Mastering the Container With Most Water Problem in Python

The Container With Most Water problem from LeetCode 75 is a classic coding interview question that tests your understanding of two-pointer techniques, greedy strategies and area calculation logic. At first glance, the problem seems simple: given a list of heights, find the two lines that together with the x-axis form a container that holds the maximum water. But solving it efficiently is where the real challenge lies.

In this blog, we’ll walk through a clean Python solution, explain it step by step, and discuss why it’s optimal for interviews and real-world scenarios.

Problem Statement

You are given an array height where each element represents a vertical line on the x-axis. Find two lines that together with the x-axis, form a container that holds the most water and return its area.

Understanding the Problem

A container’s area is calculated as: Area=width×height

Where:

width = distance between the two lines
height = minimum of the two line heights

We need to maximize this area.

Examples

Example 1:

Input: height = [1,8,6,2,5,4,8,3,7]  
Output: 49

Example 2:

Input: height = [1,1]  
Output: 1

Python Solution – Step-by-Step Explanation

Here’s an optimal Python solution using the two-pointer technique:

class Solution:
    def maxArea(self, height: List[int]) -> int:
        left, right = 0, len(height) - 1
        max_water = 0

        while left < right:
            # Calculate the width and height of the container
            width = right - left
            h = min(height[left], height[right])

            # Calculate the area and update max_water if needed
            area = width * h
            max_water = max(max_water, area)

            # Move the pointers towards each other
            if height[left] < height[right]:
                left += 1
            else:
                right -= 1

        return max_water

Step 1: Initialize Two Pointers

left, right = 0, len(height) - 1

left starts at the beginning of the array.
right starts at the end.
max_water keeps track of the largest container area found.

Step 2: Calculate Area While Moving Pointers

while left < right:
    width = right - left
    h = min(height[left], height[right])
    area = width * h
    max_water = max(max_water, area)

Calculate the width and height of the container formed by the two pointers.
Compute the area and update max_water if it’s larger than the previous maximum.

Step 3: Move Pointers Strategically

if height[left] < height[right]:
    left += 1
else:
    right -= 1

Move the pointer pointing to the shorter line inward, hoping to find a taller line and potentially a larger area.

Step 4: Return Maximum Area

return max_water

After the pointers meet, max_water contains the largest possible container area.

Why This Solution Works

Uses a greedy two-pointer strategy to efficiently explore all potential containers.
Only moves the pointer corresponding to the shorter line because the taller line limits the area.
Avoids unnecessary nested loops, achieving linear time complexity.

Time and Space Complexity

Metric	Value
Time Complexity	O(n) – each element is visited at most once
Space Complexity	O(1) – no extra space required

Edge Cases to Consider

Case	Output	Explanation
height = []	0	No container possible
height = [1,1]	1	Smallest valid container
height = [1,2,1]	2	Handles minimal and non-contiguous heights

Real-World Applications

Water storage optimization: Determining maximum capacity between barriers.
Histogram analysis: Finding maximum rectangular areas in graphical data.
Interview prep: Popular question in coding interviews to test greedy and two-pointer logic.

Conclusion

The Container With Most Water problem is a foundational coding challenge that demonstrates the power of two-pointer algorithms. It emphasizes how thoughtful traversal and greedy strategies can drastically reduce computational complexity. Mastering this problem not only boosts your confidence in solving array-based challenges but also strengthens your problem-solving skills for real-world optimization tasks.

External Links

LeetCode – Container With Most Water Problem

GeeksforGeeks – Container With Most Water

Mastering the Container With Most Water Problem in Python – LeetCode 75 Explained

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