Dijkstra's Shortest Path: Heaps Power Graph Algorithms

Concepts: pyDijkstra, pyGraphHeap, pyPipelineDAG

Dijkstra's algorithm is the most important graph algorithm that uses a heap, and it comes up in DE interviews more than most people expect. Not because you are expected to build a routing engine, but because DE systems have dependency graphs: pipeline DAGs, query plans, data lineage graphs. Finding the shortest path through a dependency graph (e.g., minimum-latency data flow path, optimal query plan route) is a real problem. Dijkstra uses a min-heap to always process the cheapest next step. If you understand why, you understand a large class of optimization problems. Dijkstra Implementation The critical line is 'if node in visited: continue'. Because Python's heapq does not support decrease-key, you might push the same node multiple times with different distances. The visited set ensures y