# Tagged Questions

The Big-O notation is used to represent asymptotic upper bounds. It describes relevant time or space complexity of algorithms. Big-O analysis provides a coarse and simplified estimate of a problem difficulty.

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### Time complexity Computation

What will be the result of the time complexity of this piece of code i.e. int sum(int A[], int n) { int sum = 0, i; for(i = 0; i < n; i++) { sum = sum + A[i]; } ...
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### Efficient way to calculate how many items to destroy if each has a 70% chance to be destroyed

We start with a variable that holds an integer for the "number of items" that we have somewhere, somehow. Then, the algorithm is applied: each one of those items have a 70% chance to be destroyed. ...
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### Should I use this very short Python Quicksort implementation?

def quicksort(N): if len(N) < 2: return N else: less = quicksort([number for number in N[1:] if number < N[0]]) more = quicksort([number for number in N[1:] if ...
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### Finding longest subsequence with sum less than or equal to a fixed number

I was trying to solve Problem 279-B. Given an natural number, t, and an array, a[0],...,a[n-1], of natural numbers, find the maximum length of a continuous subarray, a[i],...,a[j] in a where a[i]+....
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### Understanding θ(f(n)) as defined in the Structure and Interpretation of Computer Programs

I'm having trouble understanding a small passage in The Structure and Interpretation of Computer Programs, and I'm hoping someone can help me interpret it. In the book's introduction to Orders of ...
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### O(n^2 * 2^(log n)) == O(n^2)

Is O(n^2 * 2^(log n)) == O(n^2) ? Why I think that this could be the case: In big O, you only take the parts of the term that are most relevant, right? O(n^2 + 3n + 9) == O(n^2). The n^2 has a lot ...
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### Does algorithm time complexity O(5) considered as O(1)? [duplicate]

I have someone homework to make and in the instructions it says that we need to implement a function in O(1). Now, does it mean that I can make my function in O(5) or O(2) or whatever?
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### Binary Search O(log(n)) or O(n)

I see where most readings online derive that the Big-Oh notation of a Binary Search is O(log(n)), but doesn't this assume a balanced tree? What if the tree is completely unbalanced (i.e. similar to a ...
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### How to calculate big O notation according to number width?

I'm trying to understand big O with the bitwise operations. I have 2 functions those are solving the same question from different perspective. num1BitsSecondSolution starts to shift the number right ...
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### What is Big O of sqrt(1) + sqrt(2) + … + sqrt(n)? [duplicate]

Given for example this code: for(int i=1;i<n;i++) for(int j=1; j < sqrt(i); j++) foo(); //foo takes constant time can someone explain to me how to calculate the ...
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### What is Big-O notation for purely functional languages?

Is it still relevant? Instead of var result = new List<int>(); for (var i = 0; i < prev.Count; ++i) { result.Add(prev[i] * 2); } where the result.Add, prev[i], and * 2 instructions ...
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### BST to AVL in O(n) [closed]

I found in different places on the internet how to turn a Binary Search Tree into an AVL tree in O(nlog(n)). I was wondering how can this be done in O(n) (as the worst case limit). It kinda seems ...
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### Complexity of recursive calls

my brain is a little stuck as I am trying to compile an example for my blog. I am presenting an algorithm that draws a number from an array, adds it to a sum and calls itself recursively. func solve(...
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### Expressing complexity based on length of key

I've made a data structure that has insert, search, and delete functions that are base on the number of characters in the key. As an example if it's a number based key (base10), then the complexity ...
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### How does cuckoo hashing guarantee O(1) lookups in presence of persistent hash collisions

Most hash table implementations guarantee O(1) average case but O(n) maximum case for lookup (where 'n' is the number of keys in the table). But Cuckoo Hashing is described as O(1) maximum. ...
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### Time complexity of 2^sqrt(n)

I am solving an algorithm question and my analysis is that it would run on O(2^sqrt(n)). How big is that? Does it equate to O(2^n)? Is it still non-polynomial time?
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### Merge sort and O(n log n) mystery

I read every explanation here but still not convinced. I think mergesort is n * n and I know I am wrong but not sure where. Here is what I think: Suppose we are sorting 8 elements and this is the ...
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### How should I express the complexity of two nested loops over different datasets in Big O notation?

I'm more or less teaching myself big O notation, so please forgive me if this is a duplicate of a question which applied to my question without me having the wisdom to realise it. For my own amusement/...
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### Big O Notation of an example

My professor gave this example in a lecture: Example: Given an integer N, print out the values 1…N. for (int i=1; i<=N; i=i+1) { System.out.print(i); } The professor said that the loop ...
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I was solving this question in Java where the user enters a partitioned array. The computer then determines what all elements from that array can be used as pivots. (Pivots are the same pivots that ...
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### Trying to understand P vs NP vs NP Complete vs NP Hard

I am trying to understand these classifications and why they exist. Is my understanding right? If not, what? P is polynomial complexity, or O(nk) for some non-negative real number k, such as O(1), O(...
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### Big O of loop of 0…n with nested loop doing k iterations [duplicate]

My coworkers and I are discussing this code and need a third party to settle our discussion :) Random randNum = new Random(); int[] A = Enumerable.Repeat(0, 1000).Select(i => randNum.Next(0, 100))....
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### Bounded Priority queue with constant time amortized delete min and insert

Given a bounded priority queue (with keys between 1 and k), is there any data structure with amortized constant time for delete min and insert and find min, where the worst case time for these ...
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### How to sort a list containing bounded set of values in linear time when length is unknown?

Given a list of integers whose length is unknown, and each of its elements lies between 1 to 1000, how does one sort this list in linear time?
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### What is time complexity of update in binary heap?

