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Consider the following recurrence. T(n)=T(n/2)+2T(n/4)+n n4, andT(n)=1 1n <4. Prove by induction that T (n) = O(n log n). More precisely show that T (n)

Consider the following recurrence. T(n)=T(n/2)+2T(n/4)+n n4, andT(n)=1 1n<4.

Prove by induction that T (n) = O(n log n). More precisely show that T (n) an log n + b for n 1 where a, b 0 are some fixed but suitably chosen constants (you get to choose and fix them).

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