Questions tagged [breadth-first-search]

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Correctness of bft resulting in shortest path

I found the following proof concerning the correctness of a breadth-first traversal resulting in shortest path: source: https://people.eecs.berkeley.edu/~daw/teaching/cs170-s03/Notes/lecture6.pdf The ...
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Proof for Queue in BFS consists of vertices of distance k and k+1

For any vertex v reachable from s, BFS computes a shortest path from s to v (no path from s to v has fewer edges). In order to prove the above proposition, The author of the book has stated that we ...
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The distinct-vertex $\alpha$-edge variant of the all-pairs shortest paths problem

The following problem is a variant of the all pairs shortest path problem: Given a weighted, directed graph $G=(V,E), |V| = n,|E| = m,$ and an integer $\alpha\ge 1$, how can I find an efficient ...
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How to find time complexity of Breadth First Search for this tree?

This is what I got from another forum, but honestly doesn't make much sense to me. Time complexity for a single tree doesn't make a lot of sense, since the function in the big O notation might be ...
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Visiting vertices on a graph using DFS and BFS

I have this graph that I created and am wondering how DFS and BFS would work on something like this. I made this graph undirected and am going off the premise that if possible, a vertex should be ...
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Shortest path with color constraints

Find shortest path in directed graph (blue and red nodes) that never visits 3 red nodes in a row in $O(V+E)$ time. Not really sure how to approach this.
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Why can't we use BFS with modifications to find shortest paths in weighted graphs

I came across this post about how we can get to all shortest paths from source (u) to destination (v) . If the algorithm is working in O(E + V), why can't we use it (after slight modifications) for ...
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220 views

Number of shortest paths between two nodes in undirected unweighted graph

I'm trying to devise a $O(|V| + |E|)$ algorithm to calculate number of shortest paths between $s$ and $f$ on a undirected, unweighted graph. Can someone please check my pseudo-code? Also, isn't $O(|V| ...
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Is the first distance that gets assigned to a node in BFS always the shortest distance?

Consider the following bfs pseudo code that calculates distances of all nodes from $s$ in graph $G=(V,E)$. I know that if $G$ was undirected and unweighted, then the above bfs would calculate correct ...
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2k views

Print all nodes which are the endpoint of the diameter of a tree

Given a tree with n nodes, Print all nodes which are the endpoint of the diameter. 1<= n <=100000. E.g. For Above tree answer would be A,B,F,G I tried the O(n2) approach (Running Dfs from each ...
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Meaning of source here

In graph theory, a source of a directed graph $D = (V(D), E(D))$ is a vertex of it whose in-degree is zero. The book CLRS makes these statements: Given a graph $G = (V, E)$ and a distinguished source ...
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Connectivity in Directed Graph

Connectivity in undirected graph can be easily identified using Disjoint Union Set (Union Find). Is there any way to check connectivity in a directed graph efficiently other than doing Depth First ...
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2 answers
161 views

Why do basic graph algorithms (BFS, DFS, Prim, Kruskal) have a similar structure?

This is my first post on CS Stack Exchange. For some time, I have been studying basic graph algorithms, mainly BFS, DFS, minimum spanning trees and their basic algorithms (Kruskal and Prim). One thing ...
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Question about uniform cost search

I was watching this youtube video and reading this book about uniform cost search. I did not get an answer to my question from these resources. Does UCS optimally find the most optimal route from a ...
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There exists some number $x$ so in any run of BFS from vertex $w$, so the distance from $u$ to $v$ in BFS tree is always $x$

Studying for my finals and stuck on the following question: Prove or disprove: Given an undirected and connected graph $G=(V,E)$ and three different vertices $u,v,w\in V$ then there exists some ...
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3 answers
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Is DFS better than BFS for space complexity when finding path from root to a node in a tree?

For simplicity, and I think without loss of generality, we can consider a binary tree. Suppose that we want to find the path between the root node and some node in the tree (we don't know where it is ...
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Why Breadth First Search is used for shortest path

We can read on the internet: BFS finds the shortest path to the destination. But how ? Check this example: for this example we can get 40 10 20 30 60 50 70 What is ...
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Check if any path starting from a vertex in set A and reaching a vertex in set B is long at least k in $\Theta(G)$

I am trying to verify whether it exists a path from $a \in A$ to $b \in B$ whose length is $\ge k$ in $\Theta(G)$. This is what I have done: ...
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Time to form a complete graph from n vertices given that only k vertices can be used at a time [closed]

I know this problem is related to the greedy algorithm and max edges incomplete graph but can't come up with a solution. Problem You are given two numbers n and k: n >= k n is the total # of ...
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1 answer
73 views

Translating the in-order index of a node in a complete, balanced binary tree into the level-order index

Consider the topmost part of a complete, balanced binary tree of all 64-bit numbers, exemplified here. As highlighted by the lack of a 7*2^64/8 term it is not ...
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1 answer
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Algorithm for finding strongest connection for a user on social network

I am working on Problem 6-1 from MIT's Fall 2011 6.006 course. The problem reads as: Problem 6-1. [30 points] I Can Haz Moar Frendz? Alyssa P. Hacker is interning at RenBook (人书 / 人書 in Chinese), a ...
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2 answers
106 views

Is the best known algorithm for the shortest path problem for an undirected and unweighted graph $O(E)$ or $O(E+V)$?

