Question
Solve the following recurrence Using Recursion tree method
(i) T(n) = 3T(n/3) + n
(ii) T(n) = 2T(n/2) + n²
(iii) T(n) = T(n/2) + T(n/4) + T(n/8) + n
Answer :
Word Count : 206
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Skip in 10
For (i) (T(n)=3T(n/3)+n): At level 0, the cost is (n). At level 1, there are 3 subproblems of size (n/3), each contributing (n/3), so total cost is (3 \cdot (n/3)=n). At level 2, there are (3^2) subproblems of size (n/3^2), total cost (3^2 \cdot (n/3^2)=n). Thus, each level contributes (n). The recursion continues until (n/3^k=1), giving (k=\log_3 n) levels. Hence,
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