# Question 4 (15 points) In class, we discussed a divide-and-conquer algorithm for matrix multiplication that involved...

###### Question:

Question 4 (15 points) In class, we discussed a divide-and-conquer algorithm for matrix multiplication that involved solving eight subproblems, each half the size of the original, and performing a constant number of e(n) addition operations. Strassen's Algo- rithm, which we did not cover, reduces the number of (half-sized) subproblems to seven, with a constant number of e(n) addition and subtraction operations. Provide clear, concise answers to each of the following related questions. • (7 points). Express the runtime of Strassen's Algorithm as a recurrence relation . (8 points). Using the substitution (induction) method, prove that this recurrence relation is bounded above by O(nº). Carefully show all of your steps, making it clear what you are assuming, and what you are trying to prove. • (5 points extra credit). Can you identify a tighter upper-bound? If so, prove it.

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