Matrix chain multiplication

pydatastructs/MATRIX_CHAIN_MULTIPLICATION.py

@@ -0,0 +1,35 @@
+// Matrix Mi has dimension 
+// p[i-1] x p[i] for i = 1..n 
+def MatrixChainOrder(p, n): 
+
+	// For simplicity of the program, one 
+	/ extra row and one extra column are 
+	// allocated in dp[][]. 0th row and 
+	// 0th column of dp[][] are not used 
+	dp = [[0 for i in range(n)] 
+			for i in range(n)] 
+
+	// dp[i, j] = Minimum number of scalar 
+	// multiplications needed to compute 
+	// the matrix M[i]M[i+1]...M[j] = M[i..j] 
+	// where dimension of M[i] is p[i-1] x p[i] 
+
+	// cost is zero when multiplying one matrix. 
+	for i in range(1, n): 
+		dp[i][i] = 0
+
+// Simply following above recursive formula. 
+	for L in range(1, n - 1): 
+		for i in range(n - L): 
+			dp[i][i + L] = min(dp[i + 1][i + L] +
+							p[i - 1] * p[i] * p[i + L], 
+							dp[i][i + L - 1] +
+							p[i - 1] * p[i + L - 1] * p[i + L]) 
+
+	return dp[1][n - 1] 
+
+// Driver code 
+arr = [10, 20, 30, 40, 30] 
+size = len(arr) 
+print("Minimum number of multiplications is", 
+				MatrixChainOrder(arr, size))