I would appreciate if someone helps me understand how to change the Breadth First Search to Depth First Search, or which steps I need to follow.
The algorithm is basically in the next functions:
CODE:
import sys
import copy
from os import system
#Set the console title
system("title Michael Fiford - Breadth First N-Queen Solver")
class QueenSolver:
#Store for the amount of queens we're placing, or table size
tableSize = 0
#The alphabet, for nice cell referencing on the output
alphabet = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']
#The queue of possible moves that we will create and loop through
queue = []
#Whether or not the solver can be ran
canRun = False
def setup(self, queenNumber):
#Set the number of queens/table size
self.tableSize = queenNumber
#Can run, so long as there are no errors
self.canRun = True
#Show error if there is no solution, or would take too long
if queenNumber < 4:
print "ERROR: A solution is not available for this few number of queens"
self.canRun = False
elif queenNumber > 13:
print "ERROR: This solution would take too long to calculate, and your computer would probably run out of memory first!"
self.canRun = False
#Create an empty table
def blankTable(self):
table = []
for row in xrange(self.tableSize):
new = []
for col in xrange(self.tableSize):
new.append(0);
table.append(new)
return table
#Place a queen in a table
def placeQueen(self, table, row, col):
#Copy the table, as python is annoying and will change both
t2 = copy.deepcopy(table)
t2[row][col] = 1
return t2
#The main program loop
def loopBoard(self):
#The column we are currently looking at
col = 1
#Loop while the queue isn't empty, and there are still move possibilities to explore
while len(self.queue):
#Create a new empty queue
queue2 = []
#Update status
print col, "Queens Placed"
#Loop the queue, looking for positions from each status
#s is an array containing the current queen positions for this status
for s in self.queue:
#Get what moves are available from this status
availableMoves = self.getPositions(s, col)
#If we are placing the last queen, and there are solutions available, finish
if col == self.tableSize -1 and len(availableMoves):
#Clear queue
self.queue = []
#Get the solution (or one of them, we only care about the first one)
s = availableMoves[0]
break;
#Add the possible moves to the new queue
#This a table containing all queens now placed
if len(availableMoves):
queue2 += availableMoves
#Replace the old queue with the new one
self.queue = queue2
#Increase Queen/col counter
col += 1
self.finish(s, col)
#Get an array of moves that are available, given info about the current table, and the current column
def getPositions(self, table, col):
#Create a row counter, and array to contain our position info
row = 0
possiblePositions = []
#Loop all rows on the board
while row < self.tableSize:
#If we can place in this space
if self.canPlace(table, row, col):
#Add the table with the newly added queen to the list of possible moves
possiblePositions.append(self.placeQueen(table, row, col))
row += 1
return possiblePositions
#Check whether or not we can place a queen in a position, given the table and the row and col of the desired position
#Return True if space is available
def canPlace(self, table, row, col):
# - Direction
# Check left/right
x = 0
#Loop across the table
while x < self.tableSize:
if table[x][col]:
return False
x += 1
# | Direction
#Check up/down
y = 0
#Loop down the table
while y < self.tableSize:
if table[row][y]:
return False
y += 1
# / Direction
#Check up right Diagonal
#We can start in the cell 1 up and 1 right of the cell in question, as we have already checked the actual cell in the above 2 checks
x = row + 1
y = col + 1
#Loop up/right through the table
while x < self.tableSize and y < self.tableSize:
if table[x][y]:
return False
x += 1
y += 1
#Check down left Diagonal
#Again, not starting in the cell specified
x = row - 1
y = col - 1
#Loop down/left through the table
while x >= 0 and y >= 0:
if table[x][y]:
return False
x -= 1
y -= 1
# \ Direction
#Check up left diagonal
#Again, not starting in the cell specified
x = row - 1
y = col + 1
#Loop up left through the table
while x >= 0 and y < self.tableSize:
if table[x][y]:
return False
x -= 1
y += 1
#Check down right diagonal
#Again, not starting in the cell specified
x = row + 1
y = col - 1
#Loop down right through the table
while x < self.tableSize and y >= 0:
if table[x][y]:
return False
x += 1
y -= 1
return True
#Output a table to a user, looking all pretty
def display(self, table):
#Max Number Length, so we can indent our table nicely later
mnl = len(str(len(table)))
#New Line
print ""
#Top of the table, E.g " A B C D"
print " "*mnl, " ",
for x in range(self.tableSize):
print self.alphabet[x],
#New Line
print ""
#Row spacer, E.g " * - - - - *
print " " * mnl, " *",
for x in range(self.tableSize):
print "-",
print "*"
#Row Counter
#Print the actual table, with the Queens as 1's, empty space as 0
#Also prefixed by the row number, E.g " 3 | 0 1 0 0 |
x = 1
for row in table:
#If numbers are shorter than the largest number, give them extra spaces so the rows still line up
extraPadding = mnl - len(str(x))
#Show the number prefix, spaces, and | symbol, E.g " 6 | "
print "", x, " "*int(extraPadding) + "|",
#Show the value of the cell (1 or 0)
for col in row:
print col,
#End of the row
print "|"
#Next Row
x += 1
#Show the same row spacer as at the top of the table, E.g " * - - - - *
print " " * mnl, " *",
for x in range(self.tableSize):
print "-",
print "*"
#We're done! Show output to the user
def finish(self, table, col):
#If we found the right number of queens
if col == self.tableSize:
print ""
print "Total of", self.tableSize, "Queens placed!"