For a binary heap we have O(log(n)) for insert, O(log(n)) for delete min and heap construction can be done in O(n). In the context of using a binary heap in Djikstra, my exam paper involved an "...
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### Time Complexity when Loop Variable Depends upon Outer Loop Variable

What is the time complexity of the following piece of code in worst case? s = 0; for( i = 1; i <= n; ++i ) { for( j = 1; j <= i * i; j++ ) { for( k = 1; k <= j and j % i == 0; k++...
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### What's the big-O complexity of this recursive algorithm?

I am following a course of Algorithms and Data Structures. Today, my professor said the complexity of the following algorithm is 2^n. I waited till the lesson was over, approached him and told him ...
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### Big O Nested For Loop Breakdown

I understand how to get a general picture of the big O of a nested loop, but what would be the operations for each loop in a nested for loop? If we have: for(int i=0; i<n; i++) { for(int j=i+...
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### How an add vertex operation could be performed in constant time for a graph represented using adjacency list?

Adding a vertex in a graph that is represented using an adjacency list takes O(1) time complexity according to http://bigocheatsheet.com/ (graph operation > adjacency list > add vertex). It is said ...
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### why adding a vertex in a graph represented using an adjacency matrix takes O(|v|^2) time complexity?

Adding a vertex in a graph that is represented using an adjacency matrix takes O(|v|^2) time complexity according to http://bigocheatsheet.com/ (graph operation > adjacency matrix > add vertex). But ...
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### Is O(log n) + O(log n) = O(n)? [duplicate]

We know that binary search takes O(log n) in Big O notation but if we need to run twice an algorithm of O(log n), would it be the same as O(n) in time complexity? For example, if I have a method to ...
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### Why is mergesort O(log n)?

Mergesort is a divide and conquer algorithm and is O(log n) because the input is repeatedly halved. But shouldn't it be O(n) because even though the input is halved each loop, each input item needs to ...
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### Difference between O(N^2) and Θ(N^2) [duplicate]

What is the difference between O(N^2) and Θ(N^2)? I know that O is the upper bound and Θ is tight bound. Could someone explain me this concept with an example.
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### What is O(m+n) and O(m*n) in Big O notation? [duplicate]

I understand that O(n) describes an algorithm whose performance will grow linearly and in direct proportion to the size of the input data set. An example of this is a for loop: for n in 0.100 puts ...
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### Big-O for Immutable Trees

How would you calculate the time and space complexity for a tree algorithm that creates a copy of a tree, but reuses as much of the original tree as possible? For example, A /|\ B C G /|\ D ...
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### What is the time complexity of this program?

An algorithm is given on GeeksForGeeks.com for constructing a Binary Search Tree from its preorder traversal. They say that the time complexity for the following code is O(n^2). But in my opinion it ...
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### Is the time complexity of a while loop with three pointers different than 3 nested for loops?

This program (written in ruby) finds the largest 3 numbers in an array (without sorting the array). It has a while loop with three pointers. My fist instinct, since there is only one loop is to say ...
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### When speaking, how can I say that the time complexity order of an algorithm is O(N log N)?

What term can I use to describe something with O(N log N) complexity? For example: O(1): Constant O(log N): Logarithmic O(N): Linear O(N log N): ?????? O(N2): Quadratic O(N3): Cubic
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### Seeds distribution algorithm with complexity better than O(n^3)?

I have included my approach and solution. My solution works fine, however, is unoptimized with O(n^3) complexity An NGO is running seed distribution program. It has limited quantity of varied quality ...
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### What is the algorithmic time complexity of this program?

I wrote a simple program in java to create and maintain Dynamic Arrays: public class DynamicArrays { private Integer[] input = new Integer[1]; private Integer length = 0; private Integer ...
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### Time complexity of this loop [duplicate]

Is the time complexity for this loop O(n) or O(log n)? for(i=0;i<n/2;i++){} I am thinking, the time is proportional with the input size.
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### Big O equivalence for LINQ select

I'm trying to determine if there is a change in the Big O equivalence of a nested loop when I use a LINQ select instead. public void myFunc(List<Foo> fooList, List<Bar> barList) { ...
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### Big O notation of randomness

I was thinking about inefficient algorithms based on randomness and wondered how to categorise them. For instance. Say you wanted to generate all the numbers from 1 to N in a random order but only ...
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### Calculate Big-O for nested for loops

I found this nested loop to calculate the Big-O notation. for(i=0;i<n;i++) for(j=0;j<i*i;j++) for(k=0;k<j;k++) I got the time complexity for the algorithm with this polynomial ...
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### Big O Question about an algorithm with (n^2 + n) / 2 growth rate

I'm asking this question because I am confused about one aspect regarding big O notation. I am using the book, Data Structures and Abstractions with Java by Frank Carrano. In the chapter on the "...
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### Big O notation for a sub linear algorithm [duplicate]

I have a function for which the complexity raise by the square ten of the exponent of the number. Ex: +-----+----------+ |Input|Complexity| +-----+----------+ |0 | 1 | |10 | 2 | |...
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### Big graph traversal with OOP

I'm trying to solve a algorithmic contest's problem. I have a matrix 2000x2000. I want to represent it as graph and traverse it with BFS/DFS. I have time limits on app running (2s). Simple vertices ...
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### Time complexity analysis for recurrence relation

I was asked to figure out the time complexity analysis for the following recurrence relation T(n) = 4*T(n-1) + c. Basically, I did a replacement.. T(n-1) = 4 * T(n-2) + c and so on.. T(n) = 4^k T(1) ...