Add nqueens csp

csp-nqueens.py

@@ -0,0 +1,60 @@
+import numpy as np
+
+
+# 3 constraints 
+# no queens on the same row 
+# no queens on the same col 
+# no queens on the same diagonal
+
+
+def is_safe_row(board,n):
+    for row in range(n):
+        if sum(board[row,:]) > 1: # if there is a row with more than one queen, then its sum will be more than 1s
+            return False
+    return True
+
+def is_safe_col(board,n):
+    for col in range(n):
+        if sum(board[:,col]) > 1 : 
+            return False
+    return True
+
+def is_safe_diag(board,n):
+    diags = []
+    for i in range(-n+1,n):
+        # if the index i is negative, take the upper ith diagonal
+        # if the index i is positive, the the lower ith diagonal
+        diags.append(board.diagonal(i))
+
+    diags.extend(board.diagonal(i) for i in range(n-1,-n,-1))
+    for x in diags:
+        if len(x)>1:
+            if sum (x)>1:
+                return False
+    return True
+
+
+def nqueens (board, queen, n):
+    if is_safe_row(board,n) and is_safe_col(board,n) and is_safe_diag(board,n):
+        if board.sum()==n:
+            return True
+
+        for row in range (0,n):
+            board[row,queen] = 1
+            print(f'Queen: {row}')
+            if is_safe_row(board,n) and is_safe_col(board,n) and is_safe_diag(board,n):
+                if nqueens(board, queen+1,n):
+                    return True
+                board[row,queen] = 0
+            else:
+                board[row,queen] = 0
+    return False
+
+
+if __name__ == '__main__':
+    n = 4
+    board = np.zeros((n, n))
+    if nqueens(board, 0, n):
+        print(board)
+    else:
+        print('Cannot find a solution for ',n,' queens.')