def print$\_$directions$($path$)$:

# Define the movement order with flipped y$-$coordinates

movement$\_$order $=[(0,1),(1,0),(0,-1),(-1,0)]$ # UP$,$ RIGHT, DOWN, LEFT

# Initialize lists for both paths

directions$\_$with$\_$jump $=[]$

directions$\_$without$\_$jump $=[]$

for i in range$($len$($path$)-1)$:

current$\_$position $=$ tuple$($map$($int$,$ path$[$i$]))$

next$\_$position $=$ tuple$($map$($int$,$ path$[$i $+1]))$

# Calculate the direction based on the movement order

for direction, $($dx$,$ dy$)$ in enumerate$($movement$\_$order$)$:

if $($next$\_$position$[0]-$ current$\_$position$[0],$ next$\_$position$[1]-$ current$\_$position$[1])==($dx$,$ dy$)$:

# Assign the corresponding direction based on the movement order

if direction $==0$:

directions$\_$with$\_$jump.append$("$DOWN$")$

directions$\_$without$\_$jump.append$("$DOWN$")$

elif direction $==1$:

directions$\_$with$\_$jump.append$("$RIGHT$")$

directions$\_$without$\_$jump.append$("$RIGHT$")$

elif direction $==2$:

directions$\_$with$\_$jump.append$("$UP$")$

directions$\_$without$\_$jump.append$("$UP$")$

elif direction $==3$:

directions$\_$with$\_$jump.append$("$LEFT$")$

directions$\_$without$\_$jump.append$("$LEFT$")$

break

else:

# Check for jump actions

dx$,$ dy $=$ next$\_$position$[0]-$ current$\_$position$[0],$ next$\_$position$[1]-$ current$\_$position$[1]$

if abs$($dx$)>1$ or abs$($dy$)>1$:

jump$\_$direction $="$UP$"$ if dy $>0$ else "DOWN" if dy $<0$ else "LEFT" if dx $<0$ else "RIGHT"

jump$\_$distance $=$ max$($abs$($dx$),$ abs$($dy$))$

directions$\_$with$\_$jump.append$($f$"$JUMP $\{$jump$\_$direction$\}\{$jump$\_$distance$\}$ steps"$)$

# For without$\_$jump, treat the jump as a series of regular moves

for $\_$ in range$($max$($abs$($dx$),$ abs$($dy$)))$:

directions$\_$without$\_$jump.append$("$UP$"$ if dy $>0$ else "RIGHT" if dx $>0$ else "LEFT" if dx $<0$ else "DOWN"$)$

else:

return "Invalid position transition in path"

# Return both paths

return directions$\_$with$\_$jump, directions$\_$without$\_$jump

def print$\_$goal$\_$number$\_$of$\_$nodes$($result$,$ goal$\_$state, allow$\_$jump$=$False, cost$=$None$)$:

# Check if a path was found

if result is None:

return $"$No path found."

# If a path is found, calculate the number of nodes

elif isinstance$($result$,$ list$)$:

path $=$ result

# Generate both paths

directions$\_$with$\_$jump, directions$\_$without$\_$jump $=$ print$\_$directions$($path$)$

# Calculate the number of nodes for both paths

num$\_$nodes$\_$with$\_$jump $=$ len$($directions$\_$with$\_$jump$)$

num$\_$nodes$\_$without$\_$jump $=$ len$($directions$\_$without$\_$jump$)$

# Format the output

with$\_$jump $="\{\}($with jump actions$)".$format$($goal$\_$state, num$\_$nodes$\_$with$\_$jump$)$

with$\_$jump$\_$cost $="".$format$(2**($num$\_$nodes$\_$with$\_$jump $-1))$

without$\_$jump $="\{\}($without jump actions$)".$format$($goal$\_$state, num$\_$nodes$\_$without$\_$jump$)$

without$\_$jump$\_$cost $="".$format$($cost$)$ if cost is not None else None

return with$\_$jump, with$\_$jump$\_$cost$,$ without$\_$jump, without$\_$jump$\_$cost

fix the code such that the path that includes jump actions doesnt replicate the path that doesnt include jump actions like this

RoboNav.txt ast

$4($with jump actions$)$

$[\text{'}$RIGHT$\text{'},$ 'JUMP RIGHT $3$ steps', 'RIGHT', 'JUMP RIGHT $2$ steps'$]$

$7($without jump actions$)$

$[\text{'}$RIGHT$\text{'},$ 'RIGHT', 'RIGHT', 'RIGHT', 'RIGHT', 'RIGHT', 'RIGHT'$]$