Questions tagged [runtime-analysis]

Questions about methods for estimating the increase in runtime of an algorithm as the input size increases.

Filter by
Sorted by
Tagged with
1
vote
2answers
240 views

3 * O(n^2) vs O(n^3)

Currently while I was coding, I got a doubt. While I was solving a particular type of problem I found it to be solved in $O(n^3)$. I have broken that problem and solved it in $O(n^2)$. But to ...
0
votes
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
206 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 ...
2
votes
2answers
88 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 ...
2
votes
2answers
550 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 ...
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
151 views
3
votes
1answer
500 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 ...
3
votes
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) + ...
0
votes
2answers
61 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: ...
1
vote
0answers
36 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 ...
1
vote
1answer
45 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 ...
0
votes
2answers
281 views

Is there a useful algorithm with a decreasing asymptotic time?

Algorithmic complexity is usually increasing and almost always strictly increasing based on input size. This is logical since algorithms take time to execute steps, and for almost all problems, the ...
2
votes
0answers
78 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 ...
5
votes
1answer
116 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
45 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, ...
0
votes
3answers
145 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
2answers
529 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
44 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
31 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
49 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 ...
1
vote
2answers
664 views

Time complexity of Dijkstra's algorithm for sparse graph

I'm not sure I understand the answer to this question: Question 9. What is the running time of Dijkstra's algorithm in a graph that is sufficently sparse - in particular, $E=o(V^2/\log V)$, ...
2
votes
4answers
485 views

Why aren't primality tests easily linear in time complexity?

Why don't we consider them as linear? I don't understand. You just have to check for factorization up to sqrt of n. So it's even faster than linear. I assume it's not linear only if we compare the ...
1
vote
1answer
54 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 ...
0
votes
0answers
56 views

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 ...
1
vote
1answer
47 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
188 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 ...
-1
votes
1answer
112 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 ...
2
votes
1answer
58 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
vote
2answers
115 views

Running Time of Sorting Algorithm

Determine the asymptotic running time of the sorting algorithm maxSort. Algorithm maxSort(A) Input: An integer array A Output: Array A sorted in non-decreasing order ...
2
votes
1answer
195 views

Running Time for Finding Maximum

Consider the algorithm findMax that finds the maximum entry in an integer array. Algorithm findMax($A$) Input: An integer array $A$ Output: The maximum entry of $A$ ...
3
votes
1answer
73 views

Why $\Theta(n^2)$ multiplication of coefficient required for canonical form of polynomial?

I was working through a textbook (Probability & Computing by Michael Mitzenmacher & Eli Upfal) and am not able to understand the following: Let $F(x)$ be given as a product $F(x) = \prod_{...
2
votes
1answer
187 views

Complexity of brute force primality test in the number of digits

I'm wondering how to express the complexity of a brute force primality testing algorithm in the number of digits the number under test has. The brute force algorithm just checks whether $n$ is prime ...
0
votes
1answer
440 views

Why is a heap better than a linked list for implementation of a priority queue?

Using a heap, you have O(log(n)) insertion and O(log(n)) removal. Using a linked list, you have O(n) insertion and O(1) removal. Why is it better to have log-n for both than n for one and constant ...
2
votes
1answer
108 views

How to find efficiently the minimum modification to avoid close consecutive numbers?

I have an array of sorted numbers: arr = [-0.1, 0.0, 0.5, 0.8, 1.2] I want the difference (dist below) between consecutive ...
1
vote
0answers
58 views

Is this Time analysis strategy right?

I'm working in the time analysis for an algorithm with two optional optimizations variant applied and followed next approach: Create inputs of different lengths for the algorithm Using these inputs ...
0
votes
0answers
15 views

Runtime explanation of this function [duplicate]

I am trying to understand the runtime complexity of the below code in terms of n. I know that it is $Θ(n^{4/3})$, but I don't get why. I thought the outer loop runs $log(n)$ times, the second one ...
0
votes
4answers
890 views

What is the time complexity of this algorithm?

In my class my teacher calculated the time complexity for this algorithm, relative to the number of sum operations executed: She represented the cost of the algorithm by the following sum: $\sum\...
0
votes
1answer
27 views

Why $xx^TM$ requires $O(dk)$ operations?

Suppose $x \in \mathbb{R}^d$ and $M \in \mathbb{R}^{d \times k}$. Why $xx^TM$ requires $O(dk)$ operations?
0
votes
1answer
45 views

How do you find set of keywords present in set of words in linear time or log time?

I am trying to optimize a program, where I need to know whether a given set of keywords present in the set of words. I believe using the dictionary is the only way to optimize it. Any other technique ...
1
vote
3answers
89 views

Show that the following algorithm takes $O(n)$ time

You are given a linked list of size $n$. An element can be accessed from the start of the list or the end of the list. The cost to access any location is $\min(i,n-i)$, if the location being accessed ...
5
votes
1answer
65 views

Least number of guesses needed to determine all unknown subsets of a set

Say I have a set $\mathbb{S}=\{1,2,...,n\}$. I have an adversary who breaks up $\mathbb{S}$ into $k$ unknown and disjoint subsets. Denote this new set $\mathbb{A}$. I can guess any combination $s$ and ...
0
votes
1answer
49 views

What will be big O complexity for this loop? [duplicate]

I am not able to understand time complexity of this for loop. While outer loop is O(n) the inner loop jumps certain calculation. How to find the complexity? ...
0
votes
0answers
92 views

Worst case lower bound of binary search

For the question below, it is asking to prove the lower bound on the worst case is log(n). I have no problem proving this and the solution makes 100% sense to me. However, there is a comment at the ...
0
votes
1answer
87 views

Time complexity dependent on magnitude of input [duplicate]

I'm trying to analyze an algorithm that looks like this: def foo(L): for n in L: for x in range(n): ... What would be its time complexity?...
1
vote
1answer
361 views

Find the efficiency class

I have to find the efficiency class of this algorithm b = 3 a = 4 for i = 4 to n^2 if (i mod 2 == 0) a = a+2 else b = b*3 end for I ...
0
votes
1answer
144 views

Big O understanding given different input sizes

I have a question about big O notation. Let's say I have 3 algorithms which, for an input of size $n$, have time complexity $O(n)$, $O(n^2)$ and $O(n \log n)$, respectively. Assume that all 3 ...
1
vote
1answer
42 views

A hangman variation: determining a string by guessing substrings contained in it

I came up with this Hangman variation, where you must figure out the hidden word by asking whether a string is a substring of this word. E.g. if the hidden word is "abracadabra" and I guess "cad" I ...
3
votes
1answer
2k views

What is a computer year?

In one of the text book its mentioned that 'running time of this algorithm is 200 computer years'. Can somebody please explain what is the meaning of a computer year?
0
votes
1answer
485 views

Big-O notation for nested loops that might skip iterations

When you have an algorithm that may skip a lot of iterations due to a hash table lookup, do you still count the iterations that are exited immediately? Hypothetical example: ...

1 2
3
4 5
17