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# Questions tagged [algorithm-analysis]

Questions about the science and art of determining properties of algorithms, often including correctness, runtime and space usage. Use the [runtime-analysis] tag for questions about the runtime of algorithms.

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### How to compare n number of m-dimensional points among one another with minimum time complexity?

Suppose there are four points(n = 4) which are four dimensional(m = 4) . Lets say these points are - A(4,1,1,1) , B(3,2,1,1) , C(2,3,3,3) , D(1,4,4,4). What is the best data structure to compare all ...
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### 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'...
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### Proof: Quick Sort Is $O(n*logn)$

I was given the follow proof: $$T(n)=n+2T(\frac{n}{2})$$ Will prove that $$T(n)=O(n*logn)$$ For $2:$ $$T(2)=2+2T(1)=2\leq 2*log(2)$$ Assume it is correct for $n-1$ in particular for $\frac{n}{2}$ ...
6k views

### Computational complexity vs Computational cost

Is there a difference between the computational complexity and computational cost of an algorithm?
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### Induction to prove equivalence of a recursive and iterative algorithm for Towers of Hanoi

Using induction how do you prove that two algorithm implementations, one recursive and the other iterative, of the Towers of Hanoi perform identical move operations? The implementations are as follows....
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### How to detect self loop in graph using greedy algorithm if given list of number of degrees

if you are given list of n integers that represents the degree of a graph. How to detect if there self loop in the graph using greedy algorithm.
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### Why is my algorithm version so slow with this input?

Here I'm trying to do a comparison of two simple as possible algorithms, solving the symmetric travelling salesman problem, finding the optimal solution without the support of heuristics. I'm showing (...
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### Max sum cyclic path of fixed length in matrix

Given a matrix NxM of positive integer values and a starting position (that has value 0), determine the maximum sum path of length K that starts and ends at the aforementioned position. Legal moves ...
56 views

### Comparing asymptotic running time of two algorithms $\sqrt n$ and $2^{\sqrt{\log _{2}n}}$

Given two algorithms with their time-complexity $t_a(n)=\sqrt{n}$ and $t_b(n) = 2^{\sqrt{\log _{2}n}}$ and i have to show $t_b(n) = O(t_a(n))$. I´ve made a program to check this statement and it ...
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### Learning algorithm analysis

Im learning order of algorithm For x>=2, and rand(x) is function that return 1 value from 1 to x-1 which have uniform probability $\frac{1}{x-1 }$ And max(x,y) output bigger value and min(x,y) output ...
443 views

### What is the time complexity in big-O notation of Algorithm X?

Knuth's Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that solves the NP-complete problem exact cover (EC). (It actually finds all solutions to EC.) I do not ...
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### Algorithm Analysis - Binary Search Algorithm

The problem is from Data Structures and Algorithm Analysis Edition 3.2 (Java Version) Book from Clifford A. Shaffer. It is from the third chapter exercises, problem number 3.13.20. Below is how it is ...
176 views

### UCT (Upper Confidence bounds applied to Trees)

For UCT (Upper Confidence bounds applied to Trees), why If given infinite time and memory, UCT theoretically converges to Minimax. ? Besides, I do not quite understand how UCT deals with the flaw of ...
86 views

### How good (or bad) is my makeshift PRNG?

Say I have designed a makeshift PRNG for my personal amusement, now I would like to see how good it is. How do I benchmark its "randomness"? Ideally, I want to know a statistics test, such that if I ...
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 ...
22 views

### Partitioning a set based on binary predicate

Given a collection of objects $X = (x_0,x_1,...,x_{N-1})$ and a binary predicate $F$ which takes as parameters elements of the collection, find a better than $\mathcal{O}(N^2)$ algorithm which ...
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### Converting IPV4 address into Binary

So given an IP address it is converted into binary via calculating the binary of all different segments and then joining them. For example, 12.32.18.01 converted into a binary it would amount to this ...
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### When was the dynamic array first introduced as an example for amortized analysis?

I'm writing a report on amortized analysis, and I'm using the example of a dynamic array to explain each method. I think it would be nice to add a reference to when this example was first used, as it ...
2k views

### Time Complexity analysis for Map-Reduce model

I am trying to redesign my algorithm to run on Hadoop/MapReduce paradigm. I was wondering if there is any holistic approach for measuring time complexity for algorithms on Big Data platforms. As a ...
185 views

### Building maze to maximize shortest path, may be given waypoints and teleports

How would you go about solving this problem? Is it something that could be expected to be computed/solved within a couple of hours of given a starting area with (32) threads on 3.0GHz Xeon cores? (...
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### How to divide an unsorted list in linear time where every element in the first part is smaller than every element in the second list

How to divide an unsorted list into two equal parts in linear time, where every element in the first part is smaller than every element in the second part I tried to use QuickSort but in can result ...
2k views

### Longest Palindrome Brute Force

I'm confused by the running time of the following algorithm. I've been told it's $O(n^3)$, but there are only two loops. How can that be? ...
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### 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 ...
50 views

### Question about how can i determine if counting sort is the right option over other sorting algorithms

So, an exam's exercise asks me to find an alghoritm that can determine if counting sort is the best solution, otherwise use another optimal sorting algorithm. Now i find that solutions for that ...
121 views

### Runtime analysis of prime-set computation

I want to find the all primes between 2 and $k-1$. We can come up with an $O(k\log k)$ running time algorithm. I want to compute this set in $O(k)$ running time. For this algorithm is : we are ...
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### Predecessor-subgraph property

In the proof of the predecessor subgraph property (page 14 of the following notes) http://www.cs.sfu.ca/CourseCentral/307/binay/shortestpath.pdf $d[v_i] \geq d[v_{i-1}]+w(v_{i-1},v_{i})$ is assumed ...
29 views

### Hanoi towers recursive expression for EVERY algorithm

What the recursive algorithm for moving $n$ disks says, is: If $n > 1$, move $n-1$ discs from A to B. Move the $n$th disk from A to C. If $n > 1$, move $n-1$ discs from B to C. Let $T_n$ be ...
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### 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: ...
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### Study of cache behaviour of algorithms on Virtualbox

I want to study certain cache oblivious algorithms and cache behaviour of some other algorithms I wrote in general. I want to understand, is it advisable, if I do this study in an virtualized ...
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### What is the time complexity in solving a polynomial equation of degree N in one variable?

How easy/difficult(in terms of big-O) is it to solve polynomial equations of high degrees of N? Do apps like Desmos actually solve equations to get roots or do they approximate roots by iterating ...
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### Is there any scenario whereby randomly shufflying a sequence improves it's compressibility?

I'm performing some correlation assessment à la NIST Recommendation for the Entropy Sources Used for Random Bit Generation, § 5.1. You take a test sequence and compress it with a standard ...
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### Multiple choice knapsack dynamic programming

Giving a the following: A list of a store items $T=\{t_1, t_2,...,t_n\}$. A list of prices of each item $P=\{p_1, p_2,...,p_n\}$. A list of quantities of each item $Q=\{q_1, q_2,...,q_n\}$...
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### Practice question on the applications of flows and cuts

This question is from Erickson's textbook on algorithms, p. 376, question 18. Faced with the threat of brutally severe budget cuts, Potemkin University has decided to hire actors to sit in ...
38 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? ...
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### How to prove that an algorithm has no deadlock

I need to mathematically prove that this algorithm is deadlock-free: ...
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### equivalent sub-keys in DES encryption

i am trying to understand the DES cryptosystem and was wondering: what would've happened if all of the sub-keys were equal? does it reduce the security? can we actually find the keys if we know all ...