Questions tagged [loops]

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Nested Loop Time Complexity vs Successive Loops

An algorithm has a calculation whose worst case time complexity $T(x)=O(x^2)$ that outputs solutions $y$ & $z$ for input $x$ (the algorithm's worst case time complexity is greater than quadratic ...
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2answers
60 views

make Magic Square? [closed]

I need to write a function that takes in a 2D list, that is a NEARLY magic square, meaning that if you perform ONE swap, it becomes a magic square. The function would take in this nearly magic square, ...
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2answers
2k views

Runtime analysis of a nested loop

I have some difficulties performing the worst case analysis on this algorithm. The outermost loop is executed $2N$ times. The while loop, in the worst case, will increase by $2$ each time, so it ...
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1answer
30 views

What is an array that can be iterated circularly an infinite amount of times called?

I have a feeling that the answer is either a "circular linked list" or a finite state machine, but the answer is probably a circular linked list.
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1answer
296 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 ...
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2answers
780 views

Solving complexity using summation

I have the following algorithm: func() { for(i=1; i<n; i=i*2) print("aa"); } How can I find Big-Oh using summation?
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1answer
269 views

Big-O Time Complexity of nested for loops [duplicate]

My gut tells me the time-complexity of the following code is simply O(n^2). However, I'm not convinced, thinking it could possibly be O(n^3): ...
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1answer
353 views

Loop invariant: decreasing a variable and swapping it

As an example exercise, we were asked to find the loop invariant for this bit of code. ...
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1answer
2k views

Explanation of the complexity of a loop [duplicate]

I am confused on the following: In the following trivial code: ...
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1answer
1k views

Sum number of times statement is executed in triple nested loop

I have this code fragment: for( i=0; i<n; i++ ) for( j=0; j<i; j++ ) for( k=0; k<j; k++ ) S; I need to find the number of times ...
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1answer
292 views

Can a Turing machine decide if a LOOP program stops for the integer input 0

This is a question I found in a practice exam while I am preparing for my mid term exam. The answer needs justification, either a pseudo code or a logical explanation why not. What puzzled me about ...
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1answer
557 views

Asymptotic time complexity of a two-loop program

I have two pieces of code in a function which I'm trying to calculate the asymptotic running time for: ...
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1answer
73 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 ...
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1answer
28 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 &...
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1answer
350 views

is a while loop always an indefinite loop?

Building on this example and others found elsewhere we have two types of loops, definite and indefinite: definite being a loop that has its number of iterations known before it is executed. E.g. a ...
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1answer
82 views

How do you solve this [1,5,9,4] pair numbers problem?

So given an array of [1,5,9,4], find all pairs of numbers that can sum/subtract/divide/multiply to another number in the array(that number is not part of the pair), and return the total count of pairs ...
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1answer
1k views

Runtime analysis of while-loop analysis

s = n while (s > 4) s = s / 2 else s = s - 1 Let $T(n) = \Theta(S(n))$ where $S(n)$ is number of while-loop runs. $S(n)=1 + S(n/2)$ if $n$ is even $S(n)=...
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1answer
118 views

Loop termination - Loop invariant

(x >= 0 && y >= 0) q = 0; r = x; while ( r >=y ) { r = r - y; q = q + 1; } (x = q*y +r) && (r >= 0) && (r < y) For ...
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1answer
716 views

Complexity of while loop using series

For the following code fragment: i = 1; s = 1; while(s <= n) { i++; s = s+i; printf("x"); } How can we go about proving the time complexity of ...
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2answers
171 views

Complexity of the algorithm to find occurences of a given number in a given array

I have an algorithm that I think its complexity is O(n^2). However, our teacher insists that the algorithm takes O(n) time. How can it be? Here is the pseudo-code of the algorithm: ...
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2answers
323 views

Prove correctness of iterative LCM algorithm

I have been trying to prove the following algorithm, without success. Here is the C-Style pseudocode: ...
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1answer
53 views

Runtime of algorithem when the internal for depend on the external for

I'm trying to find the running time of this pseodocose: int x=0,i,j for (i=1;i<=n;i++) for(j=1;j<=n+r;j=j+i) x=x+j; What I did: First I checked ...
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1answer
482 views

Is it possible to write a universal loop program for if-then & loop programs and it is possible to write a universal while program for while progra

Is it possible to write a universal loop program for if-then & loop programs and it is possible to write a universal while program for while programs? Long version and some background: Before ...
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0answers
42 views

Why does this code return $\frac{count}{2}$ instead of $count$?

