minimax (#947)

* minimax.py

minimax algorithm is used for game like tic tac toe. It traces the path and selects the optimal move.

* minimax.py

Minimax is used in decision making and game theory to find the optimal move for a player, when your opponent also plays optimally. It is widely used in games like Tic-Tac-Toe, Chess.

* Delete minimax.py

* Update minimax.py

* Minimax is a backtracking algorithm that is used in game theory to find the optimal move for a player, assuming that your opponent also plays optimally

backtracking/minimax.py

@@ -0,0 +1,28 @@
+import math 
+
+''' Minimax helps to achieve maximum score in a game by checking all possible moves
+    depth is current depth in game tree. 
+    nodeIndex is index of current node in scores[].
+    if move is of maximizer return true else false
+    leaves of game tree is stored in scores[]  
+    height is maximum height of Game tree
+'''
+
+def minimax (Depth, nodeIndex, isMax, scores, height):  
+
+    if Depth == height:  
+        return scores[nodeIndex] 
+
+    if isMax: 
+        return (max(minimax(Depth + 1, nodeIndex * 2, False, scores, height),
+                    minimax(Depth + 1, nodeIndex * 2 + 1, False, scores, height))) 
+    return (min(minimax(Depth + 1, nodeIndex * 2, True, scores, height), 
+               minimax(Depth + 1, nodeIndex * 2 + 1, True, scores, height))) 
+
+if __name__ == "__main__": 
+ 
+    scores = [90, 23, 6, 33, 21, 65, 123, 34423] 
+    height = math.log(len(scores), 2) 
+
+    print("Optimal value : ", end = "") 
+    print(minimax(0, 0, True, scores, height))