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# Title: Dijkstra's Algorithm for finding single source shortest path from scratch

# Author: Shubham Malik

# References: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

from __future__ import print_function

import math

import sys

# For storing the vertex set to retreive node with the lowest distance

class PriorityQueue:

# Based on Min Heap

def __init__(self):

self.cur_size = 0

self.array = []

self.pos = {} # To store the pos of node in array

def isEmpty(self):

return self.cur_size == 0

def min_heapify(self, idx):

lc = self.left(idx)

rc = self.right(idx)

if lc < self.cur_size and self.array(lc)[0] < self.array(idx)[0]:

smallest = lc

else:

smallest = idx

if rc < self.cur_size and self.array(rc)[0] < self.array(smallest)[0]:

smallest = rc

if smallest != idx:

self.swap(idx, smallest)

self.min_heapify(smallest)

def insert(self, tup):

# Inserts a node into the Priority Queue

self.pos[tup[1]] = self.cur_size

self.cur_size += 1

self.array.append((sys.maxsize, tup[1]))

self.decrease_key((sys.maxsize, tup[1]), tup[0])

def extract_min(self):

# Removes and returns the min element at top of priority queue

min_node = self.array[0][1]

self.array[0] = self.array[self.cur_size - 1]

self.cur_size -= 1

self.min_heapify(1)

del self.pos[min_node]

return min_node

def left(self, i):

# returns the index of left child

return 2 * i + 1

def right(self, i):

# returns the index of right child

return 2 * i + 2

def par(self, i):

# returns the index of parent

return math.floor(i / 2)

def swap(self, i, j):

# swaps array elements at indices i and j

# update the pos{}

self.pos[self.array[i][1]] = j

self.pos[self.array[j][1]] = i

temp = self.array[i]

self.array[i] = self.array[j]

self.array[j] = temp

def decrease_key(self, tup, new_d):

idx = self.pos[tup[1]]

# assuming the new_d is atmost old_d

self.array[idx] = (new_d, tup[1])

while idx > 0 and self.array[self.par(idx)][0] > self.array[idx][0]:

self.swap(idx, self.par(idx))

idx = self.par(idx)

class Graph:

def __init__(self, num):

self.adjList = {} # To store graph: u -> (v,w)

self.num_nodes = num # Number of nodes in graph

# To store the distance from source vertex

self.dist = [0] * self.num_nodes

self.par = [-1] * self.num_nodes # To store the path

def add_edge(self, u, v, w):

# Edge going from node u to v and v to u with weight w

# u (w)-> v, v (w) -> u

# Check if u already in graph

if u in self.adjList.keys():

self.adjList[u].append((v, w))

else:

self.adjList[u] = [(v, w)]

# Assuming undirected graph

if v in self.adjList.keys():

self.adjList[v].append((u, w))

else:

self.adjList[v] = [(u, w)]

def show_graph(self):

# u -> v(w)

for u in self.adjList:

print(u, '->', ' -> '.join(str("{}({})".format(v, w))

for v, w in self.adjList[u]))

def dijkstra(self, src):

# Flush old junk values in par[]

self.par = [-1] * self.num_nodes

# src is the source node

self.dist[src] = 0

Q = PriorityQueue()

Q.insert((0, src)) # (dist from src, node)

for u in self.adjList.keys():

if u != src:

self.dist[u] = sys.maxsize # Infinity

self.par[u] = -1

while not Q.isEmpty():

u = Q.extract_min() # Returns node with the min dist from source

# Update the distance of all the neighbours of u and

# if their prev dist was INFINITY then push them in Q

for v, w in self.adjList[u]:

new_dist = self.dist[u] + w

if self.dist[v] > new_dist:

if self.dist[v] == sys.maxsize:

Q.insert((new_dist, v))

else:

Q.decrease_key((self.dist[v], v), new_dist)

self.dist[v] = new_dist

self.par[v] = u

# Show the shortest distances from src

self.show_distances(src)

def show_distances(self, src):

print("Distance from node: {}".format(src))

for u in range(self.num_nodes):

print('Node {} has distance: {}'.format(u, self.dist[u]))

def show_path(self, src, dest):

# To show the shortest path from src to dest

# WARNING: Use it *after* calling dijkstra

path = []

cost = 0

temp = dest

# Backtracking from dest to src

while self.par[temp] != -1:

path.append(temp)

if temp != src:

for v, w in self.adjList[temp]:

if v == self.par[temp]:

cost += w

break

temp = self.par[temp]

path.append(src)

path.reverse()

print('----Path to reach {} from {}----'.format(dest, src))

for u in path:

print('{}'.format(u), end=' ')

if u != dest:

print('-> ', end='')

print('\nTotal cost of path: ', cost)

if __name__ == '__main__':

graph = Graph(9)

graph.add_edge(0, 1, 4)

graph.add_edge(0, 7, 8)

graph.add_edge(1, 2, 8)

graph.add_edge(1, 7, 11)

graph.add_edge(2, 3, 7)

graph.add_edge(2, 8, 2)

graph.add_edge(2, 5, 4)

graph.add_edge(3, 4, 9)

graph.add_edge(3, 5, 14)

graph.add_edge(4, 5, 10)

graph.add_edge(5, 6, 2)

graph.add_edge(6, 7, 1)

graph.add_edge(6, 8, 6)

graph.add_edge(7, 8, 7)

graph.show_graph()

graph.dijkstra(0)

graph.show_path(0, 4)

# OUTPUT

# 0 -> 1(4) -> 7(8)

# 1 -> 0(4) -> 2(8) -> 7(11)

# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)

# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)

# 3 -> 2(7) -> 4(9) -> 5(14)

# 8 -> 2(2) -> 6(6) -> 7(7)

# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)

# 4 -> 3(9) -> 5(10)

# 6 -> 5(2) -> 7(1) -> 8(6)

# Distance from node: 0

# Node 0 has distance: 0

# Node 1 has distance: 4

# Node 2 has distance: 12

# Node 3 has distance: 19

# Node 4 has distance: 21

# Node 5 has distance: 11

# Node 6 has distance: 9

# Node 7 has distance: 8

# Node 8 has distance: 14

# ----Path to reach 4 from 0----

# 0 -> 7 -> 6 -> 5 -> 4

# Total cost of path: 21

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