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Beginner Core structures and the two basic searches. Learn these first.
Index O(1); append O(1) amortized; insert or delete in the middle O(n)
O(n); O(1) if the target is first Learn first: Dynamic array.
Push, pop, peek O(1) Learn first: Dynamic array.
Enqueue and dequeue O(1) with a deque Learn first: Dynamic array.
Lookup, insert, delete O(1) expected; O(n) worst case Learn first: Dynamic array.
Expected O(n) total Learn first: Hash table (dict and set).
O(n) Learn first: Dynamic array.
O(log n) Learn first: Linear search.
Intermediate Sorting, trees, graphs, and the patterns behind most interview questions.
Insert or delete at a known node O(1); search O(n) Learn first: Dynamic array.
Θ(n log n) in every case Learn first: Binary search.
Θ(n log n) average; Θ(n²) worst case Learn first: Mergesort.
O(n) to build; O(1) per range sum Learn first: Dynamic array.
O(n) Learn first: Two pointers.
O(n) total Learn first: Stack.
Search, insert, delete O(h): O(log n) balanced, O(n) worst case Learn first: Binary search, Linked list.
O(n) Learn first: Binary search tree, Stack.
Peek O(1); push and pop O(log n); build from n items O(n) Learn first: Dynamic array, Binary search tree.
Edge check: matrix O(1), list O(deg(u)) Learn first: Hash table (dict and set), Dynamic array.
O(V + E) Learn first: Queue and deque, Graph representations.
O(V + E) Learn first: Stack, Graph representations.
O(n log n) Learn first: Mergesort.
Advanced Weighted graphs, balanced structures, and problems that need a recurrence.
Θ(n log n) for distinct keys Learn first: Binary heap and priority queue, Mergesort.
Θ(n + k) for values in a range of size k Learn first: Quicksort.
O(n log n) worst case; O(n) on already-sorted input Learn first: Mergesort.
Search, insert, delete O(log n) worst case Learn first: Binary search tree.
Insert and search O(m) for a key of length m Learn first: Hash table (dict and set), Tree traversals.
Amortized O(α(n)) per find or union Learn first: Graph representations.
O((V + E) log V) with a binary heap Learn first: Breadth-first search (BFS), Binary heap and priority queue.
O(V · E) Learn first: Dijkstra's algorithm.
O(E log E) Learn first: Union-Find (disjoint-set union), Quicksort.
O(E log V) with a binary heap; O(V²) with an array Learn first: Dijkstra's algorithm.
O(2ⁿ) subsets; O(n · 2ⁿ) including copying each one Learn first: Depth-first search (DFS).
O(n · n!) to generate all Learn first: Backtracking and subsets.
Number of states × transitions per state Learn first: Backtracking and subsets, Hash table (dict and set).
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