Questions tagged [runtime-analysis]
Questions about methods for estimating the increase in runtime of an algorithm as the input size increases.
816
questions
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9 views
What is an $O(n \log(n))$ binary sorting algorithm with a guaranteed low scaling constant on the run-time?
Let $O_c(f(n))$ denote that $c$ is the scaling constant for the run-time (e.g. $\text{run time} \leq c\cdot f(n) + B$ if $n$ is large enough)
The absolute lower limit on the run-time for a binary ...
1
vote
1answer
17 views
If I walk through list and delete every out-of-order element I come across, on average how many elements will be left?
I have a uniformly randomly permuted list of length $n$. I walk through the list element-by-element, and delete an element if it's out-of-order (compared to the previous in-order elements of the list)....
2
votes
1answer
46 views
Why is the run time with a loop of this structure considered O(log n)
I used the search function and a good amount of google searches, but wasn't able to get a straight answer on how a loop of the form below, is translated to a proper summation where the function ...
1
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0answers
31 views
Hypothetical Situation for sorting in $O(n)$ using median finding machine that works in $O(\sqrt{n})$
In a hypothetical world, we have a machine that can find median of $n$
numbers in $O(\sqrt{n})$. (Of course this machine is not real).
Can we use this machine to sort an array in $O(n)$?
I don'...
2
votes
1answer
23 views
What's the decoding time complexity of LT codes?
LT codes are practical fountain codes that are near-optimal erasure correcting codes.
Simply stated, for encoding a $n$-block message, each packet first chooses a degree $d\in\{1,\ldots,n\}$ ...
1
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0answers
35 views
Which function grows faster: N Log N or N^(1+ε/√(log N)) [duplicate]
How would you go about solving this problem?
I thought about using a limit infinity approach, but got confused and Wolfram Alpha didn't provide any explanation.
0
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1answer
52 views
Understanding $O(2^n)$ time complexity due to recursive functions
Consider the following binary recursive fibonassi program:
...
2
votes
2answers
166 views
Complexity of cyclic sort
I have this algorithm ("cyclic sort") to sort an array which contains unique numbers from 1 to $n$:
...
2
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1answer
53 views
How memory controller reads from RAM with O(1) time complexity?
I am trying to understand how a RAM memory controller gets data with instant access while reading through the memory. Let's say initially, ram gets the data at address 0 and then to get the data at ...
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0answers
15 views
Simulating Boolean Circuit with RAM
Statement:
Every $T(n)$ size bounded Boolean circuit family, could be simulated with $(T(n))^2$ time bounded Random Access Turing Machine (RAM).
Could you please supply me with a reference to an ...
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0answers
13 views
Ideal time complexity in analysis of distributed protocol
I need some explanation about the definition of ideal time complexity.
My textbook says:
The ideal execution delay or ideal time complexity, T: the execution
delay experienced under the ...
3
votes
1answer
20 views
Smoothed analysis of the Partition problem
I am studying smoothed analysis and trying to apply it to the Partition decision problem: given $n$ real numbers with a sum of $2 S$, decide whether there exists a subset with a sum of exactly $S$.
...
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1answer
39 views
Why is $T(n)=3T(n/4) + n\log n$ solvable with Master Method but $T(n)=2T(n/2) + n\log n$ is not?
I am having difficulties in understanding why the recurrence
$$T(n)=3T(n/4) + n\log n$$
is solvable with Master Method but
$$T(n)=2T(n/2) + n\log n$$
isn't?
Despite they both look very similar ...
0
votes
1answer
37 views
In Big-O notation, what does it mean for T(n) to be upper bounded by something
I do not have much experience in mathematics but I would really like to grasp Big-O notation on its mathematical level. I already read What does the "big O complexity" of a function mean? ...
2
votes
1answer
48 views
Worst case runtime for binary search
The run time of binary search is O(log(n)).
log(8) = 3
It takes 3 comparisons to decide if an array of 8 elements contains a given element.
It takes 4 comparisons in the example below.
python2.7
<...
3
votes
1answer
38 views
Is it possible to determine if 2 arrays contain the same elements (ignoring duplicates) in faster than O(n log n) time?
So given 2 arrays of equal length, is it possible to determine whether the 2 arrays contain the same elements (ignoring duplicates and where those elements have a total order relation) with time ...
0
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1answer
27 views
runtime to a BFS flood-fill with multiple centres?