I'm a bit confused by Wikipedia's tables of algorithms for the shortest path problem. For an unweighted graph with $E$ edges and $V$ vertices, it gives the best algorithm as breadth-first search, with ...
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How does BFS guarantee the minimum path for this problem?

https://leetcode.com/problems/bus-routes/ You are given an array routes representing bus routes where routes[i] is a bus route that the ith bus repeats forever. For ...
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95 views

Number of sentences and sentential forms generated by a grammar

In this question, I'm considering only "finite grammars". A finite grammar can only produce a finite number of distinct sentences. The following grammar is finite in my definition: ...
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1 answer
108 views

Shortest Path with a twist

We are given a Graph G where, s ∈ V and t ∈ V. w:E such that w represents the time from u to v. We have to calculate shortest path between s to t with a twist. The twist is the turbocharger which can ...
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1 answer
50 views

Prove $|d_{s}(u)-d_{s}(v)|\leq1$ in BFS

Trying to prove the following problem: Given a graph $G=(V,E)$ and vertex $s\in V$, prove that: $\forall (u,v)\in E,\ |d_{s}(u)-d_{s}(v)|\leq1$ where $d_s(v)$ is the shortest path from $s$ to $v$ in ...
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4 votes
2 answers
124 views

Can Edge Belong to a cycle if it is part of multiple BFS products

Given a simple connected undirected graph. with V vertices and E edges. Let e be some edge from E. If I perform |V| different BFS runs - meaning started each time from a different vertex - and in ...
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31 views

BFS Traversal over a graph question

Starting from a random node, which of these series can be a BFS traversal (L to R)? 1 MNOPQR 2 NQMPOR 3 QMNPRO 4 QMNPOR Now, I understand that my answer (1- MNOPQR) is wrong because I got confused ...
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Find every path that passes through certain edges

I'm faced with the following problem: Given Directed and unweighted graph, where each edge E has two attributes Goal Find every path through the 3 (or more) given edges in a specific order ...
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2 votes
1 answer
278 views

Name of BFS variant with multiple queues with different priorities

Is there a name for the following variant of BFS that operates on trees with non-root starting point?: Instead of a single queue that all neighbor nodes are added to when processing a node, two ...
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1 vote
1 answer
104 views

BFS for transforming one word to another

I'm having a hard time understand the reasoning in the solution of 18.7 in Elements of programming interviews (EPI): Let $s$ and $t$ be stings and $D$ a dictionary, i.e., a set of strings. Define $s$ ...
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0 votes
1 answer
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Minimum amount of time for two enemies to reach their destinations?

Given an undirected, unweighted, and connected graph $G = (V, E)$, what is the minimum amount of time it takes for party $X$ to go from $s_x$ to $t_x$ and party $Y$ to go from $s_y$ to $t_y$? At each ...
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2 votes
0 answers
43 views

How to find more than 1 successive shortest paths between two vertices in unweighted and undirected graph using BFS?

I have tried to find and print more than one successive shortest paths between two vertices in the undirected graph. Using BFS as DFS will not be optimal in this case, as it can go deep into the stack....
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1 vote
0 answers
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Why does this BFS solution work for this question about euclidean distance and what's its complexity?

Given a matrix of 1s and 0s where 0 represents houses and 1 represents stores, find the square of minimum Euclidean distance of every house to nearest store. Return it as a vector of vector. ...
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2 votes
1 answer
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"Visited" vs "Seen" Positions in Breadth-First Search

I'm struggling to understand why there is such a radical difference in the execution time and number of steps required by two seemingly similar algorithms for Breadth-First Search in a 2d grid. In ...
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61 views

Graphs which favour BFS over DFS and vice versa

I am trying to figure out what kinds of graphs are better suited to BFS and which are better suited to DFS. However i'm struggling to visualise what kind of graphs favour which search. Could someone ...
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0 votes
1 answer
85 views

Why MIT lecture breadth-first search algorithm is so complicated?

I watched a video for BFS from MIT and the algorithm the lecturer presented was really complicated compared to what I came up. My solution seems to work fine and walk through the vertices in the ...
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2 votes
0 answers
3k views

Comparing classical tree-search algorithms (BFS,DFS,A*,IDS) - when to use one or the other?

I have a question about classical tree-search algorithms as I will have an exam soon and this is the type of questions they might be asking. Although I know how to compare the complexities, optimality,...
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