Dijkstra's Algorithm: Difference between revisions
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{{Infobox Algorithm|runtime=O(VE) or O(V^2) depending on data structure|class=[[Graph Algorithm]], [[Greedy Algorithm]]}} | |||
'''Dijkstra's algorithm''' is a solution to the [[Shortest Path Problem|shortest path problem]] for graphs with positively-weighted edges. | |||
= Approach: Greedy = | |||
Dijkstra's algorithm centers around this property: ''of all the edges leaving the source, the shortest edge must be in the shortest path.'' | |||
To reach the shortest path, Dijkstra always picks the shortest edge | |||
leaving the known nodes. In each iteration, it finalizes the distance to | |||
a node by picking the shortest one. | |||
= Implementation = | = Implementation = | ||
<pre> | <pre> | ||
| Line 7: | Line 19: | ||
pi[v] = null | pi[v] = null | ||
d[s] = 0 | d[s] = 0 | ||
Q = V // priority queue of nodes | |||
while Q is not empty: | while Q is not empty: | ||
u = Q.extractMin() | u = Q.extractMin() | ||
| Line 14: | Line 27: | ||
pi[v] = u | pi[v] = u | ||
</pre> | </pre> | ||
[[Category:Algorithms]] | |||
Latest revision as of 05:22, 20 March 2024
Dijkstra's algorithm is a solution to the shortest path problem for graphs with positively-weighted edges.
Approach: Greedy
Dijkstra's algorithm centers around this property: of all the edges leaving the source, the shortest edge must be in the shortest path.
To reach the shortest path, Dijkstra always picks the shortest edge leaving the known nodes. In each iteration, it finalizes the distance to a node by picking the shortest one.
Implementation
Dijkstra(G, w, s) {
// initialize
for all v in V:
d[v] = infty
pi[v] = null
d[s] = 0
Q = V // priority queue of nodes
while Q is not empty:
u = Q.extractMin()
for all v in adj[u]:
if d[v] > d[u] + w(u,v):
d[v] = d[u] + w(u,v)
pi[v] = u
