Finding Shortest Route

Discrete Math · Axiom Academy

EXAMPLE Finding Shortest Route: Dijkstra's Algorithm Learn to find the shortest path in a weighted graph by maintaining distance tables and updating values at each iteration. Find the shortest path from A to E Excellent work! You've successfully applied Dijkstra's algorithm to find the shortest path. Here's what we learned: Greedy Selection: Always visit the unvisited node with the smallest known distance next Distance Updates: For each neighbor of the current node, check if going through the current node provides a shorter path Predecessor Tracking: Keep track of which node led to the best distance for path reconstruction Relaxation: Update distance[v] = min(distance[v], distance[u] + weight(u,v)) Termination: Algorithm completes when the target node is visited or all reachable nodes are processed Dijkstra's algorithm is optimal for graphs with non-negative edge weights and runs in O((V + E) log V) time with a priority queue. It's widely used in GPS navigation, network routing, and many other applications!

This is the written version of the interactive lesson above. See the full Discrete Math course.