Questions tagged [runtime-analysis]
Questions about methods for estimating the increase in runtime of an algorithm as the input size increases.
789
questions
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0answers
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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.
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0answers
22 views
proving long asymptotic bounds
I'm trying to find ways this simplify this formula and assuming numbers but that doesn't seem to help, the question is asking to prove or disprove:
$$ 3n(\log_{}n)^2 + 4n = \Omega (2n^2 \log_{}n +1) $...
0
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1answer
34 views
Why does this triple loop code have a running time of 1.5lnN * N^2
Hi all, I'm currently going through the Princeton Algorithms course on coursera, and I'm having trouble understanding the answer to this quiz. I think I understand where the $\frac{1}{2} N^2$ term ...
2
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1answer
23 views
number of comparisons in searching algorithms
i was going thorugh different searching algorithms,Linear,binary and ternary search.Now i want to know the number of comparisons in these.
For linear search :
...
0
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1answer
37 views
Derive a while loop (which seemingly have some logarithmic traits) runs in $\Theta(n)$
I know for a fact that algorithm A runs in $\Theta(n)$, but how does one derive that?
Algorithm A
...
1
vote
3answers
59 views
Derive a while loop runs in $\Theta( \sqrt{n} )$
I know for a fact that algorithm A runs in $\Theta(\sqrt{n})$, but how does one derive that fact?
Algorithm A
i = 0
s = 0
while s <= n:
s += i
i += 1
...
1
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1answer
60 views
Running time of algorithm (effect of j*j in for loops) - Theta Runtime
In Theta notation what are the running times of these algorithms?
Algorithm 1
for i=1..n
j=1
while j*j <= i:
j = j + 1
Since the outer loop ...
1
vote
1answer
48 views
Why in BFPRT (median of medians) algorithm the partition of the array by $7$ blocks would work but with the $3$ fail?
I am working with the median-median algorithm or BFPRT algorithm and I seek to understand why would the partition of the array by $7$ blocks would work but with the $3$ fail?
If we divide into ...
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3answers
110 views
How to prove that ($56n^2+106n+48)(\log(264n^2+200)) = Θ(𝑛^2\log n)$
I understand that essentially we have to prove that
$$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
25 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
18 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 ...
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0answers
23 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
43 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
22 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 ...
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0answers
40 views
Proof of the average case of the Heap Sort algorithm
Consider the following python implementation of the Heap Sort algorithm:
...
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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
58 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
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2answers
37 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
61 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
34 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
42 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
81 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
19 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 ...
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0answers
19 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
30 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 ...
-3
votes
2answers
82 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
votes
0answers
30 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
35 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 ...
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0answers
15 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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2answers
41 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
71 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
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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
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1answer
73 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
86 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
443 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
63 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
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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
49 views
Big Oh Time Complexity Involving 'for i in range(n)' [closed]
Given the code below and the comment analysis:
...
3
votes
1answer
492 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
53 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 ...
3
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0answers
47 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
81 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
42 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
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0answers
63 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 ...
