Find all possible paths between two points in a matrix If the question is whether or not this is optimal: obviously no. All Paths From Source to Target - Given a directed acyclic graph (DAG) of n nodes labeled from 0 to n - 1, find all possible paths from node 0 to node n - 1 and return them in any order. Oct 3, 2025 · Given a directed graph of N vertices valued from 0 to N - 1 and array graph [] of size K represents the Adjacency List of the given graph, the task is to count all Hamiltonian Paths in it which start at the 0th vertex and end at the (N - 1)th vertex. Jul 2, 2016 · How to find all possible paths between points A and B. As the "S" in "SVFG" stands for "Sparse", the graph is not that densely connected. These generalizations have significantly more efficient algorithms than the simplistic approach of running a single-pair shortest path algorithm on all relevant pairs of vertices. Jul 4, 2020 · As an example, let's count all possible lattice paths in a 2x2 square lattice–that is, an area of two blocks by two blocks. Please note that in the cases, we have cycles in the graph, we need not to consider paths have cycles as in case of cycles, there can by infinitely many by doing multiple iterations of a cycle. In this post I will be discussing two ways of finding all paths between a source node and a destination node in a graph: Using DFS: The idea is to do Depth First Traversal of given directed graph. Jul 23, 2025 · Path in a Grid or Maze refers to problems that involve navigating through a grid-like structure from the source (starting point) to the destination (endpoint) while avoiding the obstacles i. I'm stuck on this problem. For this problem, we are given a 2D array represented as a graph and we must find all possible paths from node 0 to node n - 1 where n is the length of our input array. We are given an integer K, which represents that we can remove at most K obstacles to reach our destination. Imagine you're standing in a maze and you want to find the shortest path to reach the exit. If you want to find all the paths between two nodes of length k, just multiply the adjacency matrix by itself k times. Oct 3, 2025 · The task is to find the minimum number of steps required to go from the source (0, 0) to the destination (ROW-1, COL-1) with less than or equal to K obstacle eliminations. $2$ of them downwards and $6$ to the right. The reason for this is simple: If there is an edge ij and an edge js, then there will be a path is through j. Mar 14, 2011 · This is an excellent spot to use the A* search algorithm, a heuristic search algorithm that finds optimal paths between points very quickly even when there are obstacles present. The version of the problem where you only look for the existence of such a path is called the longest path problem. Technically, Breadth-first search (BFS) by itself does not let you find the shortest path, simply because BFS is not looking for a shortest path: BFS describes a strategy for searching a graph, but it does not say that you must search for anything in particular. May 21, 2020 · My first step however, is to find all possible paths from one start point to its corresponding end point, for each pair of points, so that I can then discard all those where a path crosses another. General Idea: Use DFS with Backtracking to explore all paths from node 0 to node n-1. ) therefore having a single algorithm that handles all of them efficiently is not possible. We observe that since the graph is directed, we only follow edges in their specified direction, and we use a visited array to avoid revisiting nodes in the current path. Aug 9, 2012 · @Tichodroma the question is to find "Number of shortest paths between two coordinate points in a graph with constraints" - Dijkstra's Algo is a graph search algorithm that solves the single-source shortest path problem for a graph. Find all possible paths between two points in a matrix using dynamic programming. , grid[0][0]). FindPath[PathGraph[Range[1, 7]], 1, 3, {2}] will give the path 1 -> 2 ->3 which has length 2. A clear path in a binary matrix is a path from the top-left cell (i. In computing, maps are represented as graphs and there are several algorithms for finding the shortest path between nodes in graphs. A* is particularly notable for its performance and accuracy, making it a cornerstone in fields like artificial intelligence, robotics, video games, and geographic information systems. We are given a graph, a source node, and a destination node and we have to Apr 5, 2021 · Dijakstra’s algorithm is one example of this that is guaranteed to find the shortest path through an exhaustive search over all possible paths between two points. Aug 5, 2022 · Upon further reading paths with non-repeating nodes are called simple paths. Oct 30, 2009 · Possible Duplicate: Graph Algorithm To Find All Connections Between Two Arbitrary Vertices I have a directed graph, what algorithm can i use to find the number of distinct acyclic paths between 2 particular vertices, and count the maximum times any path is