How to Find the Container With Most Water?

Finding the container that can hold the most water is a popular coding challenge often encountered in technical interviews, particularly in the realm of algorithms and data structures. The problem can be framed as follows: given an array of integers where each integer represents the height of a vertical line drawn at that position, determine the two lines that, together with the x-axis, form a container that holds the most water.

To visualize this, imagine a 2D graph where the x-axis represents the indices of the array, and the height of the lines corresponds to the value of the integers in the array. The water held by the container formed by two lines is determined by the minimum of the two heights multiplied by the distance (width) between them.

Problem Breakdown

1. Input: An array of integers, each representing the height of the line at that position.
2. Output: The maximum area of water that can be contained.

To achieve an efficient solution, the optimal approach uses the two-pointer technique. The idea is to start with pointers at both ends of the array and move toward the center, always calculating the area formed by the two lines pointed to by the pointers.

Steps to Solve the Problem

1. Initialize two pointers: one at the beginning (left) and the other at the end (right) of the array.
2. Keep track of the maximum area found during the process.
3. Calculate the area formed by the heights at the pointers and their distance.
4. Move the pointer that is at the lesser height inward (either left or right).
5. Repeat until the pointers meet.

Example Code

Here’s a Python implementation of the above logic:

PythonCopy code

Explanation of the Code

• Pointer Initialization: Two pointers left and right are initialized at the start and end of the array.
• While Loop: The loop continues until the two pointers meet.
• Area Calculation: For each pair of heights, the code calculates the current area and updates the maximum area accordingly.
• Pointer Movement: The pointer that points to the shorter line is moved inward because moving the taller line would not increase the height constraint.

This solution runs in O(n) time complexity, where n is the number of lines, making it significantly more efficient than a brute-force O(n²) approach, which would involve checking all pairs of lines. The two-pointer technique capitalizes on the fact that the area is limited by the shorter line, allowing for a more streamlined search for the maximum area.