How many ways do pointers move in the Two Pointers pattern

Key Takeaways:

• The Two Pointers technique is a smart way to solve problems that involve moving through data, making comparisons, or checking conditions.

• Knowing how the pointers move—whether in the same direction, opposite directions, staying still, or alternating—can help design better solutions.

• This method is useful in many areas, like searching, sorting, finding cycles, checking for palindromes, or working with subarrays.

The Two Pointers technique is a useful way to solve problems, especially with arrays or linked lists. It involves using two pointers or indices to make the solution faster and use less memory. This method is common in coding challenges and competitive programming. The key is to understand how the pointers move and work together to solve the problem efficiently.

Pointer movement in the Two Pointers pattern

The Two Pointers pattern is like having two fingers move together through a list of things. How they move depends on the problem we're solving. Learning this pattern well means understanding the different ways these fingers can move.

There are two common ways pointers move within the Two Pointers pattern:

• Same direction movements

• Opposite direction movements

1. Same direction movement

In this category, both pointers move through the data structure in the same direction, either from left to right or from right to left. They stay parallel to each other and cover the elements together.

Same-direction movements can further be categorized as:

• Fast and slow pointers

• Sliding window

A. Fast and slow pointers

This involves having one pointer move faster than the other. It's often used to detect cycles or find a specific condition within a data structure. For instance, the fast pointer might move two steps simultaneously in a linked list, while the slow pointer moves one step at a time.

Example: Cycle detection in a linked list

Given a linked list, determine if it has a cycle. Implement an algorithm to determine whether there is a cycle in the linked list.

To solve this problem, we can use the fast and slow pointers technique. Initialize two pointers, slow and fast, both initially pointing to the head of the linked list. Move the slow pointer by one step and the fast pointer by two steps in each iteration. If there is a cycle in the linked list, the fast pointer will eventually catch up to the slow pointer. If there is no cycle, the fast pointer will reach the end of the linked list.

The illustration given below will help us understand the movements of pointers in a better way:

B. Sliding window

This technique uses two pointers to maintain a window or subarray/subsequence within the data structure. One pointer marks the start of the window, and the other pointer expands or shrinks the window as needed.

Example: Minimum contiguous subarray sum

Given an array of integers and a target sum, find the minimum length of a contiguous subarray whose sum is greater than or equal to the target sum. If there is no such subarray, return 0.

This problem can be solved using the Sliding Window technique. Initialize two pointers, start and end, pointing to the array's beginning. Keep expanding the window by moving the end pointer to the right until the sum of elements within the window is less than the target sum. Once the sum becomes greater than or equal to the target, update the minimum length and move the start pointer to the right to shrink the window. Repeat this process, expanding with the end pointer and shrinking with the start pointer, until end reaches the end of the array. This technique efficiently finds the minimum length of a contiguous subarray with a sum greater than or equal to the target.

The illustration given below will help us understand the movements of pointers in a better way:

2. Opposite direction movement

In this category, one pointer moves in one direction while the other moves in the opposite direction. This means they're moving away from each other or toward each other.

Opposite-direction movements can further be categorized as:

• Converging pointers

• Diverging pointers

A. Converging pointers

When using the Two Pointer approach, converging pointers refer to the strategy where two pointers start from different ends of a data structure (such as an array or a list) and move toward each other. They get closer with each step until they eventually meet or converge at a certain point.

Example: A pair of numbers add up to the target sum

Given an array of integers sorted in ascending order and a target sum, find two numbers that add up to the target. Return the two numbers.

This problem can be solved using the Two Pointers technique. Initialize two pointers, left and right, both initially pointing to the first and last elements of the array, respectively. Calculate the sum of elements at these two pointers. If the sum is greater than the target, decrement the right pointer. If the sum is less than the target, increment the left pointer. If the sum equals the target, return the elements at these pointers. This technique efficiently finds the two numbers that add to the target sum in a sorted array.

The illustration given below will help us understand the movements better:

B. Diverging pointers

Diverging pointers is another strategy in the Two Pointer approach where two pointers start at the same point but move away from each other. They separate or diverge as they move through the data structure in opposite directions.

Example: Check palindrome

Given a string, determine if it is a palindrome or not.

To solve this problem, you can initialize two pointers, left and right, initially pointing to the center of the string. Move the left pointer to the left and the right pointer to the right while comparing the characters at these positions. If the characters are different, the string is not a palindrome. Repeat this process until the pointers reach the opposite ends of the string. If all comparisons are successful, the string is a palindrome.

The illustration given below will help us understand the movements better:

Advanced movements

Moving forward, the following can also represent possible movements in certain cases in the Two Pointer pattern:

• One pointer stationary: Sometimes, one pointer remains stationary while the other moves. This could be employed when we need to maintain a reference point and examine elements relative to it. The stationary pointer could be a reference point, pivot, or anchor for comparisons.

• Alternate movement: In more complex problems, pointers might move alternately, with each pointer taking turns to advance based on specific conditions. This can be seen in scenarios where we must perform certain operations at specific intervals or conditions.

• Multiple pointers: While the term suggests Two Pointers, there are cases where we might employ three or more pointers, each moving at different speeds or directions. These scenarios are often found in advanced problems requiring simultaneous traversal from multiple directions.