Cheapest Flights Within K Stops - Solution & Explanation

In this approach, use BFS to explore all possible paths. Utilize a queue to store the current node, accumulated cost, and the number of stops made so far. The key is to traverse by layer, effectively managing the permitted stops through levels of BFS. If we reach the destination within the allowed stops, track the minimum cost.

This solution constructs a graph from the flights list using an adjacency list. For BFS, a queue keeps track of the current city, the accumulated cost to reach that city, and the number of remaining stops allowed. Traverse each city, and only append a city to the queue if doing so reduces the cost to reach it. This ensures we explore the cheapest path first, within k stops. The process continues until all nodes are explored or the cheapest path is found.

This approach leverages a modified version of Dijkstra's algorithm to explore paths from source to destination using a prioritized data structure like a min-heap. Each entry tracks not only the cumulative cost but also the number of stops taken. The algorithm ensures the shortest paths are evaluated first and skips any path with exceeding stops, thus efficiently finding the minimum cost path within allowed stops.

This C++ solution utilizes a min-heap or priority queue data structure to maintain the current city, accumulated cost, and stops left. Priority ensures that cities with the smallest accumulated cost are processed first, following Dijkstra's logic but capped by the number of stops. Each step examines the target city, updating the cost and queuing potential paths until either the destination is reached within allowed stops or the queue is exhausted.