Two Pointers

01 / The shared mechanism

Two indices moving over the same sequence to maintain an invariant — the move rule changes per sub-pattern, but the mechanism is shared.

02 / The one-sentence essence

Two pointers advancing at different rates over the same sequence — the asymmetry lets you compress in place, locate a midpoint, or detect a cycle without extra memory.

Problemremove duplicates from a sorted array in-placeInput[1, 1, 2, 2, 3, 3]

Sorted input. The first element is always kept — slow at 0; fast will scan from 1.

step

0 / 8

slow · fast

0 · —

action

init

unique so far

0 / 8

sorted array

03 / The pattern signature

# in-place compaction variantslow ← 0for fast in 1..n−1:if arr[fast] ≠ arr[slow]:slow++arr[slow] ← arr[fast]return slow + 1# cycle-detection variant: fast moves 2x, slow moves 1x — they meet iff a cycle exists

04 / When to recognize this pattern

"in place"

You must edit the input without allocating a second array. Slow tracks where the next kept element belongs.

"cycle"

Detect or locate a cycle in a linked list or pointer chain. Fast moves twice as fast as slow — they meet iff a cycle exists.

"middle"

Find the midpoint of a list in one pass: when fast hits the end, slow is at the middle.

"compact / partition"

Keep elements satisfying some predicate at the front, discard the rest. Same mechanism as remove-duplicates with a different keep-condition.

05 / Common pitfalls

Initializing both pointers at the same position.

For compaction, slow starts at 0 and fast at 1. For cycle detection, both start at the head — but fast advances before the first comparison. Pick the convention per problem.

Advancing slow at the wrong moment.

Update slow before writing, not after — otherwise you overwrite the last kept value. The off-by-one here is the difference between a correct result and a shifted one.

Confusing this with sliding window.

Sliding window sizes a contiguous chunk. Fast/slow uses asymmetric speeds — the gap between the two pointers is the answer (or a signal), not a window over data.

06 / Go practice — on LeetCode

easy14

01Remove Duplicates from Sorted Array— LC 26→02Remove Element— LC 27→03Merge Sorted Array— LC 88→04Valid Palindrome— LC 125→05Linked List Cycle— LC 141→06Happy Number— LC 202→07Palindrome Linked List— LC 234→08Move Zeroes— LC 283→09Middle of the Linked List— LC 876→10Sort Array By Parity— LC 905→11Sort Array By Parity II— LC 922→12Squares of a Sorted Array— LC 977→13Duplicate Zeros— LC 1089→14Apply Operations to an Array— LC 2460→

medium11

01Remove Nth Node From End of List— LC 19→02Sort Colors— LC 75→03Remove Duplicates from Sorted Array II— LC 80→04Linked List Cycle II— LC 142→05Find the Duplicate Number— LC 287→06String Compression— LC 443→07Circular Array Loop— LC 457→08Swapping Nodes in a Linked List— LC 1721→09Minimize Hamming Distance After Swap Operations— LC 1722→10Delete the Middle Node of a Linked List— LC 2095→11Maximum Twin Sum of a Linked List— LC 2130→

— / When to use which

converging

Use when the array is sorted and the answer is a pair.

two-sum · palindrome · container

fast / slow

Use for in-place modification or cycle detection.

remove-dupes · linked-list cycles

sliding window

Use when the condition is about a contiguous chunk.

longest/shortest · at-most-k