Algorithm for Finding Shortest Path Between Two Nodes in a Weighted Graph

When designing and implementing an algorithm to find the shortest path between two nodes in a weighted graph, it is important to consider both time complexity and space complexity. One efficient algorithm for solving this problem is Dijkstra's algorithm.

Dijkstra's algorithm is a greedy algorithm that finds the shortest path from a starting node to all other nodes in the graph. It works by iteratively expanding the set of nodes that have been visited, updating the shortest path to each node as it goes.

When implementing Dijkstra's algorithm, you will need to maintain a priority queue to keep track of the nodes that need to be visited next, as well as an array to store the shortest path to each node. The time complexity of Dijkstra's algorithm is O(E log V), where E is the number of edges in the graph and V is the number of vertices. The space complexity is O(V) to store the shortest path to each node.

By using Dijkstra's algorithm, you can efficiently find the shortest path between two nodes in a weighted graph while minimizing both time and space complexity.