49 lines
1.6 KiB
Markdown
49 lines
1.6 KiB
Markdown
|
---
|
||
|
title: Floyd Warshall Algorithm
|
||
|
---
|
||
|
## Floyd Warshall Algorithm
|
||
|
|
||
|
Floyd Warshall algorithm is a great algorithm for finding shortest distance between all vertices in graph. It has a very concise algorithm and O(V^3) time complexity (where V is number of vertices). It can be used with negative weights, although negative weight cycles must not be present in the graph.
|
||
|
|
||
|
### Evaluation
|
||
|
|
||
|
Space Complexity: O(V^2)
|
||
|
|
||
|
Worse Case Time Complexity: O(V^3)
|
||
|
|
||
|
### Python implementation
|
||
|
|
||
|
```python
|
||
|
# A large value as infinity
|
||
|
inf = 1e10
|
||
|
|
||
|
def floyd_warshall(weights):
|
||
|
V = len(weights)
|
||
|
distance_matrix = weights
|
||
|
for k in range(V):
|
||
|
next_distance_matrix = [list(row) for row in distance_matrix] # make a copy of distance matrix
|
||
|
for i in range(V):
|
||
|
for j in range(V):
|
||
|
# Choose if the k vertex can work as a path with shorter distance
|
||
|
next_distance_matrix[i][j] = min(distance_matrix[i][j], distance_matrix[i][k] + distance_matrix[k][j])
|
||
|
distance_matrix = next_distance_matrix # update
|
||
|
return distance_matrix
|
||
|
|
||
|
# A graph represented as Adjacency matrix
|
||
|
graph = [
|
||
|
[0, inf, inf, -3],
|
||
|
[inf, 0, inf, 8],
|
||
|
[inf, 4, 0, -2],
|
||
|
[5, inf, 3, 0]
|
||
|
]
|
||
|
|
||
|
print(floyd_warshall(graph))
|
||
|
```
|
||
|
|
||
|
#### More Information:
|
||
|
<!-- Please add any articles you think might be helpful to read before writing the article -->
|
||
|
|
||
|
<a href='https://github.com/freecodecamp/guides/computer-science/data-structures/graphs/index.md' target='_blank' rel='nofollow'>Graphs</a>
|
||
|
|
||
|
<a href='https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm' target='_blank' rel='nofollow'>Floyd Warshall - Wikipedia</a>
|