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Same Direction Two Pointers

Slow pointer writes valid values; fast pointer scans ahead. Both move left to right — fast races forward while slow only advances when a valid element is found.

Array In-Place Slow / Fast Time O(n) Space O(1)

📋 When to Use

Remove duplicates or specific values from a sorted array in-place
Partition array: valid elements to front, invalid to back
Move zeroes to the end while preserving relative order
Count distinct or valid elements without extra memory
Need O(1) space — can't copy to a new array

💡 Slow = where to write next valid value. Fast = what to examine next. When fast finds something valid, slow writes it and advances. Duplicate / invalid values are silently skipped by fast.

⚡ Complexity

Time

O(n)

Space

O(1)

Fast pointer visits each element exactly once — O(n) total. Slow pointer never exceeds fast. No auxiliary array needed; modification is in-place with only two integer indices.

Invariant

nums[0..slow] = all unique valid values written so far

Problem — Remove Duplicates from Sorted Array Given a sorted array, remove the duplicates in-place so each unique element appears only once. Return the count of unique elements.
Input: nums = [0, 0, 1, 1, 2, 3, 3] · Answer: 4 (nums becomes [0, 1, 2, 3, _, _, _])

Step 1 / —

🔍 Scan — fast compares, skips duplicates

✍️ Write — slow advances, writes unique value

✅ Done

slow = write pointer (🐢)

fast = scan pointer (🐇)

orange cells = written (valid range)

nums = [0, 0, 1, 1, 2, 3, 3]

slow = 0

fast = 1

unique count = 1

Click ▶ Play or Next ▶ to start

int slow = 0; // write pointer starts at index 0

Complete Java TemplateJAVA

// Two Pointers — Same Direction (Slow/Fast)
int slow = 0;   // write pointer (always behind fast)

for (int fast = 0; fast < nums.length; fast++) {
    if (keep(nums[fast])) {    // condition: not dup, != val, != 0 …
        nums[slow] = nums[fast];
        slow++;
    }
    // else: skip — fast advances, slow waits
}
return slow;   // new length of valid portion

🎯 Practice Problems

#26Remove Duplicates from Sorted ArrayEasy #27Remove ElementEasy #283Move Zeroes — swap non-zero into frontEasy #80Remove Duplicates from Sorted Array II — allow at most 2Medium #905Sort Array By Parity — evens first, odds lastEasy #1089Duplicate Zeros — in-place two-pass trickEasy