aloalgo.comTwo Pointers Basics
Two pointers is one of the most versatile techniques in coding interviews. The idea is simple: use two pointers to traverse a data structure, avoiding the need for nested loops. This often reduces O(n²) solutions to O(n).The Core Idea
Instead of checking every pair with nested loops, we use two pointers that move based on conditions. The key insight is that by making smart decisions about which pointer to move, we can skip comparisons we know won't work.Why it works: Two pointers leverages the structure of the problem—usually sorted order or some monotonic property—to eliminate unnecessary comparisons.The Three Patterns
Almost every two pointer problem falls into one of these categories:| Pattern | Pointers Start | Movement | Classic Problems |
|---|---|---|---|
| Opposite Ends | Start and end | Move toward each other | Two Sum (sorted), Container With Water |
| Same Direction | Both at start | One fast, one slow | Remove duplicates, Merge arrays |
| Fast & Slow | Both at start | Different speeds | Cycle detection, Find middle |
When to Use Two Pointers
| Signal | Pattern |
|---|---|
| Sorted array + find pair | Opposite ends |
| Palindrome check | Opposite ends |
| In-place array modification | Same direction (slow/fast) |
| Merging sorted arrays | Same direction |
| Linked list cycle | Fast & slow |
| Find middle of list | Fast & slow |
| Reduce O(n²) to O(n) | Usually opposite ends |
Two Pointers vs Sliding Window
They're related but different:| Two Pointers | Sliding Window | |
|---|---|---|
| Goal | Find pair/triplet satisfying condition | Find subarray satisfying condition |
| Typical movement | Toward each other or same direction | Always same direction (right expands) |
| Data usually | Sorted | Not necessarily sorted |
| Example | Two Sum in sorted array | Longest substring without repeats |
Complexity
| Pattern | Time | Space |
|---|---|---|
| Opposite ends | O(n) | O(1) |
| Same direction | O(n) | O(1) |
| Fast & slow | O(n) | O(1) |
| 3Sum (with sorting) | O(n²) | O(1) |
Key Takeaways
- Identify the pattern: Determine whether you need opposite ends, same direction, or fast/slow pointers.
- Leverage structure: Two pointers works best when there's sorted order or a monotonic property to exploit.
- Think about pointer movement: The key decision is which pointer to move based on the current state.
- O(1) space: Two pointers typically uses constant extra space, making it memory efficient.
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