Analyze a standard implementation of Dijkstra's algorithm used for routing in a sparse graph with 1 million nodes. Propose an optimization to reduce the time complexity from O(V^2) to O(E + V log V) using a min-priority queue. Further, optimize memory usage by suggesting an adjacency list representation over an adjacency matrix. Discuss the trade-offs of using A* search heuristics instead of Dijkstra for this specific use case. Provide a step-by-step explanation of the logic changes required.