Question

Please provide detailed step-by-step solutions! Will give thumb-up for a good answer. Thank you!

4. Suppose we want to multiply a chain of six matrices with dimensions 4-by-7,7-by-3, 3-by-2,2-by-6, 6-by-5,5-by-8, respectively. Trace the dynamic programming algorithm Matrix-Chain-Order in Section 15.2 of the Cormen textbook. Then determine which one of the following items has the correct value. a) m[3][6)-188 b) m[21161-296 c) m[1161 300 d) m[5]16] 248

Answer 1

The Correct Option is 'a'

Matrix chain multiplication using Dynamic programming In order to Find the minimum Cost for multiplying the matrix we are using the following equation in dynamic programming. M [I, j] = min { m [i, k], + m [k + 1, j] + d_i - 1*d_k *d_j } for example, In order to multiply 3 matrices A_2 times 1 middot B_1 times 5 middot C_5 times 2 How many Possibility We have I am just writing the different possibility (A middot B) C A (B middot C) So we have two possibility here But in the given question we have 6 matrices. There will be (^(2 times 6)C_6 times 1/ 6 + 1) possibility hare (^12 C_6 times 1/6 +1) is the certain number and don't get confuse about it Coming back to given problem we need to find different possibilities like A_1, A_2, A_2 times A_2 times A_3, . . . .