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Questions tagged [loops]

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3answers
85 views

Dealing with test condition '=' for a while loop when determining a bound function/loop variant

The following is the definition of what a bound function for a while loop must satisfy: The bound function is an integer-valued, total function of some of the inputs, variables and global data that ...
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0answers
21 views

Using induction vs invariants to prove correctness of algorithms

In my algorithms class I have generally been proving algorithms by induction. So for example, given some algorithm $A(n)$ that computes $x$, I show that the algorithm works for some base case, say $A(...
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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 ...
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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 &...
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1answer
54 views

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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1answer
26 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
287 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 ...
1
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1answer
79 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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3answers
30 views

Relative efficiency of n tasks in 1 loop vs. 1 task each in n loops?

Say I have 3 simple tasks, to find the min, the max, and the average of an array of numbers. A modular approach would be to write one function for each, thus iterating over the array thrice. However, ...
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1answer
92 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 ...
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0answers
23 views

Run time analysis of inner loop [duplicate]

What is the run time of the following piece of code in Big-Oh notation? The first loop runs n times in the worst case. But I am having difficulty in finding run time of nested loop which runs V / deno[...
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4answers
647 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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1answer
47 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? ...
2
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2answers
50 views

Quotient in LOOP program [closed]

I want to construct a LOOP-computable program for the integer division (quotient): x = a DIV b The LOOP specification can be seen here: https://en.wikipedia.org/wiki/LOOP_(programming_language) I ...
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1answer
54 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?...
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1answer
89 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
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1answer
372 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
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1answer
1k views

Find Number of even subarrays $O(n)$ [explanation needed]

So I found a solution to this problem here http://marcodiiga.github.io/number-of-even-sum-subarrays but I am unsure of exactly how it works. I get the premise that in order to have an even sum it must ...
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1answer
205 views

Finding time complexity when while loop included [duplicate]

There are two sorted arrays nums1 and nums2 of size m and n respectively. Find the median of the two sorted arrays. Example 1: nums1 = [1, 3] nums2 = [2] The median is 2.0 Example 2: nums1 = [1, ...
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5answers
3k views

How can a computer run an infinite loop?

I understand the concept behind for and do/while loops, but I am trying to understand what is happening at the hardware level that allows a loop to run infinitely. Technically wouldn't it have to stop ...
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1answer
74 views

Measuring infinite loops [closed]

Theoretically, is there a way to measure how many infinite loops are running at a given point in time? In other words, is there a way to freeze everything and get a number on how many infinite lines ...
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1answer
178 views

What is the procedure to find the time complexity of python program? [duplicate]

Is there any kind of function which is used in python to calculate the time complexity of another function?
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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 ...
21
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1answer
1k views

Does a do-while loop suffice for Turing-completeness?

I know that, in imperative programming languages, a while-do loop is sufficient as a control flow construct to make the language Turing-complete (as far as control flow goes - of course we also need ...
0
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1answer
117 views

Exponential nested Loop Big O complexity calculation [duplicate]

Can I get a bit of help over here, I can't seem to get to a finish point with this code complexity. I have trouble with making notations, exponential ones in particular..... I spent hours with this ...
2
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1answer
279 views

Why does the insertion-sort algorithm have a quadratic instead of a quasi-linear time complexity?

Can someone explain how the insertion sort have quadratic time complexity and not quasi-linear time complexity in the worst-case? Even in the case of a reversely sorted list, it's not like it'll have ...
1
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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 ...
5
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0answers
213 views

How Janus (Reversible Programming Language) `if`, `while`, and Update Work

In Reversible Computing, all program statements are reversible. I understand for example that the following: \begin{align} x\ {+}&{=}\ 4\\ y\ {*}&{=}\ x\\ x\ {-}&{=}\ 10 \end{align} Has ...
0
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3answers
41 views

What is the most used way to write for-loop as pseudocode?

for $e\leftarrow1$ to 8 do for $e\in[1,8]$ do for $e\in\{x\in\mathbb{N}|1\le x\le8\}$ do What is more preferred?
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1answer
999 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)=...
2
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1answer
81 views

Big Oh notation for a function with two inputs of linear growth

I'm quite new to time-complexity analysis so I might have misunderstood some basic concepts but lets say we have the following function: ...
1
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1answer
86 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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0answers
28 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
34 views

Little bit confusing to compute time complexity of nested loop [duplicate]

1 for(i=1; i<=n; i++){ 2 for(j=1; j<=n; j*=2){ 3 a[i][j]=b[i][j-1]+1; 4 } 5 } line 1 : n+1 times lnie 2 : n/2+1 times line 3 : constant time c ...
3
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1answer
76 views

time complexity when power is involved in iteration

How do I calculate the time complexity of the following method? Would you please provide explanation? I know it's going to involve sqrt(n) * <something>. I ...
1
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2answers
596 views

Time complexity of euler totient function

Code for finding $\phi$(n) is ...
1
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2answers
539 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?
1
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1answer
484 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 ...
0
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1answer
81 views

Complexity of a loop

If the body of a simple for loop has time complexity $O(n)$ and it is executed $n-1$ times what is the time complexity of the complete loop? I am trying to figure out the correct answer to this ...
1
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1answer
286 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 ...
0
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1answer
44 views

Loop Transforms to Increase Parallelism

I have the need to parallelize as much as I can (in order to make it run fast) the following part of an algorithm: ...
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0answers
78 views

How many operations does this algorithm require?

I have the following algorithm x = 0 S = {} k = 1 while x + a[k] < n do S = S + {k} x = x + a[k] k = k + 1 end where ...
2
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1answer
2k views

Recursion call inside a for loop time

I'm analyzing a piece of code that has a recursive call inside a for loop such as: ...
1
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1answer
376 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 ...
1
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1answer
109 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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2answers
480 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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0answers
169 views

Run time analysis of a program with nested for loops

Problem Let's say we are given a program and we want to find an algorithm that analyses its asymptotic complexity. This program can only have two types of statements: ...
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1answer
299 views

How to get O(Big-oh) notation for following Code [duplicate]

What i came up with is this 1) inner loop goes to 2n and at each. step it increments n/3 times threfore 2log n times it will execute 2) outer goes to n incrementing by 1 threfore n times Hence for ...
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0answers
64 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 ...