Tagged Questions

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

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1
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1answer
16 views

Amortize time for a counter with the operations INCREMENT and DECREMENT

Let a binary counter with the operations INCREMENT and DECREMENT. I need to show that you can't implement this kind of counter with constant amortized time per operation. Hence, I need to show ...
3
votes
1answer
35 views

Runtime of Euclidean Algorithm

Given two $n$-bits numbers $a$ and $b$, I am not sure on how to find the runtime of the euclidean algorithm for finding the $\gcd$ of $a,b$. The problem (for me) in here is that apart from the size of ...
0
votes
0answers
33 views

Runtime of “Look and Say” [duplicate]

I am trying to figure out what the time complexity is for a "Look and Say" sequence generator which receives an integer n and outputs the nth term in the look and say sequence. I'm looking at the ...
1
vote
1answer
13 views

Hamming Weight to find the sum of 1 bits in the range between A and B inclusive [on hold]

I am trying to find the sum of 1 bits in the range between A and B inclusive, where -2^31 <= A <= B <= 2^31 - 1 Input Format: The first line contains the number of test cases T ...
2
votes
1answer
20 views

Expressing pseudo-polynomial runtime solely in terms of the input size

In case we have an algorithm which is pseudo-polynomial and runs in $O(n^2C)$ for some $C$ that is encoded in binary. Is it correct to say that if $C=2^n$ then $O(n^2C)=O(n^22^n)$ and because ...
1
vote
0answers
32 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
1answer
22 views

Asymptotic runtime for querying an interval tree

Suppose that we have an array of size n and we want to build an interval tree for all possible ranges that can be created inside this array. So in our leafs we have ...
0
votes
1answer
35 views

Time/Space cost of Taxicab algorithm?

The following is an algorithm for generating "Taxicab numbers" using a priority queue (pq). Vector is an arbitrary data type ...
0
votes
0answers
35 views

What is the average runtime of appending items to arrays?

It is the time of the year again in colleges for final exams and I am preparing mine as of now and I am finding myself in hot water when it comes to understanding the running times of appending items ...
2
votes
1answer
75 views

Which algorithms have runtime recurrences like $T(n) = \sqrt{n}\,T(\sqrt{n}) + O(n)$?

The algorithms using the "divide and conquer" (wiki) design strategy often have the time complexity of the form $T(n) = aT(n/b) + f(n)$, where $n$ is the problem size. Classic examples are binary ...
-1
votes
0answers
21 views

Runtime of assembler program [duplicate]

I want to analyze the asymptotic runtime of a RAM program under the uniform and the logarithmic cost. To find the asymptotic runtime under the uniform cost do I just have to count the instructions?? ...
1
vote
1answer
15 views

Average Case runtime for random choice search

Assuming we have an array with $n$ Elements and want to find an unique element by randomly (uniformly) choosing. What would be the average case runtime? My thoughts so far: The chance to find the ...
1
vote
2answers
29 views

Calculating the runtime for a recursive algorithm [duplicate]

If the runtime of a recursive algorithm could be expressed as $T(n) = \begin{cases}O(1) & n \leq c \\ k * T\left(\frac{n}{k}\right) + \left(k + n * k \right)\end{cases}$ what would be the ...
1
vote
1answer
65 views

Find all $k$ local maximums in an array of length $n$ in $O(n \log k)$ time

Given a sequence of numbers $a_1, a_2, ..., a_n$, a number $a_i$ is called the $k$ local maximum $\iff i > k$ and $a_i$ is the largest number among the $(k+1)$ numbers $a_{i-k}, a_{i-k+1}, ..., ...
0
votes
1answer
30 views

Big O Notation Explained [duplicate]

Our teacher gave us the following definition of Big O notation: O(f(n)): A function g(n) is in O(f(n)) (“big O of f(n)”) if there exist constants c > 0 and N such that |g(n)| ≤ c |f(n)| for all n > ...
2
votes
1answer
46 views

How many comparisons in the worst case, does it take to merge 3 sorted lists of size n/3?