used in these distinct paths? Sep 17, 2024 · Finding a shortest path between any two vertex in a graph means finding a path such that sum of weights of all the edges included in that path is minimum. Whenever we reach the target node, store the path. Also need help figuring out complexity, which in my best at Feb 2, 2012 · The question was to find all the paths, not to find the number of paths. Point A [5,60] is the source, Point B [60,60] is destination. To implement MapQuest, we need to solve the following shortest-path problem: Given two vertices v and v', what is the shortest path through the graph that goes from v to v' ? That is, the path for which summing up the weights along all the edges from v to v' results in the smallest sum possible. By mastering the strategies and techniques discussed in this guide – from brute force approaches to dynamic programming, DFS, BFS, and A* algorithms – you’ll be well-equipped to tackle a variety of matrix path problems in coding interviews and real-world applications. The robot tries to move to the bottom-right corner (i. Aug 21, 2014 · How to find shortest path between two points, namely S and D, in a matrix ? It should pass through multiple checkpoints named &. This way you can use optimal pre-existent graph algorithms to find the number of all paths between two vertexes in said graph. Can you solve this real interview question? Unique Paths - There is a robot on an m x n grid. The robot is initially located at the top-left corner (i. I can simply count the number of all paths using this algorithm but since it's NP-hard problem, it has ugly time complexity. Count the total number of ways or paths that exist between two vertices in the directed graph. Given the two integers m and n, return the number of possible unique paths that Jul 12, 2025 · Output : -6 Explanation : The minimum cost simple path between 0 and 2 is given by: 0 -----> 3 ------> 4 whose cost is (-2) + (-4) = (-6). Follow the steps below to solve the problem: Traverse the matrix Mar 18, 2024 · , For each two consecutive vertices , where , there is an edge that belongs to the set of edges There is no vertex that appears more than once in the sequence; in other words, the simple path has no cycles The problem gives us a graph and two nodes, and , and asks us to find all possible simple paths between two nodes and . If the path visits every node then it's called a hamiltonian path, if it visits all and ends on a node adjacent to the starting node it's called a hamiltonian cycle. How do I find and store all the possible unique paths form A to B? There are no constraint on which direction I can go from the current po Sep 13, 2014 · However, I need to have the tuples to work with them, so I wanted to get a list of paths of length N between two vertices of that simple path graph. Then, the algorithm gradually updates these distances by checking if shorter paths exist through intermediate nodes. They enable machines to navigate efficiently through complex environments by finding the shortest or most efficient path between two points. Jun 12, 2025 · Given a directed graph and two vertices src and dest, the task is to count all possible walks from vertex src to vertex dest that consist of exactly k edges. The input file contains a grid of characters, where 1 represents an obstacle and 0 represents a vacant cell. Given a Directed Graph. 5 outgoing edges per node. As an experienced programmer, I often get asked about finding the shortest path between two points. For very simple maps you can often do this just by looking at the map, but if the map looks more like a bunch of spaghetti thrown against the wall you're going to need a better method. May 24, 2018 · I'm trying to find all possible paths made of 0 from bottom left to top right, only by moving either up or to the right. Follow the steps to solve the problem: Sep 18, 2025 · Given an `M × N` matrix, find all paths from the first cell to the last cell. It uses a queue to explore all possible paths level by level. This algorithm should be very fast and scale to large graphs (The graph data structure is sparse so it only uses as much memory as it needs to). For example this is the edge list of my graph. The graph is given as follows: graph [i] is a list of all nodes you can visit from node i (i. Mar 18, 2022 · There's a bit of an ambiguity here; how do you count unique paths? In particular, where do the paths end? Do they have to keep going until they run out of non-visited non-obstacle neighbours? Is the empty path counted? All those questions would be answered if you could list all the unique paths on one small example. Path (graph theory) A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). But that is not very practical for maps with many nodes as the combinations grow exponentially. Once the destination node is found, the path is stored. Oct 11, 2016 · However, it is not necessary to examine all possible paths. As is with all shortest paths between a pair of vertices, the number of simple paths between two vertices