# Algorithms and Data Structures for Coding Interviews: The Essential Guide

> Prepare for coding interviews by mastering essential algorithms and data structures like arrays, hash tables, trees, graphs, and dynamic programming. Solve over 90% of problems.

- Repository: [Yangshun Tay/tech-interview-handbook](https://github.com/yangshun/tech-interview-handbook)
- Tags: deep-dive
- Published: 2026-02-25

---

**Mastering arrays, hash tables, trees, graphs, and dynamic programming provides the foundation to solve over 90% of coding interview questions at top tech companies.**

Coding interviews consistently test a predictable set of algorithms and data structures. According to the `yangshun/tech-interview-handbook` repository, internalizing these core concepts gives you the building blocks to tackle the vast majority of problems you'll encounter on LeetCode, HackerRank, or in on-site interviews at companies like Google, Meta, and Amazon.

## Core Data Structures for Coding Interviews

### Arrays and Strings

Arrays provide constant-time random access and serve as the starting point for most interview problems involving sequences of numbers or characters. Key patterns include index-based traversal, the **sliding window** technique for substring problems, **two-pointer** approaches for in-place modifications, and **binary search** on sorted arrays.

Reference: [`apps/website/contents/algorithms/array.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/array.md)

### Linked Lists

Linked lists excel in scenarios requiring frequent insertions or deletions without shifting elements. Essential techniques include using **sentinel/dummy head** nodes to simplify edge cases, **fast and slow pointers** for cycle detection and finding the middle node, and **in-place reversal** algorithms.

Reference: [`apps/website/contents/algorithms/linked-list.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/linked-list.md)

### Stacks and Queues

These structures model LIFO and FIFO behavior, appearing in parsing problems, expression evaluation, and tree traversals. Master the **monotonic stack** pattern for "next greater element" problems and queue-based **level-order traversal** (BFS) for trees and graphs.

References: [`apps/website/contents/algorithms/stack.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/stack.md), [`apps/website/contents/algorithms/queue.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/queue.md)

### Trees

Hierarchical data structures enable logarithmic-time search and divide-and-conquer strategies. Focus on **binary search trees (BST)**, **AVL trees**, **tries** for prefix matching, and **segment trees** for range queries. Master recursive **DFS** (in-order, pre-order, post-order) and iterative **BFS** traversals.

Reference: [`apps/website/contents/algorithms/tree.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/tree.md)

### Graphs

Graphs model arbitrary relationships essential for networking, social networks, and path-finding. Key representations include **adjacency lists** and **matrices**. Master **DFS**, **BFS**, **topological sort**, **Dijkstra's** algorithm for shortest paths, and **Union-Find** (Disjoint Set Union) for cycle detection and connected components.

Reference: [`apps/website/contents/algorithms/graph.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/graph.md)

### Hash Tables

Hash tables provide O(1) average-time lookups for frequency counting, duplicate detection, and memoization. Understand **collision resolution** strategies (separate chaining vs. open addressing) and the **"two-sum"** pattern using hash maps for complementary lookups.

Reference: [`apps/website/contents/algorithms/hash-table.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/hash-table.md)

### Heaps (Priority Queues)

Heaps offer O(log n) insertion and extraction of extreme elements, crucial for "k-largest/k-smallest" problems and **Dijkstra's algorithm**. Master **min-heap** and **max-heap** implementations, **heap-sort**, and median maintenance using two heaps.

Reference: [`apps/website/contents/algorithms/heap.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/heap.md)

## Essential Algorithmic Techniques

### Sorting and Searching

Many problems require sorted data to achieve O(log n) or O(n log n) performance. Master **QuickSort**, **MergeSort**, and **HeapSort**. For searching, go beyond basic binary search to variants like **lower/upper bound** and **search in rotated sorted arrays**.

Reference: [`apps/website/contents/algorithms/sorting-searching.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/sorting-searching.md)

### Dynamic Programming

Dynamic programming turns exponential-time recursion into polynomial-time solutions by caching sub-problem results. Learn **bottom-up tabulation** vs. **top-down memoization**. Master classic patterns: **knapsack**, **longest increasing subsequence**, **edit distance**, and **state compression** using bitmasks.

