How to get this code to actually print out a grid to show the solution of the puzzle:

def solve$($lights$,$ current$\_$depth, max$\_$depth, presses$=[])$:

$"""$Recursive backtracking search with depth limit$."""$

if current$\_$depth $>$ max$\_$depth:

return

if all$\_$lights$\_$are$\_$off$($lights$)$:

print$($f$"$Solution found in $\{$current$\_$depth$\}$ steps:"$)$

for row, col in presses:

print$($f$"$Press button at $(\{$row$\},\{$col$\})")$

exit$($

# Try all possible button presses

for row in range$($len$($lights$))$:

for col in range$($len$($lights$[0]))$:

new$\_$presses $=$ presses $+[($row$,$ col$)]$ # Record the press in a new list

lights$\_$copy $=$ flip$($lights$,$ row, col$)$ # Create a copy to avoid modifying the original grid

solve$($lights$\_$copy, current$\_$depth $+1,$ max$\_$depth, new$\_$presses$)$ # Pass the updated presses list

def all$\_$lights$\_$are$\_$off$($lights$)$:

$"""$Checks if all lights in the grid are off."""

for row in lights:

for light in row:

if light:

return False

return True

def flip$($lights$,$ row, col$)$:

N $=$ len$($lights$)$

lights$[$row$][$col$]=1-$ lights$[$row$][$col$]$

# Toggle neighbors

if row $>0$:

lights$[$row $-1][$col$]=1-$ lights$[$row $-1][$col$]$

if row $<$ N $-1$:

lights$[$row $+1][$col$]=1-$ lights$[$row $+1][$col$]$

if col $>0$:

lights$[$row$][$col $-1]=1-$ lights$[$row$][$col $-1]$

if col $<$ N $-1$:

lights$[$row$][$col $+1]=1-$ lights$[$row$][$col $+1]$

return lights

def lights$\_$out$\_$solver$($N$)$:

lights $=[[1]*4$ for $\_$ in range$(4)]$ # All lights are initially ON

max$\_$depth $=0$

while True:

print$("$Searching with max$\_$depth $=",$ max$\_$depth$)$

solve$($lights$,0,$ max$\_$depth, $[])$

max$\_$depth $+=1$

# Example usage with a $3$x$3$ grid

lights$\_$out$\_$solver$(3)$

# If you get here, there was no solution on this path: backtrack