can be huge. Learn the basics of graphs and explore popular algorithms to find the optimal route between nodes. If not, how can i make changes in BFS/Dijkstra/any other algorithm to enumerate all paths in a DAG Aug 26, 2017 · In a complete graph total number of paths between two nodes is equal to: $\lfloor (P-2)!e\rfloor$ This formula doesn't make sense for me at all, specially I don't know how $ {e}$ plays a role in Oct 25, 2019 · This problem is NP-hard, since the Hamiltonian Path problem is a special case of this problem where we set N=n and check whether the answer is strictly greater than zero. Finding all paths between two nodes in a graph I'm learning graph theory and while I'm not quite confident I'm trying to use simple examples to get some practice in. Jun 6, 2023 · Pathfinding algorithms are a crucial component in a wide range of applications, from video games to robotics and logistics. e. Jul 23, 2025 · Given a 2D matrix of dimension m n, the task is to print all the possible paths from the top left corner to the bottom right corner in a 2D matrix with the constraints that from each cell you can either move to right or down only. Jun 21, 2022 · Now, what I want to do is, I want to retrieve not one single path between two of such points, I want to retrieve all possible paths, through which a value could flow from point A to point B. Given a NxM plane, find all the possible paths between two points with three movements: right, down and diagonal (right-down, 315º). Mar 17, 2025 · Finding every path from the top-left corner to the bottom-right corner of a 2D matrix is a classic algorithmic problem-solving issue. Can you solve this real interview question? Shortest Path in Binary Matrix - Given an n x n binary matrix grid, return the length of the shortest clear path in the matrix. Finding all possible paths in a matrix seems a bit tricky when you here it for Jul 23, 2025 · Given an matrix of size m x n, the task is to find the count of all unique possible paths from top left to the bottom right with the constraints that from each cell we can either move only to the right or down. extractPath can be used to actually extract the path between a given pair of nodes. Sep 12, 2008 · The depth-first search will find all non-cyclical paths between two nodes. The time complexity of this approach is O (2^n), where n is the number of nodes, due to the possibility of Jul 9, 2016 · A path is simple if it repeats no vertices. I've seen many implementations in other programming languages but most of them used queues as in (BFS) to make them work. Dec 11, 2013 · The result of applying the matrix to the vector repeatedly essentially records all the possible paths that could be taken starting from some initial vertex. To effectively walk through the matrix and reveal every possible path, this problem requires investigating a variety of methodologies, such as dynamic programming and backtracking. allShortestPaths finds all shortest paths in a directed (or undirected) graph using Floyd's algorithm. Six unique paths start from the upper left corner. How do I find and store all the possible unique paths form A to B? There are no constraint on which direction I can go from the current po Jul 15, 2025 · The main idea here is to use a matrix (2D array) that will keep track of the next node to point if the shortest path changes for any pair of nodes. The matrix contains two types of cells, empty cells and cells which have obstacles. Looking for code review, optimizations and best practices. Note While finding all the paths, the DFS traversal techinique used here does not mark the nodes as visited while searching for the destination as a node in between can be revisited if it is present in a different path. Dijkstra's algorithm adapts BFS to let you find single-source shortest paths. I have a graph and I want to find all shortest paths between two nodes. If you need all-pairs shortest paths, other algorithms like Floyd-Warshall might be used, but for a single source, Dijkstra's is often preferred. Then all possible paths are encoded in this function, and by traversing π recursively you get all possible path combinations. How do I find and store all the possible unique paths form A to B? There are no constraint on which direction I can go from the current point, it can be up, down, left, right, or diagonal (in all four directions). Given two vertices, I'm finding all simple paths between them using a depth-first search. Even finding the kth shortest path (or longest path) is NP-Hard. and has subsequently been used in many University scripts on the subject. Original question below: I'm trying to find the complexity of an all-paths search as given by this algorithm. It explores the graph by considering the cost of each path from the starting point to other points in the graph. I have a MXN matrix and I select two given points A and B. The path can only be created out of a cell if its value is 1. , grid[m - 1][n - 1]). Aug 12, 2022 · If you need to find the shortest path between two nodes in