I am reading "Algorithms 4th Edition" by Sedgewick & Wayne. The following method computes the number of self loops of an undirected graph $G$. Why does this code return $\frac{count}{2}$ instead ...
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0answers
23 views

Nested Function stuck on iteration update

I want to solve the Sparse Extended Information Filter Slam described by Dr. Sebestian Thrun in Probabilistic Robotics.I stuck in some nested function. The algorithm is described in page 309 in this ...
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1answer
54 views

What changes do I need to make to my algorithm to make this scene from a different angle? [closed]

The code below is in F#. It creates a scene which looks like a perspective coming from the top left. I thought if I would change i % j = w then it would come from ...
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0answers
29 views

Scheduling loop

I do not understand how do you write schduled loop from unscheduled one. The unscheduled loop straightforward if you follow the stall rules. The rules say you are supposed to stall after L.D but in ...
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1answer
360 views

Run Time of Nested Loop

In the following loop for i = 1 to n doSomething O(1) for j = 1 to k doSomething O(1) Is the runtime still $O(nk)$ even with the expression in ...
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1answer
509 views

How to get Loop invariants to prove program is correct in Hoare logic

start off stating the definition of a loop invariant. It is a condition that must be true at the start of the loop and must be true after each iteration of the loop. I understand what it is but i have ...
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0answers
76 views

Hoare correctness proof for a recursive definition of multiplication

Given the program: {y=y0 ^ y>=0} z=0; while (y>0){ z=z+x; (1) y=y-1; } {z=x*y0} I am having trouble finding the ...
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1answer
124 views

Maximum value of LOOP-Program turing-computable

Lets consider the class of "simple" LOOP-Programs. A LOOP-Program P is inducively defined as: $P_1: x_i = x_j$ and $P_2:x_i = x_i +1$ are LOOP-Programs. We also define a length property $l(P)$ ...
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0answers
40 views

Time complexity of a nested loop [duplicate]

I need to figure out the complexity of the following loop in theta notation but I can't figure it out. Some help would be much appreciated. ...
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1answer
237 views

Calculate the complexity of an algorithm [duplicate]

I have an algorithm here and it wants me to calculate the complexity: ...
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0answers
59 views

Big-Oh of algorithm

I found an algorithm which sorts the digits of a number to its smallest form. IE 54321 ==> 12345. The algorithm looks like: ...
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0answers
36 views

Time complexity ( $\Theta$ ) of function [duplicate]

Let f be the function with one argument - positive integer n ...
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0answers
436 views

Bridge Crossing Problem Proof?

I'm trying to find an optimal solution that will work for the bridge crossing problem. In case you don't know it you can check out the Ted Ed video on it. They show how you can do it with 5 people but ...
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0answers
285 views

How to determine big O of a variable loop

I want to classify the runtime of this function in big O notation. This function is multiplying two whole numbers and checks the in binary digits of the multiplicand. And adding the multiplier to the ...
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0answers
165 views

Complexity of a nested for loop [duplicate]

I'm trying to work through various exercises in Skiena's "Algorithm Design Manual." One problem that I am stuck on is as follows: What value is returned by the following function? Express your ...
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1answer
782 views

Bubble sort complexity [duplicate]

So I have this code: ...
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3answers
824 views

Calculating time complexity of two interdependent nested for loops

Consider the following code segment : for (int i = 1; i <= n; i++ ) { for (int j = 1; j <= n; j = j + i ) { printf("Hi"); } } Here, the ...
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2answers
519 views

A puzzle related to nested loops

For a given input $N$, how many times does the enclosed statement executes? for $i$ in $1\ldots N$ loop $\quad$for $j$ in $1\ldots i$ loop $\quad$$\quad$for $k$ in $i\ldots j$ loop $\quad$$...
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4answers
816 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\...
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2answers
275 views

What is the Big O estimate of a nested for loop?

I am trying to figure out what the big o estimate of the following for loop is. ...
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2answers
531 views

what is halting problem? [duplicate]

i have researched it on wikipedia and it produces me an unusual example and stories about Turing,so what i understand is if an program run in loop,an electronic device in cpu or in computer structure ...
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1answer
30 views

I cannot find an invariant for the following program

I have the following: (|$y=0; x=c$|) while(x > 0){y=y+a; x=x-1;} (|$y= a*c$|) This seems like a fairly simple program and I can intuitively tell that the post ...
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1answer
860 views

Proving correctness of a loop that calculates the sum of array

I am trying to mathematically prove that the following program is correct: ...
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1answer
725 views

Finding a Hoare logic correctness proof for a Repeat-Until loop

How can we prove a program in repeat until using Hoare Logic? I've found a rule like this: {P} S {R}, {R ^ ~B -> P}, {R ^ B -> Q} for ...
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1answer
222 views

Understanding the time-complexity of Insertion Sort

From my textbook, I am studying the time-complexity of the insertion sort algorithm (shown below). ...
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1answer
26 views

Big-O Notation: Runtime Analysis

I have a problem with an exercise, I have to analyze the following For-Loops Then I have to write down the explicit notation, my problem is that I don't know how to get the right m. I tried this but ...
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1answer
57 views

Time Complexity of the below code? [duplicate]

here is a nested loop where all the variable are integers.This is another question to the thread. I understood the solution part , but stuck in the time-complexity part. What is the time complexity ...