The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [algorithms]

An algorithm is a sequence of well-defined steps that defines an abstract solution to a problem. Use this tag when your issue is related to design and analysis of algorithms.

7,657 questions
Filter by
Sorted by
Tagged with
48 views

Finding efficient randomized algorithm

I'm doing a course on randomized algorithms and I've encountered a question that I'm struggling to solve. Given a system of $m$ linear equations with $n$ variables over finite field $\mathbb{F_2}$ ...
8 views

Constant vs linear time given knowledge of input distribution

Question about computer science whether a problem is O(1) or O(N). This was a thought experiment I came up with and I’m sure it’s rather basic. But I wasn’t sure how to look it up so I apologize if ...
32 views

Finding an substring in an infinite sequence

I'm trying to find a substring in an infinite sequence of numbers (Similar to Substring in a infinite sequence of numbers) and am a little stuck on improving my algorithm. I know there is already an ...
29 views

Detecting rotational symmetries of spatial structures

I have a spatial graph-like structure. The structure consists of vertices in the 3D space and connecting edges. Are there any algorithms available that would identify the rotational symmetries of ...
28 views

Smallest segment after whose removal all elements are distinct

I am interested in the following problem: We are given an array of integers and we need to find the size of smallest subsegment such that after removing it all elements in the array are distinct. ...
38 views

How to find the smallest of the maximum edges of all paths between two nodes in a graph

Say I have an undirected weighted graph G = (V, E), and I have two vertices s and t. Now there may be a number of paths between s and t, and each path has an edge that has the maximum weight in that ...
76 views

196 views

What complexity does this 'how many ways to climb' algorithm have?

I have a solution to the following problem: Given a stairway of $n$ stairs, which you can climb from $1$ to $m$ at the time ($1 \leq m \leq n$), return all the ways you can climb the stairway. ...
105 views

A number of points on a line, with initial positions and speeds - find a minimum time that any two points meet

How can I compute the minimum time for two points to meet in $O(N)$ time? All I can think is to compute the time for all the point pairs and get the minimum. Can anyone give me some hints?
6 views

How to define the stability (or convergence) of a ordering of a list of node

I have a problem which requires ordering nodes in a graph based on some given statistics. However, the given statistics of each node may be very hard to compute. Thus, I will use some sampling ...
32 views

Weird implementation of quicksort

I met a wired question from the algorithm test of my school. For the first time I thought it is a normal quick-sort problem and feel confident to solve it but as I read the algorithm carefully, it is ...
113 views

Finding the last substring in lexicographical order in O(n) time

Given a string s, return the last substring of s in lexicographical order. Example 1: Input: "abab" Output: "bab" Explanation: The substrings are ["a", "ab", "aba", "abab", "b", "ba", "...
49 views

Algorithm to find repeated patterns in a large string

For optimization purposes I'm trying to analyze a large list of executed program commands to find chunks of commands that are executed over and over again. This problem is similar to searching ...
26 views

Binary Search Symbol Table

Hi I'm attempting to self teach myself from Algorithms (Sedgewick) and ran across the following problem: ...
15 views

Recurrence Formula for Bitonic Sorter Runtime

A Bitonic sorter takes a bitonic sequence as an input and the output is a sorted list. I want to analyse Bitonic Sorter by knowing its depth/runtime. Can anyone give an idea on its recurreence formula?...
74 views

Are every problems in EXP karp reducible to any EXP-Complete?

According to wikipedia and other references there exists complete language $L \in EXP$ such that for every languages $L'$ in $EXP$ there exists a polynomial reduction $f$ that converts instance of $L'$...
9 views

Graph with arboricity a, all verteces are marked active

So I came across this problem that I would like help solving/explaining: We have a graph with arboricity a (can be partitioned to a min of a trees). We run the following algorithm on the graph: - All ...
12 views

Algorithmic question: distribute balls, optimise for balancing (i) weights (ii) probabilities of picking balls

I have an algorithmic problem that requires some lengthy explanation, which follows below. tl;dr: distribute balls with weights among bags, optimise for balancing both (i) the weights between the ...
38 views

Solving/mitigating the free rider problem without requiring identification?

Is there any algorithm/protocol out there to solve/mitigate the free rider problem without requiring identification? In a web system, I want to distribute exactly one virtual dollar per day to each ...
49 views

Time complexity of finding predecessor for a dictionary implemented as a sorted array

I'm currently reading "The Algorithm Design Manual" by Steven Skiena. On page 73, he discusses the time complexity of implementing $Predecessor(D, k)$ and $Successor(D, k)$ and suggests that it ...
58 views

Verifying connectivity of a graph in O(n^2)

I trying to solve the following problem in $O(n^2)$: We have vertices which represents cities and a textfile containing an edge on each line. How many roads do we need to build to make the graph ...
22 views

Can anyone provide proof of second equation of rod cutting problem in CLRS section 15.1

While going through ROD CUTTING problem of DP from CLRS, I noticed the optimal structure of the rod cutting problem is : 𝑟𝑗=max{𝑝𝑛,𝑟1+𝑟𝑘−1,𝑟2+𝑟𝑗−2,...,𝑟𝑗−1+𝑟1} In overhead approach, ...
26 views

How to implement minimization of maximum regret?

We run a report, but for one of our big clients, it is taking too long. There is a loop where it loops for a list and fetches it upstream 1by1. We're making this a bulk operation now, but some items ...
86 views

What is the meaning of uniform distribution of elements in an array?

I was going through the concept of Interpolation search and it stated that when the elements are "uniformly distributed", it takes O(loglogn) to search an element using interpolation search. Can ...
28 views

How to prove an implication about an upper bound mentioned in the proof of master theorem?

How can we prove rigorously the proposition "Suppose the if in case 1 is true, the equation 4.23 is true"? For given constant b and j, the implication in green makes sense. If the upper bound of j ...
49 views

Big-O Notation and Calculus?

I was wondering if there are any calculus relationships implicit in Big-O notation. For example, an algorithm linear according to Big-O notation reduces the size of the problem by a constant amount ...