# Shortest path and 2nd shortest path using Dijkstra – code

Dijkstra’s algorithm is an algorithm to find the shortest paths between vertices in a graph. It uses greedy technique by picking the un-visited vertex with the lowest distance. When all vertices have been evaluated, the result is the shortest path. This post provides code to find shortest path and second shortest path by using Dijkstra algorithm.

Find 2nd shortest path is a Find kth problem. It can be achieved by using K_shortest_path_routing or Yen’s_algorithm. However I introduce a simple approach. The steps are: first find the shortest path using dijkstra. Second, remove each edge in the shortest path. Now find the shortest path again. Finally compare and return the shortest path among them as the second shortest path from source to destination.

In the following implementation, the graph is undirected and represented as a matrix.

Amazon Interview Question:
You are given a graph and an algorithm that can find the shortest
the path between any two nodes
Now you have to find the second shortest path between the same two nodes.

## Python

Output:
Shortest distance: 6
2nd shortest distance: 8

O Notation:
Shortest path: Time complexity: O(n^2), Space complexity: O(n)
Second shortest path: Time complexity: O(n^3), Space complexity: O(n)