Container With Most Water
Given $n$ non-negative integers representing an elevation map. Find two lines that together with the x-axis form a container, such that the container contains the most water. Use the Two-Pointer technique.
Why Interviewers Ask This
Apple interviewers ask this problem to evaluate a candidate's ability to optimize brute-force solutions using the Two-Pointer technique. They specifically test logical deduction skills: understanding why moving the shorter line is the only viable strategy to maximize area. This assesses algorithmic efficiency and the capacity to reason about constraints without relying on memorized patterns.
How to Answer This Question
1. Clarify the goal: Define the container as the area between two lines, calculated by width multiplied by height (min of the two heights).
2. Propose the naive solution: Briefly mention the O(n^2) nested loop approach to establish a baseline, then immediately pivot to optimization.
3. