Comparison of Dijkstra’s and Floyd–Warshall algorithms Last Updated : 16 Oct, 2023 Comments Improve Suggest changes Like Article Like Report Dijkstra AlgorithmDijkstra’s Algorithm is a Single-Source Shortest Path SSSP algorithm, i.e., given a source vertex it finds the shortest path from the source to all other vertices. The idea is to generate a SPT (shortest path tree) with a given source as a root and with two sets, one set contains vertices included in the shortest-path tree, other set includes vertices not yet included in the shortest-path tree. At every step of the algorithm, find a vertex that is in the other set (set not yet included) and has a minimum distance from the source. Floyd Warshall AlgorithmFloyd Warshall Algorithm is All-Pair Shortest Path algorithm, which is to find shortest distance between all pair of vertices. The idea is to use a 2-D Distance Array and initialize it with direct edge weights and then iteratively considers all possible intermediate vertices to update the array. The algorithm checks if a path through an intermediate vertex offers a shorter distance between two nodes. Comparison of Dijkstra’s and Floyd–Warshall algorithms on the basis of algorithm:Dijkstra Algorithm:Dijkstra’s Algorithm uses a Greedy approach to find the shortest path from the source to all other vertices. It starts from the source vertex and maintains a set of vertices with known minimum distances from the source. The key idea of the Greedy strategy is selecting the vertex with the currently shortest known distance from the Source and exploring it next. Floyd Warshall Algorithm:Floyd Warshall Algorithm uses Dynamic Programming approach to compute shortest distance between all pair of vertices. The idea of dp approach is to maintain a 2-D Distance Array and initialize it with direct edge weights effectively solving the subproblems for vertex pairs that have direct connections. It then considers additional intermediate vertices to optimize the paths between all pairs. Comparison of Dijkstra’s and Floyd–Warshall algorithms on the basis of Complexity Analysis:Dijkstra Algorithm:The time complexity of Dijkstra Algorithm depends on the specific implementation and data structures used. In a straightforward implementation for dense graphs where E (no. of edges) is approximately equal to V2 (no. of Vertices) time complexity is of O(V2) . However, for Sparse graphs using Priority queue or Min-heap is more optimal which gives time complexity of O(E + V*log(V)). Floyd Warshall Algorithm:For the Floyd Warshall Algorithm, the time complexity is O(V^3), where V represents the number of vertices in the graph. It involves three nested loops that iterate through all possible pairs of nodes and consider all possible intermediaries, leading to a cubic time complexity. Complete Comparison of Dijkstra’s and Floyd–Warshall algorithmsComparison Basis Dijkstra Algorithm Floyd Warshall Algorithm Introduction Dijkstra's algorithm is a single-source shortest path algorithm used to find the shortest paths from a single source vertex to all other vertices in a weighted graph. The Floyd-Warshall algorithm is an all-pairs shortest path algorithm used to find the shortest paths between all pairs of vertices in a weighted graph. Algorithm Greedy approach,as it selects the vertex with the shortest distance It uses Dynamic programming, to compute all pair shortest paths. Data Structure It Typically uses a priority queue or min-heap. It uses a two-dimensional array. Negative Edges Dijkstra's algorithm does not work correctly with graphs that have negative edge weights. The Floyd-Warshall algorithm can handle graphs with both positive and negative edge weights. Time Complexity With a priority queue or min-heap, time complexity is O(E + V*log(V)). The time complexity of the Floyd-Warshall algorithm is O(V^3). Auxilary Space O(V) with priority queue or min-heap. The auxiliary space complexity is O(V^2) because of 2D array used. Use Case It is efficient for finding shortest paths from a single source. It is suitable for finding shortest paths between all pairs of vertices Comment More infoAdvertise with us Next Article Minimum Weight Cycle in a Graph V Vineet Joshi Improve Article Tags : Misc Graph DSA Dijkstra Shortest Path Floyd-Warshall +2 More Practice Tags : GraphMiscShortest Path Similar Reads What is Dijkstra’s Algorithm? | Introduction to Dijkstra's Shortest Path Algorithm In this article, we will be discussing one of the most commonly known shortest-path algorithms i.e. Dijkstra's Shortest Path Algorithm which was developed by Dutch computer scientist Edsger W. Dijkstra in 1956. Moreover, we will do a complexity analysis for this algorithm and also see how it differs 10 min read Dijkstra's Algorithm to find Shortest Paths from a Source to all Given a weighted undirected graph represented as an edge list and a source vertex src, find the shortest path distances from the source vertex to all other vertices in the graph. The graph contains V vertices, numbered from 0 to V - 1.Note: The given graph does not contain any negative edge. Example 12 min read Dijkstra’s Algorithm for Adjacency List Representation | Greedy Algo-8 The Dijkstra's Algorithm, we can either use the matrix representation or the adjacency list representation to represent the graph, while the time complexity of Dijkstra's Algorithm using matrix representation is O(V^2). The time complexity of Dijkstra's Algorithm using adjacency list representation 15+ min read Printing Paths