Can you fill out the following code :$[$from pulp import $*$

from math import sqrt

def euclidean$\_$distance$($location$\_$coords, i$,$ j$)$:

assert $0<=$ i and i $<$ len$($location$\_$coords$)$

assert $0<=$ j and j $<$ len$($location$\_$coords$)$

if i $==$ j:

return $0\mathrm{.}0$

$($xi$,$ yi$)=$ location$\_$coords$[$i$]$ # unpack coordinate

$($xj$,$ yj$)=$ location$\_$coords$[$j$]$

return sqrt$(($xj $-$ xi$)**2+($yj $-$ yi$)**2)$

def solve$\_$warehouse$\_$location$($location$\_$coords, R$)$:

assert R $>0\mathrm{.}0,$ 'radius must be positive'

n $=$ len$($location$\_$coords$)$

prob $=$ LpProblem$(\text{'}$Warehouselocation$\text{'},$ LpMinimize$)$

#$1.$ Formulate the decision variables

#$2.$ Add the constraints for each vertex and edge in the graph.

#$3.$ Solve and interpret the status of the solution.

#$4.$ Return the result in the required form to pass the tests below.

# your code here

raise NotImplementedError

from matplotlib import pyplot as plt

def check$\_$solution$($location$\_$coords, R$,$ warehouse$\_$locs$)$:

# for each location i$,$ calculate all locations j within distance R of location i

# use list comprehension instead of accumulating using a nested for loop.

n $=$ len$($location$\_$coords$)$

assert all$($j $>=0$ and j $<$ n for j in warehouse$\_$locs$),$ f'Warehouse locations must be between $0$ and $\{$n$-1\}\text{'}$

neighborhoods $=[[$j for j in range$($n$)$ if euclidean$\_$distance$($location$\_$coords, i$,$ j$)<=$ R$]$ for i in range$($n$)]$

W $=$ set$($warehouse$\_$locs$)$

for $($i$,$ n$\_$list$)$ in enumerate$($neighborhoods$)$:

assert any$($j in W for j in n$\_$list$),$ f'Location # $\{$i$\}$ has no warehouse within distance $\{$R$\}.$ The locations within distance $\{$R$\}$ are $\{$n$\_$list$\}\text{'}$

print$(\text{'}$Your solution passed test'$)$

def visualize$\_$solution$($location$\_$coords, R$,$ warehouse$\_$locs$)$:

n $=$ len$($location$\_$coords$)$

$($xCoords$,$ yCoords$)=$ zip$(*$location$\_$coords$)$

warehouse$\_$x$,$ warehouse$\_$y $=[$xCoords$[$j$]$ for j in warehouse$\_$locs$],[$yCoords$[$j$]$ for j in warehouse$\_$locs$]$

fig, ax $=$ plt$.$subplots$()$

ax$.$set$\_$aspect$(\text{'}$equal$\text{'})$

plt$.$scatter$($xCoords$,$ yCoords$)$

for j in warehouse$\_$locs:

circ $=$ plt$.$Circle$($location$\_$coords$[$j$],$ R$,$ alpha$=0\mathrm{.}5,$ color$=\text{'}$g$\text{'},$ls$=\text{'}--\text{'},$lw$=2,$ec$=\text{'}$k$\text{'})$

ax$.$add$\_$patch$($circ$)$

for i in range$($n$)$:

$($x$,$y$)=$ location$\_$coords$[$i$]$

ax$.$annotate$($f$\text{'}\{$i$\}\text{'},$ location$\_$coords$[$i$])$

plt$.$scatter$($warehouse$\_$x$,$ warehouse$\_$y$,$ marker$=\text{'}$x$\text{'},$c$=\text{'}$r$\text{'},$ s$=30)$

location$\_$coords $=[(1,2),(3,5),(4,7),(5,1),(6,8),(7,9),(8,14),(13,6)]$

R $=5$

locs $=$ solve$\_$warehouse$\_$location$($location$\_$coords, R $)$

print$($f$\text{'}$Your code returned warehouse locatitons: $\{$locs$\}\text{'})$

assert len$($locs$)<=4,$ f'Error: There is an solution involving just $4$ locations whereas your code returns $\{$len$($locs$)\}\text{'}$

visualize$\_$solution$($location$\_$coords, R$,$ locs$)$

check$\_$solution$($location$\_$coords, R$,$ locs$)]$

such that it passes the following test:from matplotlib import pyplot as plt

def check$\_$solution$($location$\_$coords, R$,$ warehouse$\_$locs$)$:

