Bellman –FordThe bellmanFord algorithm solves the single source shortest path problems even in the cases in which edge weights are negative. This algorithm returns a Boolean value indicating whether or not there is a negative weight cycle that is reachable from the source. If there is such a cycle, the algorithm indicates that no solution exists and it there is no such cycle, it produces the shortest path and their weights. ComplexityThe BellmanFord algorithm runs in time O(VE), since the initialization takes Θ(V) time, each of the V  1 passes over the edges takes O(E) time and calculating the distance takes O(E) times. Complete Tutorial with Example : Bellman Ford Algorithm  C Program source code#include<stdio.h> Rough notes about the Algorithm and how it is implemented in the code above: Input Format: Graph is directed and weighted. First two integers must be number of vertices and edges which must be followed by pairs of vertices which has an edge between them. maxVertices represents maximum number of vertices that can be present in the graph. vertices represent number of vertices and edges represent number of edges in the graph. graph[i][j] represent the weight of edge joining i and j. size[maxVertices] is initialed to{0}, represents the size of every vertex i.e. the number of edges corresponding to the vertex. cost[maxVertices][maxVertices] represents the cost of going from one vertex to another. visited[maxVertices]={0} represents the vertex that have been visited. Initialize the graph and input the source vertex. BellmanFord function is called to get the shortest path. BellmanFord function: This function takes the graph obtained (graph[ ][ maxVertices]), cost (cost[ ][maxVertices]) of going from one vertex to other, size (size[maxVertices]) of vertices, source vertex and the total number of vertices (vertices) as arguments. Initialize an array distance[vertices] to store the shortest distance travelled to reach vertex i. Initially distance[source] = 0 i.e. distance to reach the source vertex is zero and distance to reach every other vertex is initialed to infinity (distance[i] = INF, where INF is a very large integer value). We have to repeatedly update the distance V1 times where V represents number of vertices as we visit the vertices. for iter=0 to vertices2 for from=0 to vertices1 for jter=0 to size[from] to = graph[from][jter] if(distance[from] + cost[from][jter] < distance[to]) distance[to] = distance[from] + cost[from][jter] jter + 1 from + 1 iter + 1 Lastly for every vertex print the shortest distance traveled to reach that vertex. Related Tutorials (basic Graph Algorithms) :
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