in Dijkstra's Shortest Path Algorithm Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph.We have discussed Dijkstra's Shortest Path algorithm in the below posts. Dijkstra’s shortest path for adjacency matrix representationDijkstra’s shortest path for adjacency list 15 min read Why does Dijkstra's Algorithm fail on negative weights? Dijkstra's Algorithm: It is a graph searching algorithm that uses a Greedy Approach to find the shortest path from the source node to all other remaining nodes. It solves the single-source shortest path problem for a weighted graph. This algorithm keeps track of the weights of the edges for finding 4 min read Applications of Dijkstra's shortest path algorithm Dijkstra’s algorithm is one of the most popular algorithms for solving many single-source shortest path problems having non-negative edge weight in the graphs i.e., it is to find the shortest distance between two vertices on a graph. It was conceived by computer scientist Edsger W. Dijkstra in 1956 4 min read Dijkstra's Algorithm in different languageC / C++ Program for Dijkstra's shortest path algorithm | Greedy Algo-7Problem Statement: Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph. What is Dijkstra's Algorithm? Dijkstra's algorithm is very similar to Prim's algorithm for minimum spanning tree. Like Prim's MST, we generate an SPT (shorte 5 min read Java Program for Dijkstra's shortest path algorithm | Greedy Algo-7Given a graph and a source vertex in the graph, find shortest paths from source to all vertices in the given graph. Dijkstra's algorithm is very similar to Prim's algorithm for minimum spanning tree. Like Prim's MST, we generate a SPT (shortest path tree) with given source as root. We maintain two s 5 min read Dijkstra's shortest path algorithm in PythonGiven a graph and a source vertex in the graph, find the shortest paths from source to all vertices in the given graph. Dijkstra’s algorithm is a popular algorithm for solving many single-source shortest path problems having non-negative edge weight in the graphs i.e., it is to find the shortest dis 4 min read C# Program for Dijkstra's shortest path algorithm | Greedy Algo-7Given a graph and a source vertex in the graph, find shortest paths from source to all vertices in the given graph. Dijkstra's algorithm is very similar to Prim's algorithm for minimum spanning tree. Like Prim's MST, we generate a SPT (shortest path tree) with given source as root. We maintain two s 5 min read Different ways to implement Dijkstra's algorithmDijkstra’s shortest path algorithm using setGiven a weighted undirected graph represented as an edge list and a source vertex src, find the shortest path distances from the source vertex to all other vertices in the graph. The graph contains V vertices, numbered from 0 to V - 1.Example:Input: src = 0, V = 5, edges[][] = [[0, 1, 4], [0, 2, 8], 8 min read Dijkstra's Shortest Path Algorithm using priority_queue of STLGiven a graph and a source vertex in graph, find shortest paths from source to all vertices in the given graph.Input : Source = 0Output : Vertex Distance from Source 0 0 1 4 2 12 3 19 4 21 5 11 6 9 7 8 8 14We have discussed Dijkstra’s shortest Path implementations.Dijkstra’s Algorithm for Adjacency 15+ min read Dijkstra's shortest path algorithm in Java using PriorityQueueDijkstra’s algorithm is very similar to Prim’s algorithm for minimum spanning tree. Like Prim’s MST, we generate a SPT (shortest path tree) with a given source as a root. We maintain two sets, one set contains vertices included in the shortest-path tree, other set includes vertices not yet included 5 min read Variations of Dijkstra's algorithmMinimum Cost using Dijkstra by Modifying Cost of an EdgeGiven an undirected weighted graph of N nodes and M edges in the form of a tuple lets say {X, Y, Z} such that there is an edge with cost Z between X and Y. We are supposed to compute the minimum cost of traversal from node 1 to N. However, we can perform one operation before the traversal such that 15 min read Minimum cost path from source node to destination node via an intermediate nodeGiven an undirected weighted graph. The task is to find the minimum cost of the path from source node to the destination node via an intermediate node. Note: If an edge is traveled twice, only once weight is calculated as cost. Examples: Input: source = 0, destination = 2, intermediate = 3; Output: 12 min read Find Maximum Shortest Distance in Each Component of a GraphGiven an adjacency matrix graph[][] of a weighted graph consisting of N nodes and positive weights, the task for each connected component of the graph is to find the maximum among all possible shortest distances between every pair of nodes. Examples: Input: Output: 8 0 11 Explanation: There are thre 15+ min read Comparison of Dijkstra’s and Floyd–Warshall algorithmsDijkstra AlgorithmDijkstra’s Algorithm is a Single-Source Shortest Path SSSP algorithm, i.e., given a source vertex it finds the shortest path from the source to all other vertices. The idea is to generate a SPT (shortest path tree) with a given source as a root and with two sets, one set contains v 4 min read Minimum Weight Cycle in a Graph Given an undirected, weighted graph with V vertices numbered from 0 to V-1, and E edges represented as a 2D array edges[][], where each element edges[i] = [u, v, w] denotes an edge between nodes u and v with weight w, and all edge weights are positive integers, your task is to find the minimum weigh 15+ min read Like