Reference: [`apps/website/contents/algorithms/dynamic-programming.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/dynamic-programming.md)

### Recursion and Backtracking

Recursion provides a natural way to explore combinatorial spaces for problems like **N-Queens**, **subset generation**, and **permutation generation**. Master **base case** identification, **pruning** strategies to cut impossible branches, and **backtracking** templates.

Reference: [`apps/website/contents/algorithms/recursion.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/recursion.md)

### Greedy Algorithms

Greedy algorithms make locally optimal choices when the problem satisfies the **greedy-choice property**. Key applications include **activity selection**, **interval scheduling**, **Huffman coding**, and **Minimum Spanning Tree** algorithms (**Kruskal's** and **Prim's**).

Reference: [`apps/website/contents/algorithms/interval.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/interval.md)

## How to Approach Coding Interview Problems

According to the `yangshun/tech-interview-handbook` source code, successful candidates follow a systematic four-step process:

1. **Identify the underlying data structure** – Most interview statements hint at a suitable representation (e.g., "list of numbers" suggests an array, "family tree" suggests a binary tree).

2. **Choose the right traversal or access pattern** – Use two pointers for linear scans, BFS/DFS for graph or tree traversal, or a heap for "always fetch the next greatest" scenarios.

3. **Apply the appropriate algorithmic technique** – If the problem requires optimal sub-structure, consider dynamic programming or greedy algorithms; otherwise, a simple iterative solution often suffices.

4. **Optimize time and space** – Use in-place array modifications, sentinel nodes, or hash-based look-ups to meet O(1) space constraints when the interviewer asks for optimization.

## Common Coding Patterns with Examples

Below are concise implementations illustrating the most frequently tested patterns from the `yangshun/tech-interview-handbook` repository.

### Sliding Window with Hash Map

```javascript
function lengthOfLongestSubstring(s) {
  const seen = new Map();
  let left = 0, maxLen = 0;

  for (let right = 0; right < s.length; right++) {
    const ch = s[right];
    if (seen.has(ch) && seen.get(ch) >= left) {
      left = seen.get(ch) + 1;
    }
    seen.set(ch, right);
    maxLen = Math.max(maxLen, right - left + 1);
  }
  return maxLen;
}

```

### Fast and Slow Pointers (Cycle Detection)

```javascript
function hasCycle(head) {
  let slow = head, fast = head;
  while (fast && fast.next) {
    slow = slow.next;
    fast = fast.next.next;
    if (slow === fast) return true;
  }
  return false;
}

```

### In-Place Array Reversal

```javascript
function reverseArray(arr) {
  let i = 0, j = arr.length - 1;
  while (i < j) {
    [arr[i], arr[j]] = [arr[j], arr[i]];
    i++; j--;
  }
  return arr;
}

```

### Binary Search Variant (Lower Bound)

```javascript
function lowerBound(nums, target) {
  let lo = 0, hi = nums.length;
  while (lo < hi) {
    const mid = Math.floor((lo + hi) / 2);
    if (nums[mid] < target) lo = mid + 1;
    else hi = mid;
  }
  return lo;
}

```

### Dynamic Programming (Kadane's Algorithm)

```javascript
function maxSubArray(nums) {
  let best = -Infinity, cur = 0;
  for (const x of nums) {
    cur = Math.max(x, cur + x);
    best = Math.max(best, cur);
  }
  return best;
}

```

### Heap (Merge K Sorted Lists)

```javascript
class MinHeap {
  constructor() { this.heap = []; }
  push(node) { /* heap insertion logic */ }
  pop() { /* heap extraction logic */ }
}

function mergeKLists(lists) {
  const heap = new MinHeap();
  for (const node of lists) if (node) heap.push(node);
  
  const dummy = { val: 0, next: null };
  let cur = dummy;
  
  while (heap.heap.length) {
    const node = heap.pop();
    cur.next = node;
    cur = cur.next;
    if (node.next) heap.push(node.next);
  }
  return dummy.next;
}