How many comparisons in the worst case, does it take to merge 3 sorted lists of size n/3? (where n is a power of 3) I was told it takes: $$2(n-2) + 1 = 2n-3$$ However, I can't seem to figure out ...
1
vote
1answer
29 views

Sorting with a recursive oracle

It is known that the runtime complexity of sorting is $\Theta (n \log n)$. But what if we have, for every input array of size $n$, an oracle that can sort any array of $k<n$ numbers in constant ...
8
votes
1answer
195 views

Solving recurrence relation with two recursive calls

I'm studying the worst case runtime of quicksort under the condition that it will never do a very unbalanced partition for varying definitions of very. In order to do this I ask myself the question ...
-1
votes
1answer
83 views

Runtime of nested loops

What is the asymptotic runtime of fthe ollowing piece of code in terms of number of updates to S in worst case. ...
1
vote
2answers
79 views

Finding recursion for runtime of code [duplicate]

This is the first time we have to do recursive/closed form expressions WITH code in class and I really have no idea how to approach this. My course notes that the prof put up don't really help as he ...
1
vote
1answer
50 views

Data structure for range-value-sum

I have to be able to perform insert, delete, range-value-sum, and range-2-max-values with a data structure. Range-value-sum(xl,xr): with a range [xl,xr] (for a range query), it reports the sum of ...
0
votes
0answers
30 views

Partial Sum operation & solution - Optimizing to O(logn)

I approached this problem where I have to write an add(key, value), insert(key, value), delete(key,value) and partial_sum(value) which reports the sum of all the elements in the structure that are ...
1
vote
1answer
73 views

What is the runtime of Mergesort if we switch to Insertion Sort at logarithmic depth?

Consider the Mergesort algorithm on inputs of size $n = 2^k$. Normally, this algorithm would have a recursion depth of $k$. Suppose that we modify the algorithm so that after $k/2$ levels of ...
0
votes
0answers
15 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++) ...
2
votes
1answer
57 views

What is the intuition behind the Potential Function in Amortized Analysis of some algorithm?

I have come across many amortized analysis using a potential function. They all look magical to me. Everything works perfectly but I never got the intuition behind how they come up with such a ...
0
votes
1answer
102 views

What is the runtime of the following code? [duplicate]

Can you explain to me how you get the Big O notation for the runtime of the following snippet of code? ...
1
vote
0answers
57 views

Influence of edge number and priority-queue implementation on the runtime of Dijkstra

When we try to find the shortest path of a directed weighted graph using Dijkstra’s algorithm, is there a relation between the number of edges/vertices of the graph and the different implementations ...
3
votes
0answers
24 views

Pruned FFT runtime

Pruned fast Fourier transforms compute only a specified subset of the result indices in faster time, although sometimes with a slower implementation constant (because FFT is generally so optimized). ...
2
votes
1answer
39 views

Why is Ibarra Kim for 0/1 knapsack an fully polynomial time approximation scheme (FPTAS)?

According to one of my CS lectures, there is an fully polynomial time approximation scheme for the 0/1 Knapsack problem. A first version was developed by Ibarra and Kim, but there are several improved ...
27
votes
3answers
5k views

Why is binary search faster than ternary search?

Searching an array of $N$ elements using binary search takes, in the worst case $\log_2 N$ iterations because, at each step we trim half of our search space. If, instead, we used 'ternary search', ...
1
vote
1answer
131 views

Creating a binomial heap from an array in Θ(n) time

I'm studying binomial heaps. A book tells me that insertion of a node to a binomial heap take $\Theta(\log n)$ time. So given an array of $n$ elements it would take $\Theta(n \log n)$ time to convert ...
-1
votes
1answer
60 views

Quick Sort Algorithm When Partition is Constant Time

I ran into a question about Quick Sort Algorithm. Suppose in Quick Sort, Partition procedure take C times, (need constant time). if we use random data as input, what is the order (time complexity) of ...
0
votes
0answers
19 views

How to conduct time complexity analysis for an implemented algorithm [duplicate]

Main task In my bachelor degree's thesis I've developed an algorithm for recommender systems which uses personalized PageRank with some particular features as nodes. In the recommender systems' ...
0
votes
1answer
74 views

tightest upper bound on binary search tree insertion? [closed]

The upper bound on the runtime of binary search tree insertion algorithm is O(n) which is if it is not balanced What will be the tighter upper bound on this,will it become O(logn) I have read that ...
-1
votes
4answers
263 views

