Common Backend Engineering Algorithm Questions

What backend interviewers actually want

The right data structure choice that collapses O(n²) to O(n).

Top patterns

1. HashMap for O(1) lookup — two-sum, anagram grouping. 2. Two pointers — sorted arrays, palindromes, linked list cycles. 3. Sliding window — longest/shortest contiguous subarray. 4. BFS / DFS — graph and grid problems. 5. Heap — top-K, merge k sorted lists. 6. Binary search — including on the answer. 7. Dynamic programming — count ways / min cost / longest X.

Top K frequent elements

```java
List<Integer> topK(int[] nums, int k) {
  Map<Integer, Integer> freq = new HashMap<>();
  for (int x : nums) freq.merge(x, 1, Integer::sum);

PriorityQueue<int[]> heap = new PriorityQueue<>(comparingInt(a -> a[1])); for (var e : freq.entrySet()) { heap.offer(new int[]{e.getKey(), e.getValue()}); if (heap.size() > k) heap.poll(); } List<Integer> out = new ArrayList<>(); while (!heap.isEmpty()) out.add(heap.poll()[0]); Collections.reverse(out); return out; } ```

O(n log k).

LRU cache

class LRU extends LinkedHashMap<Integer, Integer> {
  private final int cap;
  LRU(int cap) { super(cap, 0.75f, true); this.cap = cap; }
  @Override protected boolean removeEldestEntry(Map.Entry<Integer, Integer> e) {
    return size() > cap;
  }
}

How to communicate

1. Restate the problem. Ask about input bounds. 2. State a brute force with complexity. 3. Identify the bottleneck. 4. Propose a data structure that removes it. 5. Code, test on small example, then edge cases.

Process > perfection.

What to study next

• System design — see our System Design & Interviews tutorials.
• Java concurrency — ConcurrentHashMap, CompletableFuture.
• Database internals — indexes, query plans.

Related tutorials

• Big O Notation
• Dynamic Programming For Beginners
• Bfs And Dfs
• Two Pointer Technique