How to Programming with Graph-algorithm

Find a MST in O(V+E) Time in a Graph

algorithm,graph,graph-algorithm,minimum-spanning-tree

I would suggest you to do something like the second answer in the given question: This is prim's algorithm : Start by picking any vertex to be the root of the tree. While the tree does not contain all vertices in the graph find shortest edge leaving the tree and...

What's the difference between the minimum spanning tree algorithm for undirected vs directed graphs?

algorithm,graph,tree,graph-algorithm

The core of your question seems to be what makes finding an MST (technically called an optimum branching or minimum-cost arborescence) in a directed graph different and therefore harder than finding an MST in an undirected graph. Both Prim's and Kruskal's algorithms work because of the cut property. If G...

Check root node cut JAVA

java,algorithm,graph,graph-algorithm

You may just need this test: boolean isCutRoot(Vertex root) { final Edge[] rootEdges = graph.incidentEdges(root); return rootEdges != null && rootEdges.length >= 2; } However, if it is possible for multiple edges from the root to point to the same vertex, you need to modify the above method to check...

applying a function to graph data using mapReduceTriplets in spark and graphx

scala,network-programming,apache-spark,graph-algorithm,spark-graphx

I think you want to use GraphOps.collectNeighbors instead of either mapReduceTriplets or aggregateMessages. collectNeighbors will give you an RDD with, for every VertexId in your graph, the connected nodes as an array. Just reduce the Array based on your needs. Something like: val countsRdd = graph.collectNeighbors(EdgeDirection.Either) .join(graph.vertices) .map{ case (vid,t)...

Proving breadth-first traversal on graphs

algorithm,graph-algorithm,discrete-mathematics,proof

Disclaimer: I don't know how much formal you want your proof to be and I'm not familiar with formal proofs. induction on the while loop: Is it true at the beginning? Does it remain true after a step (quite simple path property)? same idea, induction on k (why k+1???): Is...

Computing Min-Cut of a Graph with No Reverse Edges

algorithm,graph,graph-algorithm,flow,edge

I believe this should work: For every edge, add a reverse edge with infinite capacity. That way if the min-cut is finite, original edges can only go from S to T, not the other way round.

Python: Comparison between list items that isn't redundant

python,for-loop,optimization,comparison,graph-algorithm

You can iterate through pairs using itertools.combinations for pair in itertools.combinations(d['people'], 2): first, second = pair if first[0] == second[0]: g.connectThem(first, second) These are the pairs that are produced from combinations [('John', 'Carry'), ('John', 'Joe'), ('John', 'Greg'), ('John', 'Carl'), ('John', 'Gene'), ('Carry', 'Joe'), ('Carry', 'Greg'), ('Carry', 'Carl'), ('Carry', 'Gene'), ('Joe',...

Codeforces #236 Div2

algorithm,graph-algorithm

That's a somewhat muddled editorial. Let's focus on creating 0-interesting graphs first. The key fact from graph theory is the following formula. sum_{vertices v} degree(v) = 2 #edges In a graph where every vertex has degree 4 (4-regular graph), the left-hand side is 4n, so the number of edges is...

How to use heaps with dictionaries to implement single source shortest path algorithm?

python,algorithm,dictionary,graph-algorithm,dijkstra

You can still use a heap even if it requires a list. graph.keys() returns a list of keys in your dictionary. The heap can then be built using the keys and if you need to find vertexes, dictionary lookup can be used. vertexes = graph[heap.pop()]....

graph traversal - finding 2 shortest paths for 2 entities such they are never in contact (both at the same node)

algorithm,graph-theory,graph-algorithm,shortest-path

I think you might consider a dynamic programming approach. At iteration 0, let s_0 = {(origin_0, origin_1)}. For iteration k+1, let s_k+1 = {(x,y) | x != y, exists an (prev_x, prev_y) in s_k s.t. e(prev_x, x) in E and e(prev_y, y) in E}. This should proceed forward with |s|...

Represent walls in a adjacency list

algorithm,graph,artificial-intelligence,graph-algorithm,maze

Well, it is hard to say anything for sure without knowing more details, but for most of the shortest path search algorithms it is fine not to create any nodes for cells that contain a wall at all.

Sampling a Large Undirected Graph

algorithm,social-networking,graph-algorithm,sampling,directed-graph

You can treat the undirected graph like a directed graph for the purposes of sampling. Any sampling strategy for a directed graph should work assuming it allows cycles. You simply want to sample the nodes and edges, so any edges that become part of the sample just accept the edge...

