup\$ Well this certainly looks like the hardest to test! Could you add an example of how to invoke it in the sandbox, for those of us who haven't touched Mathematica since our university days? My attempts of f=... f[{0,...,0;0,...,0}, 19] and similar have failed miserably. \$\endgroup\$

Dave
– Dave

2017年06月28日 18:44:38 +00:00
Commented Jun 28, 2017 at 18:44
\$\begingroup\$ @Dave, you can invoke the function with HighlightGraph[g,ConnectedComponents[h=Subgraph[g=KnightTourGraph@@Dimensions@#,Flatten@#~Position~1],#2]~Prepend~h]&[{{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,1,1,1,1,0,0},{0,0,1,1,1,1,0,0},{0,0,0,0,0,0,0,0},{0,0,1,1,1,1,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}},20] (for the first test case). I've edited that into the question — sorry it wasn't there to begin with! \$\endgroup\$

Not a tree
– Not a tree

2017年06月28日 23:19:44 +00:00
Commented Jun 28, 2017 at 23:19

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