print "Solution:"
self.display(table)
else:
print ""
print "ERROR: Could not place all queens for some unknown reason =["
#Run the script
def run(self):
if not self.canRun:
print "ERROR: Can not run"
else:
print ""
print "Working..."
print ""
self.queue = self.getPositions(self.blankTable(), 0)
self.loopBoard()
#Ask the user how many Queens they want to use
def ask():
while True:
print ""
print "How many Queens would you like use? [8]"
input = raw_input()
#Check if the input given is an integer
if input.isdigit():
return int(input)
#If no input is given, use the standard 8
elif input == "":
return 8;
print "ERROR: Invalid Input"
#Run the program
def run():
#Instantiate the solver
qs = QueenSolver()
#While ask hasn't given a valid input
while(not qs.canRun):
qs.setup(ask())
print ""
#GO!
qs.run()
#Prompt the user if they want to run the program again
def prompt():
#Has valid input been received?
while True:
print ""
print "Would you like to run the script again? Please enter Y/N [N]"
input = raw_input()
#Check if the input given is Y or N
if input == "Y" or input == "y":
return True
#Also accept an empty string in place of N
elif input == "N" or input == "n" or input == "":
return False
print "ERROR: Invalid Input"
if __name__ == "__main__":
print ""
print ""
print " #######################################"
print " ## Breadth First Search Queen Solver ##"
print " ## By: Michael Fiford - COMF3 ##"
print " ## Date: 03/12/2013 ##"
print " #######################################"
#Run the script, and prompt them after if they want to run it again
shouldRun = True
while(shouldRun):
run()
shouldRun = prompt()
The difference between DFS and BFS is in the way you are exploring the nodes of the graph. In the DFS algorithm, you are first exploring the last node added into the stack (last in first out) whereas in the BFS algorithm, you are exploring it on the basis of first in first out (queue).
The resulting change is the code shoud be quite small: in the BFS algorithm, you could use a list to implement the stack, appending new node at the top of the stack and then exploring them:
l=[]
while len(l)>0:
new_node=l.pop()
l.extend(new_node.get_neighbors())
The change is quite small to switch to the BFS algorithm: you switch from a stack to queue. This is implemented in Python in the collections module as a deque (with an efficient implementation of popleft (getting the first item of the list and remove it) and append (appending an item at the end of the queue):
import collections
l=collections.deque()
while len(l)>0:
new_node=l.popleft()
l.extend(new_node.get_neighbors())
Your code can be rewritten to fit with the previous description:
while len(self.queue):
#Create a new empty queue
#queue2 = []
#Update status
print col, "Queens Placed"
#Loop the queue, looking for positions from each status
#s is an array containing the current queen positions for this status
s=queue.pop()
#Get what moves are available from this status
availableMoves = self.getPositions(s, col)
#If we are placing the last queen, and there are solutions available, finish
if col == self.tableSize -1 and len(availableMoves):
#Clear queue
self.queue = []
#Get the solution (or one of them, we only care about the first one)
s = availableMoves[0]
break;
#Add the possible moves to the new queue
#This a table containing all queens now placed
#if len(availableMoves):
# queue2 += availableMoves
queue.extend(availableMoves)
#Replace the old queue with the new one
#self.queue = queue2
#Increase Queen/col counter
col += 1
Let me know if you need more explanations. Hope this helps.