DSA/algorithms/Python/graphs/dijkstras-algorithm.py

108 lines
2.5 KiB
Python

# Python program for Dijkstra's single
# source shortest path algorithm. The program is
# for adjacency matrix representation of the graph
"""
Time Complexity: O(V2)
Auxiliary Space: O(V)
"""
# Library for INT_MAX
import sys
class Graph():
def __init__(self, vertices):
self.V = vertices
self.graph = [[0 for column in range(vertices)]
for row in range(vertices)]
def printSolution(self, dist):
print("Vertex \tDistance from Source")
for node in range(self.V):
print(node, "\t", dist[node])
# A utility function to find the vertex with
# minimum distance value, from the set of vertices
# not yet included in shortest path tree
def minDistance(self, dist, sptSet):
# Initialize minimum distance for next node
min = sys.maxsize
# Search not nearest vertex not in the
# shortest path tree
for u in range(self.V):
if dist[u] < min and sptSet[u] == False:
min = dist[u]
min_index = u
return min_index
# Function that implements Dijkstra's single source
# shortest path algorithm for a graph represented
# using adjacency matrix representation
def dijkstra(self, src):
dist = [sys.maxsize] * self.V
dist[src] = 0
sptSet = [False] * self.V
for cout in range(self.V):
# Pick the minimum distance vertex from
# the set of vertices not yet processed.
# x is always equal to src in first iteration
x = self.minDistance(dist, sptSet)
# Put the minimum distance vertex in the
# shortest path tree
sptSet[x] = True
# Update dist value of the adjacent vertices
# of the picked vertex only if the current
# distance is greater than new distance and
# the vertex in not in the shortest path tree
for y in range(self.V):
if self.graph[x][y] > 0 and sptSet[y] == False and \
dist[y] > dist[x] + self.graph[x][y]:
dist[y] = dist[x] + self.graph[x][y]
self.printSolution(dist)
# Driver's code
if __name__ == "__main__":
g = Graph(9)
g.graph = [[0, 4, 0, 0, 0, 0, 0, 8, 0],
[4, 0, 8, 0, 0, 0, 0, 11, 0],
[0, 8, 0, 7, 0, 4, 0, 0, 2],
[0, 0, 7, 0, 9, 14, 0, 0, 0],
[0, 0, 0, 9, 0, 10, 0, 0, 0],
[0, 0, 4, 14, 10, 0, 2, 0, 0],
[0, 0, 0, 0, 0, 2, 0, 1, 6],
[8, 11, 0, 0, 0, 0, 1, 0, 7],
[0, 0, 2, 0, 0, 0, 6, 7, 0]
]
g.dijkstra(0)
# OutPut
"""
Vertex Distance from Source
0 0
1 4
2 12
3 19
4 21
5 11
6 9
7 8
8 14
"""