text: # Title: Dijkstra's Algorithm for finding single source shortest path from scratch
  # Author: Shubham Malik
  # References: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
  
  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(f"{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(f"Distance from node: {src}")
          for u in range(self.num_nodes):
              print(f"Node {u} has distance: {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(f"----Path to reach {dest} from {src}----")
          for u in path:
              print(f"{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
  