Structures Mix roadmap

Problems where two or three structures have to work together.

For: Know each structure alone, ready to combine them

Two Pointers

Walk a sequence from both ends, or at two speeds, to avoid nested loops.

Keep a moving range valid while you slide it across the input.

Precompute running totals so any range sum costs one subtraction.

Last in, first out. Use it to match pairs and undo work.

Halve the search space each step, on sorted data or on an answer range.

Keep the stack ordered to find the next greater or smaller item in one pass.

First in, first out, plus a deque for sliding maximums and level-by-level work.

Combine data structures to build a cache, a stack with extras or an iterator.

Always get the smallest or largest item next without sorting everything.

Share prefixes in a tree of characters for fast prefix and dictionary lookups.

Think recursively: solve a node from the answers for its children.

Traverse connected structures: islands, components, shortest hops in a grid.

Break a problem into overlapping subproblems and store each answer once.

Order tasks by their dependencies and detect cycles.

Track which items are connected with near-constant-time merges and lookups.

Dijkstra and Bellman-Ford for weighted graphs.

Choose items under a budget; the pattern behind coin change and partitions.

Fill a table indexed by two variables: grids, two strings, intervals.

Connect every node at minimum total cost with Kruskal or Prim.