Asymptotic complexity is an approximation of the edge case performance of an algorithm used to determine best and worst case scenarios.
Questions tagged [asymptotic-complexity]
796 questions
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votes
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Top K smallest selection algorithm - O (n + k log n) vs O (n log k) for k << N
I'm asking this in regards to Top K algorithm. I'd think that O(n + k log n) should be faster, because well.. for instance if you try plugging in k = 300 and n = 100000000 for example, we can see that O(n + k log n) is smaller.
However when I do a…
ryaner
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Big Oh notation (how to write a sentence)
I had a test about asymptotic notations and there was a question:
Consider the following:
O(o(f(n)) = o(f(n))
Write in words the meaning of the statement, using conventions from asymptotic notation.
Is the statement true or false? Justify.
I got…
Greg
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4 answers
efficiency of the closest pair algorithm
In T(n) = 2T(n/2) + M(n), where does the 2 in front of T come from. n/2 because it is dividing, and M(n) is linear, but I can't figure out what the 2 is for?
Aaron
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This algorithm's complexity is correct?
The algorithm I do not understand is :
alg(m, n)
1. if m>n then
2. return alg(m-n, n)
3. else
4. if n>m then
5. return alg(n, m)
6. else
7. return n
I think that the recurrence formula is T(m) = T(m-n) + a, where a is…
Cata
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Finding the right complexity classes for functions
I am trying to find the right complexity classes for these functions:
What I have so far is this. I will start from top to bottom:
Is this correct?
Nime
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Asymptotic analysis question: sum[log(i)*i^3, {i, n}] is big-theta (log(n)*n^4)
I've got a homework question that's been puzzling me. It asks that you prove that the function Sum[log(i)*i^3, {i, n}) (ie. the sum of log(i)*i^3 from i=1 to n) is big-theta (log(n)*n^4).
I know that Sum[i^3, {i, n}] is ( (n(n+1))/2 )^2 and that…
cjm
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Comparing functions asymptotically
I am given two functions: F1(n)=2n+20 and F2(n)=n+1. I have to show which one is better.
Our lecturer solved a similar problem. Given F1(n)=n2 and F2(n)=2n+20, he did:
F2(n)/F1(n)=(2/n)+(20/n2)
and he said it would be always less than 22, hence…
user9440643
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2
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Asymptotic Analysis compare f and g
I have to compare the function f and g to find whether:
f ∈ Θ(g), f ∈ O(g),
f ∈ o(g), f ∈ Ω(g),
f ∈ ω(g), g ∈ Θ(f),
g ∈ O(f), g ∈ o(f),
g ∈ Ω(f), g ∈ ω(f).
f(n) = n^2/ log n and g(n) = n log n.
As my understanding for the asymptotic analysis I…
Dan
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2 answers
Time complexity of naïve merge of two binary search trees
I saw a very short algorithm for merging two binary search trees. I was surprised how easy and also very inefficient it is. But when I tried to guess its time complexity, I failed.
Lets have a two immutable binary search trees (not balanced) that…
Martin Jiřička
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1 answer
Big O notation of this function
function A(n):
if n ≤ 10 then
return 1 fi;
x := 0;
for i = 1 to n do
x := x + 1 od;
return x * A(n/3) * A(n/6) * A(n/4)
My first idea was, that every call of A(n/c) is in O(log n) and since each has a for-loop from 1…
dYTe
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What is the difference between Work, Span and Time in parallel algorithm analysis?
When analysing parallel algorithms, we tend to focus Work(T1), Span(T∞) or time.
What I'm confused about is that if I was given an algorithm to analyse, what key hints would I need to look for, for Work, span and time?
Suppose this algorithm:
How…
S. Nas
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How to determine if a function is of a specific asymptotic type in algorithm analysis?
I'd like to have a better understanding of the asymptotic notation and how can one classify whether a function is of O notation of another function, and how can we tell whether f = o(g) || f != o(g)
For example:
For example, how can we tell that…
S. Nas
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Asymptotic notation properties proofs?
I am trying to prove that if f(n) and g(n) are asymptotically positive functions, then:
f(n) = O((f(n))^2)
f(n) = O(g(n)) implies 2^(f(n)) = O(2^(g(n)))
f(n) = O(g(n)) implies g(n) = O(f(n))
Hussam Hallak
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How would you n where one algorithm is preferred over another algorithm
I'm trying to compare two algorithms and their Big Oh efficiencies. I am trying to find the value for n where one algorithm becomes more efficient than the other algorithm. Any helpful examples or resources would be a huge help.
Patrick Hession
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Asymptotic time complexity
after reading many articles or answers I still can't solve a problem of determining the asymptotic time complexity o a function. The function is for example like this:
def function(n):
for i in range(n):
if i == 0:
for j in…
Denyk
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