Find a shortest path with some conditions

algorithm,graph,graph-algorithm

Here is a faster solution: Let's find paths that contain the smallest number of black cells. We can use 0-1 breadth-first search. An edge that leads to a white cell should have a weight 0 and an edge that leads to a black cell should have a weight 1. There...

Finding the smallest number of steps between two points?

java,vb.net,algorithm,graph-algorithm

For your problem, I think BFS still works. Using BFS to solve traditional Maze problem, starting from the beginning point, you have to: 1. Enqueue every point that is accessible (not a piece of wall, and not visited) and connected to the current point. 2. Dequeue current point and mark...

Find shortest path between two nodes in directed weighted graph

algorithm,graph,computer-science,graph-algorithm,shortest-path

Edited my answer based on counter example by David Eisenstat. The example you give in your question is not a good example of when Dijkstra will not work. I believe you can do this by modifying Dijkstra. The key is to keep track of multiple alternatives for each Vertex. Not...

Wraping of equispaced point set in a given direction

java,r,algorithm,geospatial,graph-algorithm

I would do it like this: may be some 2d array point grouping to match the grid that should speed up all the following operations. compute average grid sizes (img1 from left) as two vectors create blue points (img2) as: gray_point (+/-) 0.5*blue_vector create red points (img3) as: blue_point (+/-)...

Graph algorithm to collect all edges which are on any path between two nodes

algorithm,graph,graph-algorithm

To get an overall result I'll report what I did. I implemented the in the question mentioned algorithm. (Lets call it thigg's algorithm, because noone mentioned a name) Thigg's algorithm: for each node in the graph: if there is a path from src to this node and a path from...

Pairs of Vertices Unreachable from Each Other in a Directed Graph

algorithm,time-complexity,graph-algorithm

If you can find all strongly connected components in the linear O(V + E) time requested then you are done. This may seem a bit overkill but it solves the problem. To find all strongly connected components, assuming your graph is represented as an adjacency list, perhaps the simplest O(V...

Algorithm to find k neighbors in a certain range?

algorithm,data-structures,graph-algorithm,nearest-neighbor,point-clouds

Your problem is part of the topic of Nearest Neighbor Search, or more precisely, k-Nearest Neighbor Search. The answer to your question depends on the data structure you are using to store the points. If you use R-trees or variants like R*-trees, and you are doing multiple searches on your...

Should D. B. Johnson's “elementary circuits” algorithm produce distinct results?

algorithm,graph,go,graph-theory,graph-algorithm

The redundant permutations are filtered out because the start node of each returned permutation is always less than all the remaining elements (under some ordering). I suspect the problem is in a missing implementation of these steps: AK:= adjacency structure of strong component K with least vertex in subgraph of...

Find if there is a non-simple path from v to t on a directed graph

algorithm,graph,computer-science,graph-algorithm,dfs

Step 0: If there is no path from v to t, then answer is NO. Step 1: Make the graph G' after collapsing all the strongly connected components of G. Step 2: If the vertex 'v' is a part of some SCC consisting of more than 1 vertex, then there...

Finding a minimal tree-type network of a graph where each node is connected to each other and find the sum of each node to all the other nodes

algorithm,tree,graph-theory,graph-algorithm

There are 13^11 ~ 1.8e12 spanning trees on 13 nodes, so brute force is out of the question. I believe that the intended solution is dynamic programming. For each pair comprised of a nonempty subset of nodes and a distinguished node belonging to the subset (the root), compute the optimal...

Undirected, weighted graph partitioning

algorithm,language-agnostic,graph-algorithm

What you are looking for is called the minimum cut of a graph. By the Max-flow_min-cut_theorem the value of the minimum cut is equal the the value of the maximum flow. Computing the maximum flow in a network is a standard problem and there are several algorithms for computing this...

A Dynamic Programming or Graph Algorithm, a Nice Questions

algorithm,math,graph,dynamic-programming,graph-algorithm

To my understanding, the problem can be solved as a Maximum Bipartite Matching, however the modelling requires the graph to be relatively large compared to the original input; for every feasible edge (s_i,b_j) introduce s_i nodes for the producer partition and b_j for the consumer partition and connect each producer...

To print the boundary of Binary Tree

algorithm,tree,binary-tree,binary-search-tree,graph-algorithm

I guess this should do the trick: traverse(BinaryTree *root) { if (!root) return; cout << p->data << " "; if (root->left ) traverseL(root->left ); //special function for outer left if (root->right) traverseR(root->right); //special function for outer right } traverseL(BinaryTree *p) { cout << p->data << " "; if (root->left )...

