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When BFS Isn't Enough
BFS layers equal shortest paths only while every edge costs 1 — see why weights break that, and how always expanding the cheapest frontier node (Dijkstra's idea) fixes it.
Complete codeMultiple choice - 2
Shortest Path in Binary Matrix
Classic BFS layers with two twists: neighbors connect in 8 directions, and path length counts CELLS — the start is 1, not 0.
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Shortest Path with Alternating Colors
The state-augmentation lesson: the BFS state is (node, last edge color), not the node — one node can be visited twice, once per arriving color.
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Path with Maximum Probability
Dijkstra flipped upside down: MAXIMIZE a product of probabilities with a max-heap, relaxing when prob[u] * w beats prob[v] — and see why the greedy guarantee survives the flip.
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Path With Minimum Effort
Dijkstra on a different metric: a route's cost is its single WORST step — relax with max(effort so far, height diff), not a sum. Bonus: the same problem falls to binary-search-the-answer.
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Cheapest Flights Within K Stops
The constraint that breaks Dijkstra: with at most K stops, a pricier route using fewer flights can be the right answer — so run K+1 Bellman-Ford rounds over a SNAPSHOT of the previous round's distances.
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Shortest Paths CheckpointCheckpoint
No new concepts — carry the island's tools into unseen territory: fee-loaded toll roads, a board game crossed in dice spins, a maze with one breakable wall, and a flooding grid where only the worst step counts.
Complete codeCode orderMultiple choiceTrace - 8
Shortest Paths ReviewReview
Mixed recap of the island: when plain BFS is enough, the Dijkstra loop with stale-entry skipping, swapping the metric (sum, max, product), states bigger than a node, hop budgets that demand rounds, and what the heap costs you.
Complete codeCode orderMultiple choice - 9
Boss: Network Delay TimeBoss
The island's final duel: one signal, n listeners. Run Dijkstra from node k, skip the heap's stale entries, and remember what the question asks — the network is done when the LAST node hears, so answer with the max arrival time, or -1 if anyone never hears at all.
Complete codeDebugCode orderMultiple choiceTrace
Trees & Graphs is part of AlgoFox Pro
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