DSA patterns and problem roadmap

You need fast lookup, frequency counting, duplicate detection, or complement matching.

Recognition clues: “frequency,” “duplicates,” “pair sums to target,” “longest consecutive,” “number of subarrays.”

You can move two indices to reduce the search space, especially on sorted arrays or strings.

Recognition clues: Sorted input, pair/triplet search, in-place array changes, left/right boundaries.

You need to examine contiguous ranges and can maintain a window as it expands or shrinks.

You need cumulative sums, range-sum calculations, or to count subarrays with a particular sum.

Recognition clues: “subarray sum equals K,” “sum between indices,” “divisible by K,” “number of ranges.”

Finding the maximum sum of a contiguous subarray.

Data is sorted, or the answer can be searched through a monotonic condition.

Recognition clues: Sorted data, first/last occurrence, minimum feasible capacity, minimum speed, maximize/minimize an answer under constraints.

Ranges overlap, need merging, or ordering simplifies the problem.

Recognition clues: Start/end times, overlapping ranges, meeting schedules, minimum rooms or removals.

You need to process start/end events in chronological order, often to find the maximum number of simultaneous events.

Matching nested structures, processing elements in reverse order, or finding next greater/smaller elements.

Recognition clues: Brackets, nested expressions, next greater element, nearest smaller element, histogram.

You need FIFO processing or the maximum/minimum in a moving window.

Manipulating nodes, reversing pointers, detecting cycles, or finding middle nodes.

Recognition clues: Fast/slow pointers, dummy node, reverse links, merge sorted lists, operations near the tail.

Calculating height, checking tree properties, finding paths, or exploring ancestors.

The tree's ordering property can eliminate unnecessary searches.

A matrix represents connected cells, regions, or movement between locations.

Recognition clues: Islands, regions, grid movement, shortest path by number of steps, multi-source BFS.

Nodes are connected by edges and you need reachability, connected components, or shortest paths in unweighted graphs.

Tasks have dependencies and you need a valid ordering or need to detect a dependency cycle.

You need to connect groups, determine whether two nodes belong to the same component, or detect redundant edges.

Edges have weights or you need the cheapest way to connect a graph.

You repeatedly need the smallest/largest item, top K results, or the next task by priority.

You must explore multiple choices, build candidates, and undo a choice before trying another.

Searching words by prefix, implementing a dictionary, or sharing common prefixes efficiently.

The answer for a larger problem depends on solutions to smaller prefixes or states.

The state depends on two dimensions, such as two strings, two indices, or grid coordinates.

You select items or numbers subject to a capacity, target, or constraint.

A locally optimal choice can be shown to lead to a globally optimal solution.