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Author: Manasi2001

Backtracking/Knight's_Tour.py

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+'''
+Aim: To check whether it is possible for a Knight to visit each
+         cell of the N*N chessboard without visiting any cell
+         twice starting from (X, Y) position.
+Intution: To visit each and every positions which are available from
+          the current position and recursively repeat this until
+          all the cells are covered.
+        
+'''
+
+from time import time
+
+
+def move_Knight(n, pos, move, ans, step):
+    x, y = pos
+
+    # Base Case
+    if step == n * n:
+        return ans
+    for i in move:
+        r = x + i[0]
+        c = y + i[1]
+        if 0 <= r < n and 0 <= c < n and not ans[r][c]:
+            ans[r][c] = step + 1
+            temp = move_Knight(n, (r, c), move, ans, step + 1)
+            if temp is not False:
+                return temp
+            ans[r][c] = 0
+    return False
+
+
+def Knight_Tour(n, pos):
+    x, y = pos
+
+    # All valid moves that a Knight can make
+    move = [[2, 1], [2, -1], [-2, 1], [-2, -1],
+            [1, 2], [1, -2], [-1, 2], [-1, -2]]
+
+    # To keep a track of already visited cells and
+    # Answer Matrix
+    answer = [[0]*n for i in range(n)]
+
+    # To mark (X, Y) cell as visited
+    answer[x][y] = 1
+
+    return move_Knight(n, pos, move, answer, 1)
+
+
+# ------------------------DRIVER CODE ------------------------
+
+if __name__ == "__main__":
+
+    # Input the initial Position of the Knight
+    N = int(input("Enter the size of the Chessboard: "))
+    X, Y = map(int, input("Enter Initial Position of the Knight: ").split())
+    start = time()
+    ans_mat = Knight_Tour(N, (X-1, Y-1))
+    if ans_mat is False:
+        print("Knight's Tour form the given initial position is not possible")
+    else:
+        print("The desired Knight's Tour :")
+        for i in ans_mat:
+            print("\t\t", *i)
+    print("Time taken: ", time()-start)
+
+'''
+
+Sample Working:
+    
+Enter the size of the Chessboard: 5
+Enter the Initial Position of the Knight: 1 1
+The desired Knight's Tour :
+                1 6 15 10 21
+                14 9 20 5 16
+                19 2 7 22 11
+                8 13 24 17 4
+                25 18 3 12 23
+Time taken:  0.10171318054199219
+
+COMPLEXITY:
+    
+     Time Complexity ->  O(8^N)
+     Space Complexity -> O(N^2)
+
+'''