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Questions and Answers
What is the first step in applying the recursion tree method to the recurrence $T(n) = 2T(\frac{n}{2}) + 4n$?
What is the first step in applying the recursion tree method to the recurrence $T(n) = 2T(\frac{n}{2}) + 4n$?
- Draw the recursion tree. (correct)
- Estimate the height of the tree.
- Identify the base case.
- Calculate the total contributions from leaf nodes.
What is the contribution from the leaves at the bottom of the recursion tree for $T(n) = 2T(\frac{n}{2}) + 4n$?
What is the contribution from the leaves at the bottom of the recursion tree for $T(n) = 2T(\frac{n}{2}) + 4n$?
- $4n$
- $4n^{\log_2 2}$
- $4n^2$
- $4n \log n$ (correct)
How does one compute the height of the recursion tree for the recurrence $T(n) = 2T(\frac{n}{2}) + 4n$?
How does one compute the height of the recursion tree for the recurrence $T(n) = 2T(\frac{n}{2}) + 4n$?
- $\log n$ (correct)
- $n$
- $\frac{n}{2}$
- $2n$
What characterizes the expansion of the recursion tree for $T(n) = 2T(\frac{n}{2}) + 4n$?
What characterizes the expansion of the recursion tree for $T(n) = 2T(\frac{n}{2}) + 4n$?
What is the total time complexity for the recurrence $T(n) = 2T(\frac{n}{2}) + 4n$ after applying the recursion tree method?
What is the total time complexity for the recurrence $T(n) = 2T(\frac{n}{2}) + 4n$ after applying the recursion tree method?
Flashcards
Recurrence Relation
Recurrence Relation
An equation that defines a function in terms of its own previous values.
T(n)
T(n)
A function that represents the time complexity of an algorithm.
Divide-and-conquer
Divide-and-conquer
Algorithm design technique. Breaking a problem into smaller subproblems, recursively solving them, and combining the results.
2T(n/2)
2T(n/2)
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4n
4n
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Study Notes
Example 1 - Recursion Tree Method
- Solve the recurrence relation: T(n) = 2T(n/2) + 4n
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