your graph, you may need a weighted graph (where the edges carry a distance. In this comprehensive guide, I‘ll be sharing my insider knowledge on using Dijkstra‘s algorithm to solve […] Sep 27, 2020 · I have a MXN matrix and I select two given points A and B. Mar 6, 2018 · Suppose to have a graph, represented through its adjacency matrix. , there is a directed edge from node i to node graph [i] [j]). Uniform Cost Search or Dijkstra algo is a search algorithm used to find the shortest path between two points in a graph. Jul 23, 2025 · Finding minimum steps using BFS (Breadth-First Search) The idea is to use Breadth-First Search (BFS) to find the minimum number of steps required to reach the destination. Keep storing the visited vertices in an array say ‘path []’. It cannot pass through G. However, as I noticed, all of these algorithms compute all the paths in that graph or grid, not only those between the two points we are interested in. Jun 26, 2024 · Intuition When faced with the task of finding a path between two nodes, one natural approach is to explore all possible paths starting from the source node. Sep 27, 2020 · I have a MXN matrix and I select two given points A and B. May 11, 2013 · You will have to maintain a special visited set variation that is relevant only for the current path, and not global. Jul 15, 2025 · Given an undirected and unweighted graph and two nodes as source and destination, the task is to print all the paths of the shortest length between the given source and destination. While often it is possible to find a shortest path on a small graph There are other shortest-path problems of interest, such as the all-pairs shortest-path problem: find the lengths of shortest paths between all possible source–destination pairs. For the weighted version you might want to use uniform cost search Note that also in every graph which May 12, 2010 · This finds the shortest path between all pairs of points, but it doesn't find all of the shortest paths between two points. The brute force approach is using backtracking which is $O (n!)$. A* can help you with that. Learn how to handle weighted graphs and calculate the shortest paths between nodes. Or not: perhaps "shortest path" is defined as the least number of intermediate nodes between A and B. Discover the power of combinatorics with our Lattice Path Calculator. If they start and end on the same node, with no other repeating nodes they are called simple cycles. The robot can only move either down or right at any point in time. While often it is possible to find a shortest path on a small graph Apr 26, 2023 · So, this was the general way of finding our path. You can have a closed formula to get the number of them for each length (I described this formula in my answer). A well-known problem in May 13, 2025 · Output: 1 Using Breadth First Search - O (n*m) Time and O (n*m) Space The idea is to use Breadth-First Search (BFS) to explore the matrix level by level to find the shortest path from 's' (source) to 'd' (destination). Jan 8, 2021 · I know that we can calculate number of walks with n length between two vertices of an undirected graph by calculating the nth power of the adjancy matrix but what if you want to avoid repetition in May 28, 2025 · Efficiency for Single Source: It's highly efficient for finding the shortest paths from a single starting point to all other points in the graph. Know how to optimize and tweak the algorithm for performance in Python. So, you need the correct model: a set of nodes, and a set of edges, defined by the 2 nodes it connects. The total number of possible paths would be all possible permutations of UUURRR, namely 6!/ (3!3!) = 20. Gain hands-on experience by solving a real-world shortest path problem using Python. Mar 15, 2023 · Shortest path algorithms come in a variety of forms. Each cell is a Jul 23, 2025 · The main idea is to use Breadth-First Search (BFS) to find all paths from a source to a destination in a directed graph. 1) Initialize an empty list `result` to store all valid paths. How do I find and store all the possible unique paths form A to B? There are no constraint on which direction I can go from the current po May 14, 2025 · Output: No Explanation: There is no path from 0 to 3. By using Depth First Search, we can get all paths between two nodes in a graph. Approach : The main idea to solve the above problem is to traverse through all simple paths from s to t using a modified version of Depth First Search and find the minimum cost path amongst them. I counted an average of 2. This tool helps you calculate the number of unique lattice paths between two points in a grid of any size, taking only right and downward steps. [7]: 196 This MATLAB function returns a matrix, d, where d(i,j) is the length of the shortest path between node i and node j. The idea is to convert the grid into a graph where each cell in the grid is a node and in which there is an edge between any two adjacent cells that aren't obstructed from one another. A graph is like a map that shows how different