# Kenneth Rosen Edition 7th Exercise 8.3 Question 10 (Page No. 535)

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Find $f (n)$ when $n = 2^{k},$ where $f$ satisfies the recurrence relation $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$

Use Master Theorem with  $a = 1, b = 2, c = 1, d = 0.$

Since $a = b^{ d} ,(d=log_{a}b)$

we know that f(n) is   $O(n^{ d} log n) = O(log n).$

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