Write an algorithm to find single source shortest path for a graph G whose edge weights arepositive
Question
Write an algorithm to find single source shortest path for a graph G whose edge weights are positive.
Solution
Sure, here is a simple algorithm known as Dijkstra's algorithm to find the shortest path from a single source in a graph with positive edge weights:
-
Initialize a list or array
distances
wheredistances[i]
is the shortest known distance from the source to vertexi
. Setdistances[source] = 0
and for all other vertices, setdistances[i] = infinity
. -
Initialize an empty priority queue
Q
. This queue will keep track of vertices to be examined. Insert the source vertex intoQ
. -
While
Q
is not empty, perform the following steps:- Dequeue the vertex
u
with the smallest distance fromQ
. - For each neighbor
v
ofu
, calculate the alternative path distancealt = distances[u] + weight(u, v)
. - If
alt < distances[v]
, then we've found a shorter path tov
. Updatedistances[v] = alt
and enqueuev
intoQ
.
- Dequeue the vertex
-
Once
Q
is empty, the algorithm is done. The shortest path from the source to any other vertex can be found indistances
.
This algorithm works by iteratively improving the distances
estimate until it contains the shortest possible distances. The priority queue ensures that vertices are examined in increasing order of their distance from the source.
Similar Questions
From a given vertex in a weighted connected graph, find shortest paths to other vertices using Dijkstra’s algorithm.
Solve the following instance of single source shortest paths problem with vertex 'a' as the source usingsuitable method.
The shortest path in a graph with weighted edges can be found using:A. Depth-first searchB. Breadth-first searchC. Dijkstra's algorithmD. Kruskal's algorithm
The shortest path problem can be solved using:A. Depth-first searchB. Breadth-first searchC. Dijkstra's algorithmD. Floyd-Warshall algorithm
What is the best time complexity we can achieve to precompute all-pairs shortest paths in a weighted graph?
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