If we have a flood fill algorithm which, given a number of centres reprenting pixels on an image, runs a BFS flood-fill on them, checking the pixels 4 neighbours, changing their colours and adding ...
0
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1answer
42 views
Upper bound for runtime complexity of LOOP programs
Recently I learned about LOOP programs, which always terminate and have the same computational power as primitive recursive functions.
Furthermore primitve recursive functions can (as far as I ...
5
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0answers
146 views
Time Complexity for Nearest Neighbor Searches in kd-trees
Nearest neighbor searches in kd-trees run in logarithmic time, as shown by Friedman et al. However, I have some difficulty to fully understand the proof.
In order to calculate the average number of ...
0
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0answers
29 views
sequence of insert and delete operation in (2,3)-tree
I need help by understanding a theorem and its proof from a script. It says "There is a sequence of $n$ insert and delete operations in a (2,3)-tree that require $\Omega ($n log n$)$ many split and ...
0
votes
1answer
17 views
Determining whether a change in an memoized algorithm will improve the performance
I have an algorithm that constructs an optimal binary tree using dynamic programming. After introducing what I thought would be an optimization, the algorithm became over 2 times slover. Question: Is ...
1
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1answer
38 views
Is log(n) equivalent to (log(n))^x for big-O analysis?
My professor noted that we could treat any logarithmic function with an exponent as equivalent to log(n) for the purposes of big-O analysis.
ie. $(n log(n) + 1)^2 + (log(n) + 1)(n^2 + 1)$
From the ...
0
votes
1answer
53 views
Time Complexity of the below code? [duplicate]
here is a nested loop where all the variable are integers.This is another question to the thread. I understood the solution part , but stuck in the time-complexity part.
What is the time complexity ...
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3answers
61 views
How to mathematically prove that a relation T(n)=T($\sqrt{n}$)+c is O(log(log(n))?
following question, I understood the intuition behind how cutting down the size of input by square root on each iteration leads to O(log(log(n))) complexity.
I tried to derive it on paper.
Let T(n) =...
2
votes
1answer
41 views
Time complexity of finding a node with no incoming edges in a DAG: O(n) or O(m+n)
I'm reading Algorithm Design by Jon Kleinberg. In section 3.6, in order to compute the topological ordering of a DAG, one first finds a root node in this DAG, then deletes it from the DAG. The author ...
1
vote
1answer
28 views
Given a set of sets, find the magnitude (number of elements) of the smallest set containing at least one element from each set
I know that the hitting problem is NP hard, but is it possible to find the magnitude of the smallest set? Also, provide the runtime.
0
votes
1answer
23 views
Necessary conditions for proving If f(n) = O(g(n)), then is log(f(n)) = O(log(g(n)))
I am learning about algorithmic complexities and I read that if f(n) and g(n) are asymptotically positive functions and if $f(n) =O(g(n))$ then the relationship $log(f(n)) = O(log(g(n)))$ holds.
I ...
0
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0answers
41 views
time complexity of 2 sum problem using binary search
this is a popular searching problem and the question is :
Given an array of integers that is already sorted in ascending order, find two numbers such that they add up to a specific target number.
The ...
1
vote
1answer
39 views
Do problems that have unary encodings automatically become unary languages?
This problem has confused me a lot, can any of you help me out.
Thank you.
0
votes
1answer
39 views
Why does this triple loop code have a running time of 1.5lnN * N^2
Hi all, I'm currently going through the Princeton Algorithms course on coursera, and I'm having trouble understanding the answer to this quiz. I think I understand where the $\frac{1}{2} N^2$ term ...
2
votes
1answer
35 views
number of comparisons in searching algorithms
i was going thorugh different searching algorithms,Linear,binary and ternary search.Now i want to know the number of comparisons in these.
For linear search :
...
0
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1answer
46 views
Derive a while loop (which seemingly have some logarithmic traits) runs in $\Theta(n)$
I know for a fact that algorithm A runs in $\Theta(n)$, but how does one derive that?
Algorithm A
...
1
vote
3answers
93 views
Derive a while loop runs in $\Theta( \sqrt{n} )$
I know for a fact that algorithm A runs in $\Theta(\sqrt{n})$, but how does one derive that fact?
Algorithm A
i = 0
s = 0
while s <= n:
s += i
i += 1
...
1
vote
1answer
67 views
Running time of algorithm (effect of j*j in for loops) - Theta Runtime
In Theta notation what are the running times of these algorithms?