# for each location i$,$ calculate all locations j within distance R of location i

# use list comprehension instead of accumulating using a nested for loop.

n $=$ len$($location$\_$coords$)$

assert all$($j $>=0$ and j $<$ n for j in warehouse$\_$locs$),$ f'Warehouse locations must be between $0$ and $\{$n$-1\}\text{'}$

neighborhoods $=[[$j for j in range$($n$)$ if euclidean$\_$distance$($location$\_$coords, i$,$ j$)<=$ R$]$ for i in range$($n$)]$

W $=$ set$($warehouse$\_$locs$)$

for $($i$,$ n$\_$list$)$ in enumerate$($neighborhoods$)$:

assert any$($j in W for j in n$\_$list$),$ f'Location # $\{$i$\}$ has no warehouse within distance $\{$R$\}.$ The locations within distance $\{$R$\}$ are $\{$n$\_$list$\}\text{'}$

print$(\text{'}$Your solution passed test'$)$

def visualize$\_$solution$($location$\_$coords, R$,$ warehouse$\_$locs$)$:

n $=$ len$($location$\_$coords$)$

$($xCoords$,$ yCoords$)=$ zip$(*$location$\_$coords$)$

warehouse$\_$x$,$ warehouse$\_$y $=[$xCoords$[$j$]$ for j in warehouse$\_$locs$],[$yCoords$[$j$]$ for j in warehouse$\_$locs$]$

fig, ax $=$ plt$.$subplots$()$

ax$.$set$\_$aspect$(\text{'}$equal$\text{'})$

plt$.$scatter$($xCoords$,$ yCoords$)$

for j in warehouse$\_$locs:

circ $=$ plt$.$Circle$($location$\_$coords$[$j$],$ R$,$ alpha$=0\mathrm{.}5,$ color$=\text{'}$g$\text{'},$ls$=\text{'}--\text{'},$lw$=2,$ec$=\text{'}$k$\text{'})$

ax$.$add$\_$patch$($circ$)$

for i in range$($n$)$:

$($x$,$y$)=$ location$\_$coords$[$i$]$

ax$.$annotate$($f$\text{'}\{$i$\}\text{'},$ location$\_$coords$[$i$])$

plt$.$scatter$($warehouse$\_$x$,$ warehouse$\_$y$,$ marker$=\text{'}$x$\text{'},$c$=\text{'}$r$\text{'},$ s$=30)$

location$\_$coords $=[(1,1),(1,2),(2,3),(1,4),(5,1),(3,3),(4,4),(1,6),(0,3),(3,5),(2,4)]$

## TEST $1$

R $=2$

print$("$R $=2$ Test:"$)$

locs $=$ solve$\_$warehouse$\_$location$($location$\_$coords, R $)$

print$($f$\text{'}$Your code returned warehouse locatitons: $\{$locs$\}\text{'})$

assert len$($locs$)<=4,$ f'Error: There is an solution involving just $4$ locations whereas your code returns $\{$len$($locs$)\}\text{'}$

visualize$\_$solution$($location$\_$coords, R$,$ locs$)$

check$\_$solution$($location$\_$coords, R$,$ locs$)$

print$(\text{'}$Test with R$=2$ has passed'$)$

## TEST $2$

print$("$R$=3$ Test:"$)$

R $=3$

locs$3=$ solve$\_$warehouse$\_$location$($location$\_$coords, R $)$

print$($f$\text{'}$Your code returned warehouse locatitons: $\{$locs$3\}\text{'})$

assert len$($locs$3)<=2,$ f'Error: There is an solution involving just $4$ locations whereas your code returns $\{$len$($locs$)\}\text{'}$