Advanced Test - Algorithms

Both are self-balancing binary search trees that bound their height at O(log n). AVL trees keep subtree heights within one and rebalance with rotations, giving stricter balance and faster lookups. Red-black trees allow looser balance with color rules, so they rebalance less often and favor frequent insertions and deletions.

Dynamic programming applies when a problem has overlapping subproblems and optimal substructure, solving each subproblem once and combining results. Greedy works only when locally optimal choices lead to a global optimum, such as in minimum spanning trees. When greedy choices can trap you in a suboptimal path, dynamic programming is required.

Dijkstra finds shortest paths from a source to all nodes in a graph with non-negative edge weights. Using a binary heap as the priority queue, it runs in O((V+E) log V) time. It repeatedly extracts the closest unvisited node and relaxes its edges, but it cannot handle negative weights.

A trie stores strings by shared prefixes, so searching, inserting, or checking a word of length m takes O(m) time regardless of how many words are stored. This makes tries ideal for autocomplete, spell checking, and prefix queries, though they can use more memory than hash-based structures.

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