points (called nodes) are connected by lines (called edges). Examples: Input: matrix [] [] = { {0,0,1}, {1 Interview question for Software Development Engineer. Use backtracking to ensure all possible paths are explored. Each edge has a number, called a weight, that represents the distance or cost to travel between two nodes. The best solution would be coding this problem into a graph, by assigning a unique ID to each cell of the grid and then build either a list of adiacences or an adjacency matrix (if the graph is dense - with a lot of edges - prefer the matrix over the list). One good pseudocode which uses this notation can be found in Introduction to Algorithms by Cormen et al. Feb 11, 2017 · I would like to ask about how I implement a code that can find all paths between two vertices or nodes based on an adjacency matrix. Jul 24, 2025 · The thought process is to recursively explore all possible paths by visiting unvisited neighbors and backtrack to try alternative routes. But I can't seem to get that with the builtin functions. You are exploring all possible paths from source to destination which would mean revisiting nodes again and A tree has exactly one path between any two nodes, but in this problem, we're finding all possible paths from source to target, implying multiple paths can exist. Path-finding is closely related to graph theory, and solves the shortest route/path problem based on some criteria such as which one is shortest/cheapest path. To get from point x (not square x) to point y there are $8$ steps to be taken. This algorithm works for both the directed and undirected It combines the strengths of Dijkstra's algorithm with additional heuristic information to efficiently find the shortest path between two points in a graph. Jul 23, 2025 · Given an M x N matrix where each element can either be 0 or 1. Jul 14, 2020 · Dijkstra’s Algorithm Below are the fundamental steps that are taken by the Dijkstra’s algorithm to find the shortest path between two nodes: Find the start node and initialize its cost/distance to zero and set the cost/distance of all other nodes to infinity. Using Depth First Search - O (V + E) time and O (V) time The idea is to start from the source vertex and explore as far as possible along each branch before moving backFind if there is a path between two vertices in a directed graphFind if there is a path between two vertices in a directed We would like to show you a description here but the site won’t allow us. Lets look at one more application of $A$, Jul 18, 2024 · Given a directed graph, a source vertex ‘src’ and a destination vertex ‘dst’, print all paths from given ‘src’ to ‘dst’. Possible Duplicate: How can I find the number of the shortest paths between two points on a 2D lattice grid? If we have a point $P (x,y)$ in a coordinate system $ [$with $x \geq 0$, $y \geq 0$; that Nov 28, 2013 · Is there any standard algorithm that finds all possible paths in a directed a-cyclic graph. We will use an adjacency matrix and priority queue. Think about a regular polygon and the two paths connecting each opposite pair of corners. , following rules and constraints. The shortest route between points A and B may not always be the same as the shortest route between A and every other point in the graph. Path finding is the problem of finding the shortest route between two given points. I record the network using an adjacency matrix stored in a pandas dataframe, in a way that network [x] [y] store the value of the arrow which goes from x to y. We can only move down or to the right from the current cell. Feb 9, 2013 · If the question is whether or not DFS can find a shortest path in unweighted or weighted graph: the answer is YES! You simply have to traverse ALL possible paths from source to destination and keep the minimum path sum. Dec 26, 2022 · In this paper, we de veloped an intuitive and nature-inspired algorithm to compute all possible shortest paths between two nodes in a graph: Resonance Algorithm (RA). , (n - 1, n - 1)) such that: * All the visited cells of the path are 0 May 22, 2023 · Understand what is Dijkstra shortest path algorithm with full implementation in Java. I noticed that the graph you specified above has only one edge that is directional (B,E). Discover how to implement the shortest path algorithm in Java graphs. Let's say I have the following graph: This MATLAB function returns all paths in graph G that start at source node s and end at target node t. , (0, 0)) to the bottom-right cell (i. If there is no clear path, return -1. However, it just gives me one of the shortest paths if there exists one A* (pronounced "A-star") is a popular pathfinding algorithm used in computer science and artificial intelligence. Dijkstra in 1956 and published three years later. For example, map applications that we use to find our way in daily life usually use algorithms based on the Dijkstra algorithm. By "continuous" I mean that we can travel without lifting up your pencil/digit. Algorithms such as Greedy, Dijkstra’s algorithm, and