How to start Dijkstra's algorithm on a graph stored in a dictionary

python,algorithm,dictionary,graph-algorithm,dijkstra

Dijkstra's algorithm solves the single-source shortest-path problem. Given a graph and a vertex in the graph, it finds the shortest path to every other vertex. If you want your implementation to run fast, you must use a priority queue. It's fine to use a dictionary to represent the graph initially,...

Find the path with minimum cost between multiple nodes

javascript,angularjs,graph-algorithm

It is called Hamilton cycle problem. Or travelling salesman problem. https://en.wikipedia.org/wiki/Travelling_salesman_problem...

Graph with colored edges: shortest paths with at most k color changes?

algorithm,graph,time-complexity,graph-algorithm,shortest-path

This can be solved in time O(nm + n2 log n) by running Dijkstra's algorithm on an appropriately-constructed graph. To motivate the intuition for where we're going, let's assume for now that the optimal path makes at most one color change and starts by following a red edge. The path...

How I can represent a graph in java? [closed]

java,algorithm,graph,graph-algorithm

You can also use adjancy list using the following code snippet - int n; List<Integer>[] adj; AdjacencyLists(int n0) { n = n0; adj = (List<Integer>[])new List[n]; for (int i = 0; i < n; i++) adj[i] = new ArrayStack<Integer>(Integer.class); } Then add edge using the function - void addEdge(int i,...

Finding the number of edges and performing a topo sort in my graph implementation

c++,graph,graph-algorithm,topological-sort

First, for the number of edges, it would be simpler to count them directly when you build the graph (just add a counter in your Digraph class and increment it each time you add an edge … ) For the topological sort, first I have a question: your edges are...

Number of unique sequences of 3 digits (-1,0,1) given a length that matches a sum

algorithm,math,graph-algorithm

You can use a dynamic programming approach. The sketch of a recurrence is: M(0, 1) = 1 M(t, n) = T(t-1, n-1) + T(t-1, n) + T(t-1, n+1) Of course you have to consider the border cases (like going off the board or not allowing to exit the end of...

Approximation Algorithm for non-intersecting paths in a grid

algorithm,graph-algorithm,approximation

Here's a program written in Python that walks all potential paths. It uses recursion and backtracking to find the paths, and it marks a grid to see which locations are already being used. One key optimization is that it marks the start and end points on the grid (10 of...

Shortest paths with 2 constraints (Weight and Colour)

algorithm,graph,graph-theory,graph-algorithm,dijkstra

I think your approaches are actually equivalent, provided that for approach #1, you record only the shortest distance to each node for each number of red edges used -- you don't need to record the entire path (just as you don't need to record it for ordinary Dijkstra on an...

Can Bellman-Ford algorithm be used to find shorthest path on a graph with only positive edges?

algorithm,graph-algorithm,dijkstra,bellman-ford

Yes, it will give the same results. It will run slower, though, as it could also have been used for graphs with negative edges (subject to the absence of negative cycles). If you look at the proof of BF's correctness, there is no assumption there that some of the edges...

Graph Theory - Length of Cycle UnDirected Graph - Adjacency Matrix

algorithm,graph,graph-algorithm

Given the conditions in the question (that is, the only edges in the graph are part of the cycle), the length of the cycle is the number edges in the graph, which is half the number of 1s in the adjacency matrix (each edge (i, j) appears twice in the...

How to compare communities in two consecutive graphs

r,graph-algorithm,igraph

Actually this is not an easy question. In general you need to match the communities in the two graphs, using some rule or criteria that the matching optimizes. As you can have different number of communities, the matching is not necessarily bijective. There were several methods and quantities proposed for...

Getting a DFS from a BFS?

algorithm,search,data-structures,graph-algorithm

If you take a classic BFS algorithm and replace the FIFO queue with a LIFO stack, you will indeed get DFS vertex discovery order - so called DFS pre-ordering. I.e. the order in which your algorithm will visit graph vertices for the very first time will be exactly the same...

Finding best paths in a fully connected graph

algorithm,graph,graph-algorithm

The problem you're describing ends up being NP-hard (via a reduction from the longest path problem), so unless P = NP there aren't going to be any algorithms that are correct on all inputs and efficient on all inputs. You'll either need to be willing to accept answers that aren't...

