Create game_optimal_strategy_DP.py

Author: careermonk

dynamic-programming/game_optimal_strategy_DP.py

@@ -0,0 +1,43 @@
+# Copyright (c) June 02, 2017 CareerMonk Publications and others.
+# E-Mail           		: [email protected]
+# Creation Date    		: 2017-06-02 06:15:46
+# Last modification		: 2017-06-02
+# Modified by		        : Narasimha Karumanchi
+# Book Title			: Algorithm Design Techniques
+# Warranty         		: This software is provided "as is" without any
+# 				 warranty; without even the implied warranty of
+# 				 merchantability or fitness for a particular purpose.
+
+def game(coins):
+	n = len(coins)
+	V = [[0 for i in range(n)] for j in range(n)]
+	#Initialize for length=1
+	for i in range(n):
+		V[i][i] = coins[i]
+
+	#Generate coins for length=2, 3 ....
+	#size+1 to include all coins!	
+	for l in range(2, n+1):
+		#start value range 0  & 1
+		for i in range(0, n):
+			#end coins changes based on i and length(l)
+			#size =2  -> [0, 1] [1, 2],[2, 3]
+			#size =3  -> [0, 2], [1, 3]
+			j = i + l - 1
+
+			#IMPORTANT: break when i or j index is not valid
+			if i >= n or i+1 >= n or i+2 >= n or j >= n:
+				break
+
+			#option 1: pick i	
+			path1 = coins[i] + min(V[i+2][j],V[i+1][j-1])
+
+			#option 2: pick j
+			path2 = coins[j] + min(V[i+1][j-1],V[i][j-2])
+			V[i][j] = max(path1, path2)
+	#print(V)
+	return V[0][n-1]
+
+# row of n coins
+coins = [4,  3,  3,  4,  2,  3]
+print game(coins)