What Is the Two Pointers Technique?
The two pointers technique uses two index variables that traverse a data structure — usually from opposite ends or at different speeds — to solve problems without nested loops.
It reduces many O(n²) brute-force solutions down to O(n) time with O(1) space.
When to Use It
- Sorted array / string problems
- Finding pairs that sum to a target
- Removing duplicates in-place
- Reversing or palindrome checks
- Sliding window variants
Pattern 1 — Opposite Ends
Start one pointer at the left, one at the right. Move them toward each other based on a condition.
def two_sum_sorted(arr, target):
left, right = 0, len(arr) - 1
while left < right:
s = arr[left] + arr[right]
if s == target:
return [left, right]
elif s < target:
left += 1
else:
right -= 1
return []
Classic problems: Two Sum II, Valid Palindrome, Container With Most Water.
Pattern 2 — Same Direction (Fast & Slow)
Both pointers start at the same end. The fast pointer advances every step; the slow one only moves when a condition is met.
def remove_duplicates(arr):
if not arr:
return 0
slow = 0
for fast in range(1, len(arr)):
if arr[fast] != arr[slow]:
slow += 1
arr[slow] = arr[fast]
return slow + 1
Classic problems: Remove Duplicates, Move Zeroes, Linked List Cycle Detection.
Pattern 3 — Sliding Window
A window defined by two pointers expands and contracts to track a subarray satisfying a constraint.
def longest_substring_no_repeat(s):
seen = {}
left = 0
best = 0
for right, ch in enumerate(s):
if ch in seen and seen[ch] >= left:
left = seen[ch] + 1
seen[ch] = right
best = max(best, right - left + 1)
return best
Classic problems: Longest Substring Without Repeating Characters, Minimum Window Substring.
Key Insight
Ask yourself: can I express this constraint as a comparison between two positions in the array? If yes, two pointers likely applies.