What is the optimal time complexity of solving Container With Most Water?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Container With Most Water?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Container With Most Water?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Container With Most Water?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Container With Most Water

Learn how to solve the 'Container With Most Water' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the ith line are (i, 0) and (i, height[i]).

Find two lines that together with the x-axis form a container, such that the container contains the most water.

Return the maximum amount of water a container can store.

Notice that you may not slant the container.

Write a function maxArea(height: List[int]) -> int.

Constraints

•n == len(height)
•2 <= n <= 10^5
•0 <= height[i] <= 10^4

Examples

Example 1

Input

height = [1, 8, 6, 2, 5, 4, 8, 3, 7]

Output

Explanation

The max area is between lines at index 1 (height 8) and index 8 (height 7). Area = min(8, 7) * (8 - 1) = 7 * 7 = 49.

Example 2

Input

height = [1, 1]

Output

Explanation

Area = min(1, 1) * (1 - 0) = 1.

Need a Hint?

Use two pointer variables starting at different bounds (e.g. left = 0, right = length - 1) and shrink the search window.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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