A* eliminate paths either using educated guesses (heuristics) or distance from We would like to show you a description here but the site won’t allow us. Jun 5, 2025 · The Floyd-Warshall algorithm is a method used in computer science to find the shortest paths between all pairs of nodes in a graph. Jul 4, 2019 · Finding all paths between two vertices in a graph can be a tricky challenge. These paths doesn’t contain any cycle. Aug 2, 2024 · The use of backtracking ensures that all possible paths are explored without missing any. Aug 13, 2016 · 26 The powers of the adjacency matrix don't give you the number of paths but the number of walks between any two vertices. The all-pairs shortest path problem, in which we have to find shortest paths between every pair of vertices v, v' in the graph. Start the traversal from source. Nov 1, 2023 · In this article, we will find the shortest path between two points in a matrix. How would you discover how many paths of arbitrary length n link any two nodes? Dec 21, 2023 · Given a matrix grid [] [] of size M * N, where grid [i] [j] represents the value of the cell at position (i, j), the task is to determine an optimal path from the top-left corner to the bottom-right corner while minimizing the maximum value of |grid [i1] [j1] - grid [i2] [j2]| for adjacent cells along the path. We need to find the shortest path between a given source cell to a destination cell. Paths can p Oct 15, 2017 · In this tutorial we will learn how to find all the simple paths (paths without a cycle) between two nodes in a graph. The Floyd-Warshall algorithm is a good way to solve that problem efficiently. Be able to implement Dijkstra’s Algorithm in Python. Feb 6, 2018 · In the context of graph theory, I'm trying to get all the possible simple paths between two nodes. An algorithm finding all these paths could be to put all 'U's and 'R's in a pool and select one from the pool. It can handle any undirected, directed, or mixed graphs, irrespective of loops, unweighted or positively weighted edges, and can be implemented in a fully decentralized manner. Initially, this array is filled using only the direct edges between nodes. Jun 4, 2020 · The exponential dependency is inherent in the fact that there can be exponentially many paths, and you need to output all of them, so it takes exponential time even to output them all, let alone to find them in the first place. Jun 15, 2023 · In computer science, one of the fundamental problems is finding the shortest path between two nodes in a graph. To do so, every time you "finish" exploring a vertex, you will have to remove it from the set. Whether it‘s routing directions, network traffic optimization, or analyzing social connections, determining the most efficient path is a common need across many domains. 2) Define a helper function `dfs(node, path)`:. The thought process is that BFS guarantees the shortest path in an unweighted grid, making it ideal for this problem. In other words, you need to consider walks such that some vertices/edges are repeated (which do exist). Single-source shortest path on unweighted graphs When you visit a website like Google Maps or use your Smartphone to ask for directions from home to your Aunt’s house in Pasadena, you are usually looking for a shortest path between the two locations. These algorithms work with undirected and directed graphs. Aug 31, 2014 · Now if I choose A as starting point and E as ending point then I have to find all possible paths between A and E whose path length is at most 4 in a time efficient manner. May 28, 2024 · Dijkstra's algorithm helps find the shortest route between two points in a network, like finding the quickest path on a map, by checking and updating distances step-by-step. Dec 14, 2017 · For small maps, one could perhaps calculate all possible routes to the destination and select the shortest. Once you have this graph, the Jan 13, 2020 · I am interested in determining all of the possible "continuous" paths of an NxN matrix in R and returning their result. This can be done by very different methods at different levels. In order to retrieve the shortest path from the origin Jul 17, 2015 · @KingCronus- There can be multiple different paths between two nodes that both have the shortest length among all possible paths between them. Note: Hamiltonian path is defined as the path which visits every vertex of the graph exactly once. Sep 27, 2020 · How do I find and store all the possible unique paths form A to B? There are no constraint on which direction I can go from the current point, it can be up, down, left, right, or diagonal (in all four directions). Here Dec 1, 2017 · At the moment I have implemented an algorithm to find all paths between two nodes. Mar 19, 2015 · Finding all possible paths is a hard problem, since there are exponential number of simple paths. [4][5][6] Dijkstra's algorithm finds the shortest path from a given source node to every other node. If that's not possible, finding a sample of paths that will cover all edges may be alternative. Dijkstra's