N-Queens

Author: Gaurav-pandey04

Maths/N-queens.py

@@ -0,0 +1,60 @@
+# Function to check is it safe to place queen at board[row][col]
+def isSafe(mat, row, col):
+ n = len(mat)
+
+ # check this col on upperSide
+ for i in range(row):
+ if mat[i][col]:
+ return False
+ 
+ # check upper diagonal on left side
+ for i, j in zip(range(row-1, -1, -1), range(col-1, -1, -1)):
+ if mat[i][j]:
+ return False
+ 
+ # check upper diagnoal on right side
+ for i, j in zip(range(row-1, -1, -1), range(col+1, n)):
+ if mat[i][j]:
+ return False
+ 
+ return True
+
+def placedQueen(row, mat):
+ n = len(mat)
+ 
+ # If all queens are placed return True
+ if row == n:
+ return True
+ 
+ # consider the row and try placing queen in all columns one by one
+ for i in range(n):
+ # check if queen can be placed
+ if isSafe(mat, row, i):
+ mat[row][i] = 1
+ if placedQueen(row+1, mat):
+ return True
+ mat[row][i] = 0
+
+ return False
+
+# Function to find the solution to N-Queens problem
+def nQueens(n):
+ # Intialise the board
+ mat = [[0 for _ in range(n)] for _ in range(n)]
+
+ # If the solution exist
+ if placedQueen(0, mat):
+ # to store column of the queens
+ ans = []
+ for i in range(n):
+ for j in range(n):
+ if mat[i][j]:
+ ans.append(j+1)
+ return ans 
+ else:
+ return [-1]
+
+if __name__=="__main__":
+ n = 4
+ ans = nQueens(n)
+ print(" ".join(map(str, ans)))