Two Pointer Problems Pattern

1. Opposite Direction (Two-pointer from Ends)

✅ Use When:

• You need to find pairs in a sorted array.

• You need to check if a string/array is a palindrome.

• You are finding an optimal solution between two boundaries (like maximum area, min/max sum).

🔹 Examples:

• Two Sum (Sorted Array) → Find if two numbers add up to a target.

• Checking Palindrome → "racecar" → Yes, "hello" → No

• Container with Most Water → Find the max area between two vertical lines.

🛠 How to Apply:

• Start with one pointer at the beginning and one at the end.

• Move pointers towards each other based on conditions.

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2. Same Direction (Two-pointer moving forward)

✅ Use When:

• You need to merge two sorted arrays/lists.

• You need to find the longest or shortest subarray/substring.

• You are iterating through a sorted structure while maintaining constraints.

🔹 Examples:

• Merging Two Sorted Arrays → arr1 = [1,3,5], arr2 = [2,4,6] → [1,2,3,4,5,6]

• Finding Longest Subarray with Sum ≤ K → Find the longest contiguous subarray where sum ≤ K.

🛠 How to Apply:

• Use two pointers that move forward while checking conditions.

• Advance one or both pointers as needed.

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3. Sliding Window (Variable Size)

✅ Use When:

• You need to find the longest/shortest subarray that satisfies a condition.

• You need to find the smallest window that contains certain elements.

• You are working with substring/subarray optimization problems.

🔹 Examples:

• Longest Substring Without Repeating Characters → "abcabcbb" → "abc"

• Smallest Subarray with Sum ≥ K → [2,3,1,2,4,3], K=7 → [4,3]

🛠 How to Apply:

• Start with one pointer expanding the window.

• Move the other pointer to shrink when constraints are exceeded.

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4. Split & Merge (Divide & Conquer)

✅ Use When:

• You need to divide an array into two halves and solve recursively.

• You are implementing Merge Sort or Quick Sort.

• The problem involves breaking down and recombining.

🔹 Examples:

• Merge Sort (Recursive Merge Step)

• Find the Median of Two Sorted Arrays → Divide both arrays and find the median.

🛠 How to Apply:

• Recursively split an array into two halves.

• Use merge logic (often a two-pointer technique) to recombine sorted halves.

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5. Running from the Beginning of Two Arrays (Merging Two Arrays)

✅ Use When:

• You need to merge sorted lists/arrays efficiently.

• You are finding the intersection/union of two sorted lists.

• The problem involves scanning two lists in a linear pass.

🔹 Examples:

• Merging Two Sorted Arrays → arr1 = [1,3,5], arr2 = [2,4,6]

• Intersection of Two Sorted Arrays → arr1 = [1,2,3,4], arr2 = [2,4,6] → [2,4]

🛠 How to Apply:

• Use two pointers, one on each list, moving forward.

• Compare elements at both pointers and take the smaller one.

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6. Slow & Fast Pointers (Floyd’s Tortoise and Hare)

✅ Use When:

• You need to find the middle of a linked list.

• You need to detect a cycle in a linked list.

• The problem involves skipping elements at different speeds.

🔹 Examples:

• Finding the Middle of a Linked List → head → [1,2,3,4,5] → middle = 3

• Cycle Detection in a Linked List (Floyd’s Algorithm)

🛠 How to Apply:

• Use one slow pointer (moves 1 step) and one fast pointer (moves 2 steps).

• There is a cycle if the fast pointer catches up to the slow pointer.

• If you want to find the middle, stop when the fast pointer reaches the end.

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Summary Table