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117 lines
3.2 KiB
Plaintext
117 lines
3.2 KiB
Plaintext
---
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title: 'Two Pointers'
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description: 'Converging/parallel index walk that prunes the O(n^2) pair space using order.'
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---
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## The idea
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Checking every pair costs O(n²). That is n² boxes to open.
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But if the array is **ordered**, you do not need every pair.
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Put one pointer at each end. Look at the sum:
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- Too small? Only a bigger left value can help. Move left in.
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- Too big? Only a smaller right value can help. Move right in.
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Each move kills a whole row of the pair space. O(n²) → O(n).
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## The picture
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```mermaid
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flowchart TD
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A["2 7 11 15 target 18<br/>L R"] --> B["2 + 15 = 17 < 18<br/>too small → move L right"]
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B --> C["2 7 11 15<br/> L R"]
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C --> D["7 + 15 = 22 > 18<br/>too big → move R left"]
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D --> E["2 7 11 15<br/> L R"]
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E --> F["7 + 11 = 18 ✓"]
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style F fill:#2e7d32,color:#fff
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```
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## Not the same as binary search
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Binary search **jumps** to the middle and discards half unseen — O(log n).
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Two pointers **walks** — every element gets inspected once — O(n).
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Both need order. Different moves.
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## Two Sum II (LC 167) — the pure template
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```python
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def two_sum(numbers: list[int], target: int) -> list[int]:
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lo, hi = 0, len(numbers) - 1
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while lo < hi:
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total = numbers[lo] + numbers[hi]
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if total == target:
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return [lo + 1, hi + 1]
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if total < target:
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lo += 1 # only a bigger value helps
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else:
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hi -= 1 # only a smaller value helps
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```
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## Container With Most Water (LC 11) — move the shorter wall
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Water = width × shorter wall.
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Moving the taller wall can never help — width shrinks, height cannot grow.
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So always move the shorter one. Say this proof in the interview.
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```python
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def max_area(height: list[int]) -> int:
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lo, hi = 0, len(height) - 1
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best = 0
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while lo < hi:
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best = max(best, (hi - lo) * min(height[lo], height[hi]))
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if height[lo] < height[hi]:
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lo += 1
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else:
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hi -= 1
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return best
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```
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## 3Sum (LC 15) — fix one, converge two
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Sort first. Fix the smallest number. Now it is Two Sum II on the rest.
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Skip duplicates at every level or you get repeat triplets.
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```python
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def three_sum(nums: list[int]) -> list[list[int]]:
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nums.sort()
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result = []
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for i in range(len(nums) - 2):
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if i > 0 and nums[i] == nums[i - 1]:
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continue # skip duplicate anchor
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lo, hi = i + 1, len(nums) - 1
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while lo < hi:
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total = nums[i] + nums[lo] + nums[hi]
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if total < 0:
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lo += 1
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elif total > 0:
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hi -= 1
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else:
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result.append([nums[i], nums[lo], nums[hi]])
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lo += 1
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while lo < hi and nums[lo] == nums[lo - 1]:
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lo += 1 # skip duplicate pair
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return result
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```
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## Complexity
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| | Time | Space |
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|---|---|---|
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| Converging pair | O(n) | O(1) |
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| 3Sum | O(n²) — sort + n passes | O(1) extra |
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## Close-out ritual
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Before you submit, say out loud:
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1. Time and space complexity.
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2. One edge case trace: two elements, all duplicates, or no valid answer.
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## Plan problems
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**A-set:** LC 125 · 167 · 15 · 11 · 42
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**B-set:** LC 392 · 977 · 189 · 80
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