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Professor Caesar wishes to develop a matrix-multiplication algorithm that is asymptotically faster than Strassen’s algorithm. His algorithm will use the divide and conquer method, dividing each matrix into pieces of size $n/4 *n/4$,and the divide and combine steps together will take $\Theta(n^2)$ time. He needs to determine how many subproblems his algorithm has to create in order to beat Strassen’s algorithm. If his algorithm creates $a$ subproblems, then the recurrence for the running time $T(n)$ becomes $T(n)=aT(n/4)+\Theta(n^2)$.What is the largest integer value of $a$ for which Professor Caesar’s algorithm would be asymptotically faster than Strassen’s algorithm?
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