# 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