Proving Quicksort has a worst case of O(n²)

I am sorting the following list of numbers which is in descending order. I am using QuickSort to sort and it is known that the worst case running time of QuickSort is $O(n^2)$ ...
0
votes
1answer
50 views

Inserting vertex in an adjacency matrix

If a graph with $v$ vertices is represented in the form of adjacency matrix . Then, adding a new vertex to the existing graph requires how much time ? Is it $O(v^2)$ or $O(2v)$ . We have the ...
-1
votes
1answer
79 views

How the below program is taking O(n!) time? [closed]

The complexity of the below program is given to be O(n!) ...
0
votes
1answer
43 views

Connection of “modern” runtimes and number of steps on a Turing machine

Why an evaluation of Turing machine efficiency is equal to the algorithm which is implemented by this machine and vise versa? For example, we can say that efficiency of merge sorting algorithm is ...
3
votes
0answers
116 views

Complexity of a naive algorithm for finding the longest Fibonacci substring

Given two symbols $\text{a}$ and $\text{b}$, let's define the $k$-th Fibonacci string as follows: $$ F(k) = \begin{cases} \text{b} &\mbox{if } k = 0 \\ \text{a} &\mbox{if } k = 1 \\ F(k-1) ...
2
votes
2answers
121 views

Where does the lg(lg(N)) factor come from in Schönhage–Strassen's run time?

According to page 53 of Modern Computer Arithmetic (pdf), all of the steps in the Schönhage–Strassen Algorithm cost $O(N \cdot lg(N))$ except for the recursion step which ends up costing $O(N\cdot ...
1
vote
1answer
46 views

Runtime analysis of sorting an array with known number of inversions

I'm having difficulties with analyzing the worst-case runtime of this following case: I'm given an array that has $n$ natural numbers. Out of all $\binom{n}{2} = \frac{n(n-1)}{2}$ possible pairs ...
4
votes
1answer
151 views

Complexity of Hopcroft-Karp

I have a rather basic question about the number of operations taken by the Hopcroft-Karp algorithm for finding a maximum matching in a bipartite graph. It is commonly reported as $O(m \sqrt{n})$ where ...
2
votes
1answer
60 views

What is the complexity of depth first traversal that don't label nodes as discovered?

I've found an algorithm that acts like a depth first traversal that don't recognizes nodes that have been visited before. A / \ B C \ / D | E If run ...
1
vote
2answers
87 views

How fast can we identifiy almost-duplicates in a list of strings?

I'm having trouble figuring out the upper bound running time for this scenario: Input: $N$ number of strings $M$ upper bound of string length $T$ threshold for edit distance (2 strings with a ...
2
votes
2answers
86 views

Why do compute time complexity for algorithms? [closed]

I read about Big-O notation with modular arithmetic. So, Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, where an elementary operation ...
0
votes
0answers
23 views

Using arithmetic progression sum to show an algorithm is both $\Theta(n^2)$ and $O(n^2)$ [duplicate]

Exercise 4 in http://discrete.gr/complexity/ askes to give an arithmetic progression sum to show that the following algorithm is both $O(n^2)$ and $\Theta(n^2)$. ...
1
vote
2answers
81 views

Time cost of thread creation

While creating an algorithm, the following question came up: In uniform cost, what is the time cost of a process that creates a thread? Is there a difference between creating a thread in a ...
4
votes
5answers
2k views

Optimal Algorithm for checking if a number is a multiple of three

I'm just starting a course on Computational Number Theory and have very little Computer Science background but definitely know enough about the big-O notation. I currently have an assignment to work ...
0
votes
0answers
49 views

What is the time complexity of Matlab's Hierarchical Clustering?

I'm using mat lab's implementation of hierarchical clustering algorithm, with pdist, linkage , cophenet, dendrogram, and cluster. But I'm not exactly sure where or how to find the time complexity It ...
2
votes
1answer
60 views

Number of iterations of the Euclidean algorithm

I have a doubt about the runtime of the Euclidean algorithm; the slide of my Professor says: The calculation of $\mathrm{GCD} (a, b)$ stops at the most after $2\log_2 a$ iterations. Since ...