26k views

Is there a system behind the magic of algorithm analysis?

There are lots of questions about how to analyze the running time of algorithms (see, e.g., runtime-analysis and algorithm-analysis). Many are similar, for instance those asking for a cost analysis ...
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255 views

Determining Big O [duplicate]

i<--2 while (i<n) someWork (...) i <-- power (i,2) done Given that someWork(...) is an O(n) algorithm, what is the worst case ...
192 views

How to get an O(n) for a search algorithm [duplicate]

Given an two sorted arrays X and Y, both of size n. Determine if there is an element x of X and an element y of Y such that x = 3y. The algorithm needs to run in linear time in the worst case. At the ...
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115 views

Analysis of Algorithms: Applying Concepts [duplicate]

I believe I understand the concepts of algorithm analysis. However, I'm not fully confident in applying those concepts. I'd appreciate help in bridging the gap between concept and application. I ...
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1 vote
144 views

What exactly is bigO notation? [duplicate]

I've heard of bigO notation but I don't really understand how do I determine it for my code and what exactly does it represent? I heard that there are two: RunTime Memory Complexity How can I learn ...
82 views

How to calculate Complexity Time O()? [duplicate]

Can anybody give me a way that i can use to calculate Complexity Time problems, i mean a way that will work on any complex code whatever it was. I can solve basic problems, but whenever the problem ...
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35k views

How does one know which notation of time complexity analysis to use?

In most introductory algorithm classes, notations like $O$ (Big O) and $\Theta$ are introduced, and a student would typically learn to use one of these to find the time complexity. However, there are ...
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35k views

Time complexity of a backtrack algorithm

I've developed the following backtrack algorithm, and I'm trying to find out it time complexity. A set of $K$ integers defines a set of modular distances between all pairs of them. In this algorithm, ...
15k views

How is the complexity of recursive algorithms calculated and do they admit better complexity than non-recursive algorithms?

How are asymptotical time complexities calculated for recursive algorithms? Recursive algorithms call themselves and therefore take up more space compared to non-recursive algorithms. But are they ...
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711 views

• 131
1 vote
125 views

Big-O in computer Science [duplicate]

As the title states, I am asking for how the big-O in asymptotic analysis is used in theoretical computer science. It would be helpful if an example would be given.
141 views

Understanding time complexity of algorithm to determine if parenthesis are matching

Both these algorithms determine if all the parenthesis in a string are balanced and properly nested. The first algorithm uses "a constant amount of memory, regardless of the length of the string.&...
60 views

Reccurrence equation and finding suitable algorithm

I'm given the following recurrence equation: \begin{align*} T(1) &= 0\\ T(n) &= T(n/2) + 1 && \text{when $n > 1$ is even}\\ T(n) &= T((n+1)/2) + 1 && \...
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81 views

Converting a algorithm to a runtime function

I need to find an upper limit for the runtime of $f(n)$. ...
• 143
1 vote
61 views

How to calculate the basic steps in Fibonacci sequences to get nFn and n^2

I am reading Algorithms by Sanjoy Dasgupta, Umesh Vazirani, Christos Papadimitriou and I am trying to understand how the number of steps $nF_n$ and $n^2$ were calculated. Here's the part of the book ...
70 views

Time complexity of this for-loop

I know, the inner loop here is O(log n). But, I get confused by the multiplication in the outer loop part. ...
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1 vote
66 views

Big-Oh of algorithm

I found an algorithm which sorts the digits of a number to its smallest form. IE 54321 ==> 12345. The algorithm looks like: ...
31 views

Am I doing this correctly? Recurrence Relations [duplicate]

The function is this: ...
19 views

Big o notation for the algo [duplicate]

Asked this at programmers Stack Exchange, was recommend to ask here : What would be the big o for the algo: for (i=0; i < n*n; i++) for(j=0; j<i*i; j++) ...
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