The 7 Algorithm Patterns That Cover 80% of Coding Interview Problems

When to use it: You need to find the maximum, minimum, or some property of a contiguous subarray or substring of a fixed or variable size. The key signal: the problem involves an array or string and asks about a 'window' of elements.

Interview tip: Start with a brute-force O(n²) and ask yourself: 'What changes as I move one step forward?' If the answer is 'I only add one element and remove one,' a sliding window brings it to O(n). Interviewers love when you verbalize this transition.

When to use it: The input is sorted (or can be sorted) and you're looking for pairs, triplets, or need to partition elements. Also applies to linked list problems involving cycle detection or finding a midpoint.

Interview tip: There are two variants: same-direction (fast/slow) and opposite-direction (left/right). Make sure you know which one applies. In interviews, draw the array and physically move the pointers — it makes your reasoning visible and reduces errors.

When to use it: You need the shortest path in an unweighted graph, need to process a tree level by level, or need to explore all neighbors before going deeper. BFS guarantees the shortest path in terms of number of edges.

Interview tip: The queue is everything in BFS. In an interview, always state explicitly: 'I'm using a queue to process nodes level by level.' Then explain why that gives you the shortest path. Knowing the O(V+E) complexity and being able to justify it out loud is what separates average from strong candidates.

When to use it: You need to explore all possibilities, build combinations or permutations, or traverse a tree/graph looking for a specific path. Backtracking adds the ability to undo choices and explore alternatives.

Interview tip: The backtracking template is always: choose → explore → unchoose. Write that structure explicitly in interviews. The most common mistake is forgetting to 'unchoose' — make sure your solution restores state before returning from each recursive call.

When to use it: The search space is sorted or monotonic. This is broader than 'find an element in a sorted array' — binary search applies whenever you can answer 'is the answer ≥ X?' for any X in a sorted range. This includes problems like finding the minimum capacity, the kth smallest, or the optimal resource allocation.

Interview tip: The off-by-one errors in binary search are a common failure point. Internalize one template (lo=0, hi=n-1, while lo<=hi) and stick to it. For the 'search on answer' variant, always verify: 'Is my search space monotonic? Can I define a condition that splits it cleanly?' If yes, binary search works.

When to use it: The problem asks for a count, minimum, maximum, or existence of something, and the naive recursive solution has overlapping subproblems (you compute the same sub-answer multiple times). DP caches those sub-answers to avoid recomputation.

Interview tip: Always start DP with the recursive definition. Define dp[i] (or dp[i][j]) in plain English before writing any code. Then convert to bottom-up if needed. In interviews, saying 'dp[i] represents the minimum cost to reach step i' shows structured thinking — that's what the interviewer wants to see, not just a working solution.

When to use it: You need the shortest path in a weighted graph (all non-negative weights). BFS doesn't work here because edges have different costs — you need to always expand the cheapest node first. That's Dijkstra with a min-heap.

Interview tip: Dijkstra requires a min-heap (priority queue). The pattern is always: push (cost, node) → pop cheapest → skip if already visited → process neighbors. Know the O((V+E) log V) complexity. For interviews involving negative weights, mention Bellman-Ford — it shows you understand the boundaries of each algorithm.