Create Knight's Tour Problem.py

Author: mohatagarvit

puzzles/Knight's Tour/C++/Knight's Tour Problem.py

@@ -0,0 +1,79 @@
+# Chessboard Size 
+n = 8
+  
+def isSafe(x,y,board): 
+    ''' 
+        A utility function to check if i,j are valid indexes  
+        for N*N chessboard 
+    '''
+    if(x >= 0 and y >= 0 and x < n and y < n and board[x][y] == -1): 
+        return True
+    return False
+  
+def printSolution(board): 
+    ''' 
+        A utility function to print Chessboard matrix 
+    '''
+    for i in range(n): 
+        for j in range(n): 
+            print(board[i][j],end =' ') 
+        print() 
+  
+  
+def solveKTProb(): 
+    ''' 
+        This function solves the Knight Tour problem using  
+        Backtracking. This function mainly uses solveKTUtil()  
+        to solve the problem. It returns false if no complete  
+        tour is possible, otherwise return true and prints the  
+        tour.  
+        Please note that there may be more than one solutions,  
+        this function prints one of the feasible solutions. 
+    '''
+      
+    # Initialization of Board matrix  
+    board = [[-1 for i in range(n)]for i in range(n)] 
+      
+    # move_x and move_y define next move of Knight.  
+    # move_x is for next value of x coordinate  
+    # move_y is for next value of y coordinate 
+    move_x = [2, 1, -1, -2, -2, -1, 1, 2] 
+    move_y = [1, 2, 2, 1, -1, -2, -2, -1] 
+      
+    # Since the Knight is initially at the first block 
+    board[0][0] = 0
+      
+    # Step counter for knight's position 
+    pos = 1
+      
+    # Checking if solution exists or not  
+    if(not solveKTUtil(board, 0, 0, move_x, move_y, pos)): 
+        print("Solution does not exist") 
+    else: 
+        printSolution(board) 
+  
+def solveKTUtil(board,curr_x,curr_y,move_x,move_y,pos): 
+    ''' 
+        A recursive utility function to solve Knight Tour  
+        problem 
+    '''
+      
+    if(pos == n**2): 
+        return True
+      
+    # Try all next moves from the current coordinate x, y 
+    for i in range(8): 
+        new_x = curr_x + move_x[i] 
+        new_y = curr_y + move_y[i] 
+        if(isSafe(new_x,new_y,board)): 
+            board[new_x][new_y] = pos 
+            if(solveKTUtil(board,new_x,new_y,move_x,move_y,pos+1)): 
+                return True
+              
+            # Backtracking 
+            board[new_x][new_y] = -1
+    return False
+          
+# Driver program to test above function  
+if __name__ == "__main__":  
+    solveKTProb()