Java: Uniform Cost Search with Node class

java,graph-algorithm,priority-queue,comparable

To satisfy the sorting capability of the PriorityQueue class (used by UniformCostSearch), your Node class must implement the Comparable interface, not the Comparator interface. To use the node parent in your comparison, you might try this: @Override public int compareTo(Node that) { if (this.parent != null && that.parent != null)...

Can a non-oriented graph have more than one Eulerian cycle?

graph-theory,graph-algorithm

The cycle is called Eulerian, iff it contains all edges, exactly one time each. That means that Eulerian cycles can only differ by edge's order (I propose to exclude edge's cyclical permutations as trivial option). It is possible to find Eulerian cycle, using Fleury's algorithm: in short, move as you...

How to apply Dijktra algorithm on this graph?

algorithm,graph-algorithm

You apply the Dijkstra algorithm the normal way and the shortest path from a to c is really 3. However, you should read the pseudocode for Dijkstra to understand that table. Firstly, Dijkstra returns an array (or another data structure, depending on implementation, for our purposes just say it's an...

Algorithm For Vertex Removal From Tree

algorithm,tree,graph-algorithm

Create a recursive function that does a post-order traversal of the tree. The function returns the subtree size and a vertex, or the vertex can be global (in which case you just set it instead of returning it). Call the function for the root. Call the function on each child's...

Find linearity in a graph

c,algorithm,graph,graph-algorithm

Do you mean constant or linear? If you mean linear: Why not take the differences of adjacent values and search for a sequence that stays close to constant? If you mean constant: Why not take the differences of adjacent values and search for a sequence that stays close to 0?

Betweenness centrality Brandes algorithm

algorithm,graph,graph-algorithm

The Brandes' algorithm gives the exact centrality of each vertex. I don't know which implementation of the algorithm is used in Sage, but chances are that it's a precision problem. The accumulation part of the algorithm is probably the trickiest. When you reach that part, you have in sigma...

Partially coloring a graph with 1 color

algorithm,graph,graph-algorithm

This problem is NP-Hard as well, and is known as maximum independent set problem. A set S<=V is said to be Independent Set in a graph if for each two vertices u,v in S, there is no edge (u,v). The maximum size of S (which is the number you are...

Detecting cycles in an oriented dependency graph and detecting if a vertex is part of the cycle or just depending on one

algorithm,language-agnostic,graph-algorithm

Tarjan algorithm for searching strongly connected components of a directed graph http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm allows you to make the distinction you need.

depth first search algorithm working

java,data-structures,tree,graph-algorithm,depth-first-search

You don't need stack here. Only recursion: public void dfs(Node node) { if (node == null) { return; } System.out.println("Node: " + node.getVertex()); node.state = State.Visited; for (Node n : node.getAdjacent()) { if (n.state != State.Visited) { dfs(n); } } } UPDATE To check path existence: public boolean isPath(Graph graph,...

Datastructure related. Find all arrays elements greater than or equal to given input

java,algorithm,data-structures,graph-algorithm

The approach that comes to mind could be to keep an ordered list of the orders and perform a binary search for the limit amount. All orders before that point in the ordered list will be less than the limit amount. // Generate a random array of numbers Random r...

Maximum weighted pairing algorithm for complete graph

algorithm,graph-algorithm,matching,scilab

I do not know Scilab I am afraid, but if you are willing to use Python it is very easy as the Networkx library provides support for this function: import networkx as nx import networkx.algorithms.matching as matching def C(i,j): return i*j n=40 G=nx.Graph() for i in range(n): for j in...

Maximum weighted independent set in bipartite graph

algorithm,graph-algorithm,independent-set

In any graph, the complement of an independent set is a vertex cover and vice versa, so your problem is equivalent to finding the minimum weight vertex cover in the graph. The latter can be solved using maximum flow techniques: Introduce a super-source S and a super-sink T. connect the...

Generate states for depth first search

java,algorithm,graph,graph-algorithm,depth-first-search

Switch 4 : Toggles all numbers that have modulus 1 with 3 1 % 3 = 1 4 % 3 = 1 7 % 3 = 1 10 % 3 = 1 Switch #1: 0000000000 <- Switch #2: 0101010101 <- Switch #3: 1010101010 Switch #4: 0110110110 <-...

Reduction from 3-Coloring to Fair-3-Coloring

algorithm,graph-algorithm,np

They don't have to be connected. Just throw in some loose nodes. Those nodes are just there to fix the number of colours, they shouldn't be affecting colourability. You have to add more than just 1 or 2 (which would be enough to get a multiple of 3) in general....

