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
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 _______ _________ _____ _______ _________.
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____.
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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 _______ _________ _____ _______ _________.
_______ ___ ___ _______ _______.
___ ______ _____ ______ ______ __________ _________ ______.
________ ____ _____ ________ ___.
____ ________ ___ _____ ______.
_________ ____ ____ ______ _______ _______ _____ _____ _______ ______ _________ _____.
_________ _____ _________ ________ ______.
________ ____ __________ _______ ______ _________ ___ __________.
_____ _______ _______ ___ _____ ________ ____ _____ __________.
____ _____ _______ _____ ___ _________ _______ _______.
___ ________ ___ _____ _____.
_____ ____ ____ ______ _____ ___ _____ __________ _____ __________ _______ ____.
__________ ______ _____ ________ ____ ______ _________ ________ _______ _________.
_____ _____ _____ _____ ___ ________ _____ _______ ___ ___.
___ __________ ________ ________ ____ __________ ________ _________ ________ __________ ________.
__________ _________ _____ _________ __________.
_______ ____ ___ ____ ________ ___ _________.
___ _______ ___ _____ ___ ________ __________ ___ ______ _______ _______.
__________ __________ ________ ___ _______ _________ __________ _____.
___ ______ _______ _____ _____ _______ __________ _______ _________ _____ _______ ______.
________ ________ ______ ____ ________ ______ _____ ____ _________ ______.
____.
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Related Questions
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) Merge sort
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
Prove the following proposition using induction:
P(n): 1² + 2² + 3² + 4² + ... ... ... ... . + n² = n(n+1)(2n+1) / 6
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