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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Why using heuristics in an algorithm takes away asymptotic optimality?
I was reading about some geometric routing algorithms, there it says that when employing heuristics in a version of the main algorithm it may improve performance, but takes away asymptotic optimality.
Why is that the case? Should we prefer…
Kristof Pal
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Asymptotic proof examples
I came across two asymptotic function proofs.
f(n) = O(g(n)) implies 2^f(n) = O(2^g(n))
Given: f(n) ≤ C1 g(n)
So, 2^f(n) ≤ 2^C1 g(n) --(i)
Now, 2^f(n) = O(2^g(n)) → 2^f(n) ≤ C2 2^g(n) --(ii)
From,(i)…
Andrew
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What is the asymptotic running time for variance?
As you can see I'm still pretty new with all these run time analyses and want to make sure each step I'm calculating is right..
Also I hate writing in pseudocode form so I did this in Python instead.. here goes
def mean(n):
sum = 0 …
compski
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Instruction execution of a C++ code
Hello I have an algorthm in C++ and I want to find the instructions executed. The code is below
cin >> n;
for(i=1;i<=n;i++)
for (j = 1; j <= n; j ++)
A[i][j] = 0;
for(i=1;i<=n;i++)
A[i][i] = 1;
now, after my calculation, I got this…
helpdesk
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Asymptotic lower bound of O(n^2)
Are there problems in P that have a proven asymptotic lower bound of O(n^2) or higher? (n is the number of bits a problem instance can be represented by). This is not a homework question, just curiosity.
Konstantin Weitz
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Proving log(n!) is in Ω(n log(n))
The total cost of our operations are: Σ(i=1 to n) log(i).
Prove that this sum is Ω(n log(n)).
I'm a little bit stuck on how to go about proving this. I realize the summation comes out to be log(n!), since log(1) + log(2) + log(3) = log(3!) (and so…
user677786
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Is this generalization of Big-Theta notation correct?
Say you have an algorithm that completes in a polynomial number of steps for the input of size n, like, for example, P(n)=2n^2+4n+3. The asymptotic tight bound for this algorithm Θ(n^2).
Is it true to say that the Big-Theta notation for any…
Govind Parmar
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Studying for my final: Asymptotic notation
I am currently studying for my final in algorithms. This is not a homework problem and comes from an old final exam.
Show that f(n) = 4logn + log log n is big theta of logn.
It is obvious that log log n is considerably smaller than log n and thus…
SamuelN
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Is it true or false that, for any algorithm, its average-case performance is always better than the worst-case performance asymptotically
I'd like to think this is true, but I'm not too confident in that answer. Is there an algorithm that has an equal running time in the both the average and worst case. I'm not sure if the answer would be true then.
blutuu
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Different upper bounds and lower bounds of same algorithm
So I just started learning about Asymptotic bounds for an algorithm
Question:
What can we say about theta of a function if for the algorithm we find different lower and upper bounds?? (say omega(n) and O(n^2)). Or rather what can we say about…
supertoniefy
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Algorithm analysis (big-O) for algorithm
I'm trying to help a friend analyze the complexity of his algorithm but my understanding of Big-O notation is quite limited.
The code goes like this:
int SAMPLES = 2000;
int K_SAMPLES = 5000;
int i = 0; // initial index position
while (i <…
karlphillip
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Is (log n)^k = O(n^1/2)? For k greater or equal to 0
In big-O notation is O((log n)^k) = O(log n), where k is some constant right? So what's happening with the (log n)^k when k>=0?
User1911
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time complexity for the following
int i=1,s=1;
while(s<=n)
{
i++;
s=s+i;
}
time complexity for this is O(root(n)).
I do not understood it how.
since the series is going like 1+2+...+k .
please help.
SeasonalShot
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Computational complexity of for loops-Contradicting with myself
I have a contradiction by analyzing the running time of a program. For example, consider the following piece of code:
for(int i=0;i
user2110714
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Number of times a code is executed
I have a piece of code that says:
for i = 4,16, . . . , n
I am trying to find an upper bound in terms of big oh notation for the number of times the statement gets executed. I believe here it goes like 4,42,43 ... and so on. Since it grows…
yrazlik
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