Compute costs only of paths between all pairs in weighted graph

algorithm,graph-algorithm

No, there is no algorithm better then O(n2). The algorithm will need to at least go over each pair. There are O(n2) possible pairs in the graph: . Therefore the algorithm bottom boundary is = O(n2)....

Heuristic to find the maximum weight independent set in an arbritary graph

algorithm,graph,graph-algorithm,linear-programming,np-complete

It's possible to formulate this as the following problem. Suppose each vertex v in the graph has weight w(v). You define a variable x(v), and use some out-of-the-box linear programming solver to solve max \sum_v w(v) x(v) (maximize the weight of chosen vertices) subject to x(u) + x(v) <= 1,...

PageRank toy example fails to converge

python,web-crawler,graph-algorithm,pagerank

It was the edge adding function that ruined it all. Fixed it to: def update_graph_links(): """register each node with neighbours pointing at it""" global pr_nodes for node in pr_nodes.itervalues(): for u in node.links_to_node: if u in pr_nodes: pr_nodes[u].links_from_node.add(node.url) return After a few adjustments, some refactoring and adding proper comments it...

How to efficiently update such a directed graph?

c#,algorithm,graph-algorithm

You can have each node maintain a list of dependent nodes and also a "dirty" flag. Then whenever a node changes, recursively set the dirty flag on every dependent node. (If a node is already marked dirty, don't recurse.) You can then make a second pass to re-evaluate each dirty...

How to store a Euler graph struct?

algorithm,graph,graph-algorithm

You can use an adjacency matrix to store graphs with multi-edges. You just let the value of c[i][j] be the number of times that vertex i is adjacent to vertex j. In your first case, it's 1, in your second case, it's 3. See also Wikipedia -- adjacency matrices aren't...

Query ArangoDB general-graph for common neighbors with more than 2 start vertices?

graph,graph-algorithm,arangodb

You can simply pass the same set of vertices as both parameters for common neighbors. Then repack the result in a better format for AQL to compute the intersection: let res = ( let nodes = ["a/A","a/B","a/C"] for n in GRAPH_COMMON_NEIGHBORS("g",nodes , nodes) for f in VALUES(n) return VALUES(f) )...

What data structure or design pattern to use to map a defined sequence of steps

java,oop,design-patterns,graph-algorithm

It does feel a bit like a flavor question. If I understand correctly you have data driven flow , by which I mean you have some data (in this case in form of xml's and scripts) that dictates what actions will be taken (so it's not known at compile time,...

Decompose a network into components with equal number of vertices

r,algorithm,graph,network-programming,graph-algorithm

Given the set Sn of all n-tuples of connected node subsets, construct the set of all n+1-tuples of connected node subsets by iterating over all s={a1,a2,...an} and there iterating over all ai to find a connected node ax which isn't in s. Build s'={a1,a2,...an,ax} and add to Sn+1 (which, as...

Shortest paths that are impossible for BFS to find?

algorithm,search,graph-theory,graph-algorithm,breadth-first-search

The Example Let G = (V,E) a graph with V = ℕ ∪ {-1, 0} and E = { {-1,t}, {t,0} | t ∈ ℕ } and let s = -1 and f = 0. There exist an infinite number of paths of length 2 from s to f, but...

Modified shortest path algorithm - vertices have points

algorithm,graph,graph-algorithm

So after this experience, I found that you should look into the ant colony algorithm and apply it to the traveling salesman problem. You could alternatively use a modified greedy algorithm approach that starts at a random point and chooses the next location based on a random sided die based...

Detecting connectedness of nodes over a long time in a graph

algorithm,graph-algorithm

There are ways to solve this problem fully online, but they're more complicated than this answer. The algorithm that I'm proposing is to maintain a spanning forest of the available edges, together with the number of components of the spanning forest (and hence the graph). If we were attacking this...

Finding the largest subsets of nodes in a tree subject to some constraints?

tree,binary-search-tree,graph-algorithm,depth-first-search,breadth-first-search

The problem you're trying to solve is called the maximum independent set problem applied to trees. As a hint, think about the following: For each complete subtree of the tree, think about the optimal solution for that subtree in two cases - the case where you include that node in...

Algorithm to arrange randomly sized rectangle images with optimally maximum spacing between them

algorithm,random,graph-algorithm,overlap

Here is the description of an algorithm that finds an optimal envelop for image sprites. You can easily bound it to your container side. Then as per my comment: find all the center points of your rectangles, and enlarge those points from the middle of the container by a ratio...