Algorithm 1
for i=1..n
j=1
while j*j <= i:
j = j + 1
Since the outer loop ...
1
vote
1answer
153 views
Why in BFPRT (median of medians) algorithm the partition of the array by $7$ blocks would work but with the $3$ fail?
I am working with the median-median algorithm or BFPRT algorithm and I seek to understand why would the partition of the array by $7$ blocks would work but with the $3$ fail?
If we divide into ...
0
votes
3answers
159 views
How to prove that ($56n^2+106n+48)(\log(264n^2+200)) = Θ(𝑛^2\log n)$
I understand that essentially we have to prove that
$$c_1(n^2\log n)\le
(56n^2+106n+48)(\log(264n^2+200))
\le c_2(n^2\log n)\,.$$
I am confused on how to simplify this further? And ...
1
vote
1answer
28 views
Runtime-Analysis for single loop incremented by a factor of 3
So, I'm trying to understand how to get the run time of this loop:
for(int i = 1; i < n*n*n; i*=3) {...}
So, far I know:
loop starts at 1
finishes when $i &...
1
vote
1answer
33 views
Maximum-cardinality matching in unbalanced bipartite graphs
Let $G = (X+Y, E)$ be a bipartite graph, and suppose we want to find a maximum-cardinality matching in $G$.
The Hopcroft-Karp algorithm runs in time $O(|E|\sqrt{|V|})$, where here $|V| = |X|+|Y|$. So ...
0
votes
0answers
25 views
Time complexity of simple function related to bits
I am wondering about correct answer to this task from a yesterday's test:
A function Pow which calculates $y = a^k$ is given, where $k$ is an
integer of length ...
0
votes
1answer
49 views
What time complexity is more significant? [closed]
A certain algorithm executes $n$ operations of three types: insert, delete, and find.
We know that $n/10$ of the operations are inserts, and the rest are deletes and finds.
You are given two ...
0
votes
1answer
28 views
Complexity Class of an Algorithm with two Inputs
Consider a problem with two inputs like (P,L) and |P|=n and L is some positive integer. If my algorithm had a complexity of O(n^L), would that still be polynomial? Or is it exponential? I'm not sure ...
0
votes
0answers
46 views
Proof of the average case of the Heap Sort algorithm
Consider the following python implementation of the Heap Sort algorithm:
...
1
vote
1answer
63 views
Analyzing time complexity of solution in tutorial
Could someone explain time complexity of solution of in this tutorial?
I'm having hard time figuring out, how asymptotic bounds for first solution is $O(3^k k)$.
What I figured so far is, for ...
0
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0answers
26 views
How many inputs N can be placed into a function ln to get a certain amount of time?
it's "gardening" time, which means studying algorithms. A question in Intro to Algorithms 3rd Edition is a chart asking me how many of N inputs can be placed into a function to get a certain amount of ...
2
votes
1answer
63 views
runtime of 2 dependent nested for loops [duplicate]
for (i=1; i<=n ;i=i*2){
for (j=1; j<=i ;j++){
basic_step;
}
}
Regarding the above nested loops, I can't seem to understand why is the following ...
0
votes
3answers
64 views
Is there a unit of measurement that can express code execution speed in absolute terms?
I've always seen code execution speed measured either in units of time (e.g. t milliseconds), or using asymptotic analysis (e.g. O(n log n)). Execution speed will vary depending on hardware ...
0
votes
2answers
55 views
Karatsuba Multiplication Rule in dividing a Number in two parts
In Karatsuba algorithm for multiplying two numbers, we divide each number into two. For example:
x= 1234
y= 2456
Then a = 12, b = 34, c = 24 , d = 56
What if ...
1
vote
1answer
64 views
How to find an algorithm's complexity from actual running times
I have a certain algorithm which I can run, but I do not have access to its code. Thus, it works as a black box. I would like to now the order of complexity of this algorithm on a certain set of ...
2
votes
1answer
38 views
Average Case Running Time of Quicksort Algorithm
From this website, it states that the average case of Quicksort algorithm is
T(n) = T(n/9) + T(9n/10) + θ(n)
Im a bit confused. Is it supposed to be ?
...
1
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1answer
59 views
Recursion Time Complexity (Half n' Half)
This is my solution for Leetcode 395, and I'm wondering how I can come up with its time complexity:
Input: string $s = s_1,\ldots,s_n$, integer $k$
Go over all symbols $s_1,\ldots,s_n$, one by one
...
