Questions tagged [runtime-analysis]
Questions about methods for estimating the increase in runtime of an algorithm as the input size increases.
776
questions
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0answers
32 views
Proof of the average case of the Heap Sort algorithm
Consider the following python implementation of the Heap Sort algorithm:
...
0
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0answers
24 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
44 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
61 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
30 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
59 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 ...
1
vote
1answer
32 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
vote
1answer
37 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
...
0
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2answers
70 views
How to find i-th root of n whose remainder is the smallest?
Given a number n, what is the most assymptotically fast algorithm to express it in terms of base^exponent + rem such that rem is the smallest possible and base is limited from 2 to some relatively ...
2
votes
1answer
16 views
Analysis of straight insertion
I'm currently reading through N. Wirths': Algorithms + Data Structures = Programs. I'm not sure, but I think there might be an error in the analysis of the provided straight insertion sort. Screenshot ...
0
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0answers
11 views
How to apply AC-3(Arc-consistency 3) algorithm in N-Queen problem?
I am building N-Queen Solver with java.
I confused with AC-3 algorithm.
I heard that AC-3 can be applied with backtracking algorithm before processing and during the search.The latter is called MAC-3 ...
0
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0answers
28 views
Choosing algorithms and/or data structures at runtime based on input characteristics
I've been reading about Adaptive Computing, i.e. the idea of computer programs taking feedback from the environment at runtime to improve the output in some way. More precisely, my current focus is in ...
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votes
2answers
47 views
BigO time complexity of 3 nested for loops
I'm debating with a friend whether a particular function I wrote is $O(N^3)$ or $O(N \times M \times X)$
I believe it is the latter since all 3 variables differ in size. $N = 100, M = 50, X = 10000$
...
0
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0answers
9 views
Shortcuts/Patterns for being able to calculate the running time of a loop/algorithm? [duplicate]
This is my first question here. I, like many people, suffer from the lack of the ability to be able to determine the running time of algorithms just by looking at them. I've picked up on a few ...
0
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0answers
28 views
Big oh notation run time [duplicate]
I have this Question , I want the answer and show me how to solve it Please :
Analyze the running time of the following algorithm using Big-Oh notation
...
2
votes
1answer
29 views
Understanding proof of upper bound on complexity of recursive computation of graph chromatic polynomial
This question is about section 2.3 of Wilf's ``Algorithms and Complexity''
https://www.math.upenn.edu/~wilf/AlgoComp.pdf
in which he analyses the complexity of a recursive computation of the ...
0
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0answers
14 views
Growth rate and runtime [duplicate]
Sorry if this maybe a dumb question, just a little confused
But with Big-Oh notation, does it measure the runtime or growth rate of an algo? or both?
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votes
2answers
37 views
Karp-Rabin - what is the input for the worst case time complexity?
I'm trying to determine the input for the worst case time complexity of Karb-Rabin regardless of the used hash function. However, I'm seeing both of these answers on the Internet:
String "AAAAAAAA" ...
2
votes
1answer
43 views
Running time for Breadth-First-Search vs Depth-First-Search
Can someone explain why BFS is $O(V + E)$ whereas DFS is $\Theta(V + E)$.
I understand the definitions of both notations, but I just don't see why the bound for DFS should be tighter than that of BFS.
...
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0answers
73 views
Convex hull partition of a set of points
Given a set $S$ of $n$ points in $\mathbb R^2$, denote by $\mathrm{convb}(S)$ the boundary of the convex hull of $S$. Let
\begin{align*}
S_1 &= \mathrm{convb}(S)\\
S_{i+1} &= \mathrm{convb}\...
1
vote
2answers
41 views
Running time correct with Omega?
I have the following statement. I would say it's correct as it's either equal or higher than $\Omega(\log^{10}(n))$.
Because:
I know $\log(2^n) = n$.
By that I would guess the same goes for $\log(n^{...
0
votes
1answer
30 views
Big O of runtime operation n-m+1 [duplicate]
I have a loop that runs n-m+1 times where
m = len(list_m)
n = len(list_n)
for i in range(n-m+1):
Is this time complexity O(n-m+1)?
0
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0answers
19 views
Run time of pseudo code in big theta notation [duplicate]
I am looking for the run time of the following pseudo code.
...
0
votes
1answer
47 views
Worst Case Scenario for Quicksort algorithm with pivot element n/2
What would the worst case array look like if I decide to always take the element on the position $\frac{n}{2}$ as the pivot element?
I know that if I choose the left or rightmost element as pivot ,the ...
1
vote
3answers
83 views
What should I call algorithms with non-linear non-constant time?
I am writing a paper in which I want to refer to a group of algorithms. Some of these algorithms are of complexity O(NlogN), and some of the are more complex (e.g ...
2
votes
2answers
400 views
All superlinear runtime algorithms are asymptotically equivalent to convex function?
Is it true that every algorithm with runtime complexity of $T(n)=\Omega(n)$ satisfies that $T(n)=\Theta(f(n))$ for some convex function $f$?
All the examples that I could think of satisfy the above ...
2
votes
2answers
58 views
Is purely functional programming in some situations less efficient than imperative programming?
I am used to implementing algorithms in imperative languages. Many of the algorithms I have implemented use hash maps, hash sets, mutable arrays, heaps, doubly linked lists, etc. I understand that ...
0
votes
0answers
15 views
Why does the knapsack dynamic programming solution has runtime of O(nW)? [duplicate]
Can you please help me analyse the runtime of the knapsack dynamic programming (which i have seen somewhere is O(nW))?
This is the algorithm i an using:
Define M[i,s] to be the maximum value that ...
1
vote
1answer
48 views
Big Oh Time Complexity Involving 'for i in range(n)' [closed]
Given the code below and the comment analysis:
...