Efficiently build a graph of words with given Hamming distance

python,algorithm,graph-algorithm,hamming-distance

Assuming you store your dictionary in a set(), so that lookup is O(1) in the average (worst case O(n)). You can generate all the valid words at hamming distance 1 from a word: >>> def neighbours(word): ... for j in range(len(word)): ... for d in string.ascii_lowercase: ... word1 = ''.join(d...

Disconnecting a connected graph

algorithm,graph,graph-algorithm

You can use a maximum flow algorithm to compute the minimum cut between A and B in your graph. Runtime: O(n*m) with an excess-scaling push-relabel variant (since you have only unit capacities). Your solution is O(2^m * (n + m)) if you use DFS or BFS for reachability in the...

Minimal spanning tree with degree constraint

algorithm,graph,graph-algorithm,minimum-spanning-tree,degrees

To summarize the suggested algorithm [with tightened requirements on epsilon (which you called x)]: Pick a tiny epsilon (such that epsilon * deg(u) is less than d, the smallest non-zero weight difference between any pair of subgraphs). In the case all the original weights are natural numbers, epsilon = 1/(deg(u)+1)...

Best graph algorithm for least transfer in an electric grid

c++,graph,graph-algorithm

Your problem is easily reduced to a well-known minimum-cost flow problem: The minimum-cost flow problem (MCFP) is to find the cheapest possible way of sending a certain amount of flow through a flow network. This reduction can be done the following way. Add a dummy "source" and "sink" vertices to...

Flawed logic in A* implementation

java,algorithm,code-review,graph-algorithm,path-finding

First of all, you are mostly on track. I strongly suspect the code you posted is still under development and has some problems. But, still your assumption of distance is positive is not correct in general. A* is a graph search algorithm and edges can have negative weights as well...

Detect cycle in a graph using Kruskal's algorithm

c++,algorithm,graph-algorithm,disjoint-sets,union-find

MAKE-SET(v) means that you're initializing a set consisting of only the vertex v. Initially, each vertex is in a set on its own. FIND-SET(u) is a function that tells you which set a vertex belongs to. It must return a pointer or an ID number that uniquely identifies the set....

Algorithm for coloring a hexagon tile map with minimum distance (3) for reoccurring colors

algorithm,graph-algorithm,tile,hexagonal-tiles

Let's set up a coordinate system where the hex with coordinates (i,j) is adjacent to (i-1,j), (i-1,j+1), (i,j-1), (i,j+1), (i+1,j-1), (i+1,j). (0,3) (2,2) (4,1) (1,2) (3,1) (0,2) (2,1) (4,0) (1,1) (3,0) (0,1) (2,0) (1,0) (0,0) I'm going to apply a shear transform so that I can draw hex grids compactly...

When adding a random edge to a graph, which bridge edges are not bridge edges any longer?

algorithm,graph,graph-algorithm

If you allow preprocessing, there is a fast method: Construct the bridge-block forest, whose vertices are 2-connected components, and whose edges are bridges. (It's a tree if the graph is connected.) When you add an edge, if this connects points in the same 2-connected component, nothing happens. If you connect...

is bellman-ford can be done in a single iteration?

algorithm,graph-algorithm,bellman-ford

Sort a shortest path tree topologically.

Find separated lines in a 2D coordinate system

c#,algorithm,swift,coordinates,graph-algorithm

Here is an example I come up with: (tested in a Playground with Swift 2 Xcode 7 beta 2) struct Point{ var x, y: Int init(_ x: Int, _ y: Int) { self.x = x self.y = y } /** get points around it (Xs around P) if all {...

How to design an O(m) time algorithm to compute the shortest cycle of G(undirected unweighted graph) that contains s?

graph-algorithm

You can run a BFS from your node s as starting point, this will give you a BFS-tree. Afterwards you can built a lowest-common-ancestor (LCA) data structure on this BFS-tree. This can be done for example with Tarjan's lowest-common-ancestor algorithm. I will not got into details here. Given two nodes...

Algorithm for finding the path that minimizes the maximum weight between two nodes

algorithm,graph,graph-algorithm,shortest-path

Here is a simple solution: Sort the edges by their weights. Start adding them one by one(from the lightest to the heaviest) until X and Y become connected. To check if they are connected, you can use a union-find data structure. The time complexity is O(E log E). A proof...