mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
831558d38d
* Adding nqueens.py for backtracking * Adding sum_of_subsets.py for backtracking * Update nqueens.py * Rename nqueens.py to n_queens.py * Deleting /other/n_queens.py
85 lines
2.4 KiB
Python
85 lines
2.4 KiB
Python
'''
|
|
|
|
The nqueens problem is of placing N queens on a N * N
|
|
chess board such that no queen can attack any other queens placed
|
|
on that chess board.
|
|
This means that one queen cannot have any other queen on its horizontal, vertical and
|
|
diagonal lines.
|
|
|
|
'''
|
|
solution = []
|
|
|
|
def isSafe(board, row, column):
|
|
'''
|
|
This function returns a boolean value True if it is safe to place a queen there considering
|
|
the current state of the board.
|
|
|
|
Parameters :
|
|
board(2D matrix) : board
|
|
row ,column : coordinates of the cell on a board
|
|
|
|
Returns :
|
|
Boolean Value
|
|
|
|
'''
|
|
for i in range(len(board)):
|
|
if board[row][i] == 1:
|
|
return False
|
|
for i in range(len(board)):
|
|
if board[i][column] == 1:
|
|
return False
|
|
for i,j in zip(range(row,-1,-1),range(column,-1,-1)):
|
|
if board[i][j] == 1:
|
|
return False
|
|
for i,j in zip(range(row,-1,-1),range(column,len(board))):
|
|
if board[i][j] == 1:
|
|
return False
|
|
return True
|
|
|
|
def solve(board, row):
|
|
'''
|
|
It creates a state space tree and calls the safe function untill it receives a
|
|
False Boolean and terminates that brach and backtracks to the next
|
|
poosible solution branch.
|
|
'''
|
|
if row >= len(board):
|
|
'''
|
|
If the row number exceeds N we have board with a successful combination
|
|
and that combination is appended to the solution list and the board is printed.
|
|
|
|
'''
|
|
solution.append(board)
|
|
printboard(board)
|
|
print()
|
|
return
|
|
for i in range(len(board)):
|
|
'''
|
|
For every row it iterates through each column to check if it is feesible to place a
|
|
queen there.
|
|
If all the combinations for that particaular branch are successfull the board is
|
|
reinitialized for the next possible combination.
|
|
'''
|
|
if isSafe(board,row,i):
|
|
board[row][i] = 1
|
|
solve(board,row+1)
|
|
board[row][i] = 0
|
|
return False
|
|
|
|
def printboard(board):
|
|
'''
|
|
Prints the boards that have a successfull combination.
|
|
'''
|
|
for i in range(len(board)):
|
|
for j in range(len(board)):
|
|
if board[i][j] == 1:
|
|
print("Q", end = " ")
|
|
else :
|
|
print(".", end = " ")
|
|
print()
|
|
|
|
#n=int(input("The no. of queens"))
|
|
n = 8
|
|
board = [[0 for i in range(n)]for j in range(n)]
|
|
solve(board, 0)
|
|
print("The total no. of solutions are :", len(solution))
|