```

## Key Study Resources

The `yangshun/tech-interview-handbook` repository provides detailed cheat-sheets for each topic. Reference these files for comprehensive explanations, complexity analysis, and curated practice problems:

- [`apps/website/contents/algorithms/array.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/array.md) – Sliding window, two-pointer techniques, and binary search variants
- [`apps/website/contents/algorithms/linked-list.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/linked-list.md) – Sentinel nodes, fast/slow pointers, and in-place reversal
- [`apps/website/contents/algorithms/stack.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/stack.md) – Monotonic stacks and parsing patterns
- [`apps/website/contents/algorithms/queue.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/queue.md) – BFS implementations and circular buffers
- [`apps/website/contents/algorithms/tree.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/tree.md) – DFS/BFS traversals, BST operations, and trie structures
- [`apps/website/contents/algorithms/graph.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/graph.md) – Adjacency representations, shortest paths, and Union-Find
- [`apps/website/contents/algorithms/hash-table.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/hash-table.md) – Collision resolution and frequency counting patterns
- [`apps/website/contents/algorithms/heap.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/heap.md) – Priority queue operations and median maintenance
- [`apps/website/contents/algorithms/sorting-searching.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/sorting-searching.md) – QuickSort, MergeSort, and binary search patterns
- [`apps/website/contents/algorithms/dynamic-programming.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/dynamic-programming.md) – Memoization, tabulation, and state compression
- [`apps/website/contents/algorithms/recursion.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/recursion.md) – Backtracking templates and base-case optimization
- [`apps/website/contents/algorithms/interval.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/interval.md) – Greedy scheduling and sweep-line algorithms

## Summary

- **Arrays and hash tables** form the foundation for most linear-time solutions, offering O(1) access and efficient lookups.
- **Trees and graphs** require mastery of **BFS** and **DFS** traversals, with special attention to binary search trees and Union-Find for connectivity problems.
- **Dynamic programming** transforms exponential recursive solutions into polynomial time using memoization or tabulation.
- **Two-pointer, sliding window, and fast/slow pointer** patterns appear repeatedly across array and linked-list problems.
- **Heaps** enable efficient access to extreme elements, crucial for "top k" problems and graph algorithms like Dijkstra's.

## Frequently Asked Questions

### What are the most important data structures for coding interviews?

Arrays, hash tables, trees, and graphs constitute the essential data structures for coding interviews. Arrays provide constant-time random access and serve as the basis for two-pointer and sliding window patterns. Hash tables enable O(1) lookups for frequency counting and duplicate detection. Trees and graphs test your ability to implement recursive DFS and iterative BFS traversals, with binary search trees and adjacency lists being particularly common.

### How do I know which algorithm to use during an interview?

Follow the four-step framework from the `yangshun/tech-interview-handbook`: first, identify the underlying data structure suggested by the problem statement. Second, select the appropriate traversal pattern—two pointers for linear data, BFS/DFS for hierarchical or networked data, or heaps for ordered access. Third, determine if the problem exhibits optimal substructure (suggesting dynamic programming) or can be solved with a greedy approach. Finally, optimize for the requested time and space complexity constraints.

### Should I memorize sorting algorithms for coding interviews?

You should understand the implementation and complexity of QuickSort, MergeSort, and HeapSort, but modern interviews rarely ask you to write them from scratch. Instead, focus on **binary search** and its variants (finding insertion points, searching rotated arrays, and lower/upper bound calculations), as these patterns appear frequently in array manipulation problems. Review the [`apps/website/contents/algorithms/sorting-searching.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/sorting-searching.md) file for specific binary search templates.

### Is dynamic programming necessary for every coding interview?

While not every question requires dynamic programming, DP is a high-yield topic that distinguishes mid-level from senior-level candidates. You should master classic patterns including the **0/1 knapsack**, **longest increasing subsequence**, **edit distance**, and **Kadane's algorithm** for maximum subarray problems. Study both top-down memoization and bottom-up tabulation approaches, as documented in [`apps/website/contents/algorithms/dynamic-programming.md`](https://github.com/yangshun/tech-interview-handbook/blob/main/apps/website/contents/algorithms/dynamic-programming.md).