algorithm (/ ˈdaɪkstrəz / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. find all possible paths between two points in a matrix. * represents an open gate. Jul 23, 2025 · Find whether there is path between two cells in matrix using Recursion: The idea is to find the source index of the cell in each matrix and then recursively find a path from the source index to the destination in the matrix. So it just comes to electing exactly $2$ of the $8$ consecutive steps to be the steps downwards. I just need to find all possible paths somehow to see every behavior of system. The algorithm works by exploring different possible paths, evaluating each one based on Jul 23, 2025 · Floyd Warshall Algorithm: The Floyd–Warshall algorithm works by maintaining a two-dimensional array that represents the distances between nodes. We will call this the cost object. Finding the Shortest Path Imagine you are given a road map and asked to find the shortest route between two points on the map. Oct 16, 2024 · Learning Outcomes Understand the principles behind Dijkstra’s Algorithm. An obstacle elimination is defined as changing a cell's value matrix [i] [j] from 1 to 0. Jul 23, 2025 · As we know there are various types of graphs (weighted, unweighted, negative, cyclic, etc. Dec 13, 2009 · I get a little confused over Big-O complexity when recursion is involved. The BFS algorithm helps explore all possible paths from the starting point (0,0) to the destination point (n-1, m-1). It helps find the shortest path between two points in a graph or a grid. The shortest path problem is applicable in various real-world scenarios such as navigation systems, network routing, traffic optimization, and social network analysis. The algorithm involves recursively finding all the paths until a final path is found to the destination. In this video I have shown how to find all possible simple paths from one source vertex to destination vertex using a simple Depth First Search, something wh Shortest Paths # Compute the shortest paths and path lengths between nodes in the graph. In the previous video, you learnt to count all possible paths between two points in a matrix from top left to bottom right corner and this DP problem is very similar to it. When you visit a website like Google Maps or use your Smartphone to ask for directions from home to your Aunt’s house in Pasadena, you are usually looking for a shortest path between the two locations. One possible solution to find all paths [or all paths up to a certain length] from s to t is BFS, without keeping a visited set. Dec 26, 2022 · In this paper, we developed an intuitive and nature-inspired algorithm to compute all possible shortest paths between two nodes in a graph: Resonance Algorithm (RA). Mar 29, 2014 · Given a directed connected graphs, find all paths from source to destination. I have an undirected, unweighted graph, and I'm trying to come up with an algorithm that, given 2 unique nodes on the graph, will find all paths connecting the two nodes, not including cycles. These computer applications use representations of the street maps as graphs, with estimated driving times as edge weights. It was conceived by computer scientist Edsger W. Initially, the shortest path between any two nodes u and v is v (that is the direct edge from u -> v). This problem is actually #P-hard wich is believed to be strictly harder than NP. May 11, 2021 · A popular kind of question in combinatorics is to count the number of paths between two points in a grid (following simple constraints). Path in a Maze/Grid Grid and Maze Representation: A grid or a maze is generally represented as a 2D array or matrix consisting of rows and columns. I've found a shortest path between two nodes by BFS. Currently I'm trying to create a function that finds all simple paths between two vertices in a graph, but I'm not sure if my approach is correct. Jan 19, 2012 · How do you trace the path of a Breadth-First Search, such that in the following example: If searching for key 11, return the shortest list connecting 1 to 11. If no path is possible then return -1. Dec 20, 2022 · Your All-in-One Learning Portal: GeeksforGeeks is a comprehensive educational platform that empowers learners across domains-spanning computer science and programming, school education, upskilling, commerce, software tools, competitive exams, and more. What would be a nice and clean method of finding all simple paths between two vertices? Assume the input graph is undirected, simple, and it may have cycles in it. Jul 9, 2016 · 38 I know that many algorithms are available for calculating the shortest path between two points in a graph or a grid, like breadth-first, all-pairs (Floyd's), Dijkstra's. In order to tackle different problems, we have different shortest-path algorithms, which can be categorised into two categories: Single Source Shortest Path Algorithms: The problem is we have to count number of paths between a source and a destination in a graph. It's a slight distinction, but the problem is a bit different.