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Results tagged with algorithms
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user 144324
An algorithm is a sequence of well-defined steps that defines an abstract solution to a problem. Use this tag when your issue is related to design and analysis of algorithms.
2
votes
1
answer
269
views
Prove by induction $T(n) = T(\lfloor\frac{n}{2}\rfloor)+n^2 \in \Theta (\log_2 n)$
Text of the problem:
Solve the following recurrence equation and prove it by applying the principle of
induction:
$T(n) = \begin{cases} 3, \ n \le 2 \\ T(\lfloor\frac{n}{2}\rfloor)+n^2, \ n \ge 3 \en …
- 145
1
vote
1
answer
92
views
Design an optimal algorithm that finds 2 array indices in a sorted array such that $A [i] + ...
Text:
Given a non-descending ordered array A and an integer k, design an algorithm to find,
if any, the indices of a pair of elements whose sum is equal to k.
Discuss the complexity and the optimality …
- 145
1
vote
2
answers
80
views
Determine the time complexity of repeated logarithm until not greater than 1
t <- n
while t>1 do
t <- log_2(t)
I tried to do it this way:
$f^\text{(1)}(t)=\log_2(t) \\ f^\text{(2)}(t)=\log_2\log_2(t) = \log_2^{(2)}(t) \\f^\text{(3)}(t) = \log_2^{(3)}(t) \\ f^\ …
- 145
0
votes
Determine the time complexity of repeated logarithm until not greater than 1
I got it: this algorithm has a nearly-constant complexity, specifically the complexity is $\Theta(\log^{*}(n))$ where $\log^{*}(n) \le 5 \ \forall n \le 2^{16}$
- 145