3
votes
1answer
491 views
Complexity of many constant time steps with occasional logarithmic steps
I have a data structure that can perform a task $T$ in constant time, $O(1)$. However, every $k$th invocation requires $O(\log{n})$, where $k$ is constant.
Is it possible for this task to ever take ...
0
votes
2answers
48 views
Does my solution converge to O(N) for worst-case time complexity?
Forgive me if this should be in StackOverflow or Mathematics instead!
I was given the following question at an interview:
...
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0answers
30 views
Time and space complexity of a recursive problem (code included)
I am having trouble finding out the time and space complexity for this recursive solution. I have to create a list of words in order of word length. Each word, must be one character insertion off from ...
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0answers
44 views
Worst Case Analysis of a Multivariate Recurrence of a Graph Algorithm
I have a graph algorithm that runs in:
$$ T(n, m) = \begin{cases}
c_1 & n \leq 2 \lor m = 1\\
T(n - i,\ m - j - k) + T(i, k) + c_2 m + c_3 n & m \leq (n-i)i\\
T(n - i,\ m) + T(i, m) + ...
1
vote
1answer
44 views
Are all hypothetical machine models for calculating runing time of an alogrithm same?
Im learning about time complexity analysis, and cant seem to figure out why do we consider a hypothetical machine that takes 1 unit of time for arithemitic and logical instructions and 1 unit of time ...
5
votes
1answer
67 views
How to prove that the time complexity of this algorithm is O($\sqrt{N}$)?
int n;
cin >> n;
int sum = 0;
for (int i = 1; sum <= n; i++) {
sum += i;
}
If I assumed that $N = 100$, the loop will run $13$ steps, ...
-1
votes
1answer
40 views
Mergable heap with no key knowledge cannot EXTRACT-MIN in $o(\log n)$ amortized time
We are looking into Fibonacci heaps in class at the moment, but I am stuck with this problem. Let $H$ be a mergable heap structure, by which is meant a data structure, where each element has a key, ...
1
vote
0answers
59 views
How to find big-O for an in-place perfect shuffle algorithm
I've found a simple algorithm to interleave two halves of an array in place. It involves swapping the first 1/2 of the items into the correct place, then unscrambling the permutation of the 1/4 of ...
0
votes
2answers
73 views
How to find the big o running time if the recursion function have different cases of recursion with different fraction of n?
How to find the big o running time if the recursion function have different cases of recursion with different fraction of n?
If I have a recursive function like this for example (This is just an ...
1
vote
2answers
31 views
Running time complexity of finding maximal power of divisor that divides natural number
Given $n \in \mathbb{N}$, a divisor $p\vert n$, I would like to efficiently find $e\in\mathbb{N}$ with $p^e \vert n$, and $e$ maximal with this property. I will assume that multiplication/division of ...
0
votes
1answer
45 views
algorithm analysis - complex dependant nested loop
First of all, I know there are many questions like this on the site. But I think this case is a bit different.
Consider the following code:
...
0
votes
1answer
24 views
Optimal scalability of a distributed algorithm
What's the optimal scalability of some algorithm when I implement it in a distributed manner?
Intuitively, it seems to me that any algorithm can scale at most linearly with number of computing nodes....
4
votes
0answers
47 views
Highest stack of rectangles
Suppose we have a set of $n$ dimensional rectangles $R = \{(x_{i,1}, \ldots, x_{i,n}), i \in 1 \ldots k\}$. We want to create the highest stack in say the first dimension such that each side of the ...
0
votes
0answers
38 views
Reccurent runtime
If $T(n) = T\left(\frac{n}{2}\right) + 5$ (binary search), then the runtime in Big-O notation is $O(\log(n))$.
If $T(n) = T\left(\frac{n}{2}\right) + 0$, then is it correct to say that the the ...
1
vote
1answer
44 views
Euclidean algorithm and well define ness on the underlying set
Euclidean algorithm is given below:
gcd($a$,$b$):
if $a=0$, return $b$
otherwise, return gcd($b \bmod a$, $a$)
Let us first argue that the algorithm terminates. The reason ...
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0answers
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Finding runtime of a recurrence relation with a fractional power
Consider the following algorithm and find the tightest Big-$O$:
Assume $\texttt{multiplyKS}$($A,B$) is $O(n^{1.58})$ and $\texttt{Add}($A,B$)$ is $O(n)$.
If my runtime is $T(n)$, I have:
Lines 1 ...
0
votes
3answers
68 views
What is the asymptotic complexity of the following code snippet?
for (i = 2; i < n; i = i * i) {
for (j = 1; j < i / 2; j = j + 1) {
sum = sum + 1;
}
}
I know that the outer loop can run for a maximum of $n^2$ ...
1
vote
1answer
41 views
Heap operating in time $\Gamma^{-1}(n)^2$
I have a priority queue implementation which I claim has the following worst case asymptotic run-times for the given operations:
PEEK_MIN …………………………… O(1)
POP_MIN…………………………… O( (INVERSE_Γ(n)) ^2).
...
4
votes
2answers
105 views
Run-time of Hungarian algorithm - matrix formulation
There are many different explanations of the Hungarian algorithm. My favorite explanation is the one based on matrices, for example here, since it is very intuitive and easy to carry out in a ...
2
votes
1answer
50 views
Djikstra algorithm analysis
My textbook says that the Dijkstra algorithm's runtime is $O(n) + O(m \log(n)) = O((n+m) \log(n))$. How did they come up with that?
Dijkstra algorithm pseudocode:
...
-1
votes
1answer
75 views
What would be the big-o time complexity of this scenario? [duplicate]
I am wondering what the time complexity of a for loop that increments the control variable, but also multiplies it inside the loop. For example
...
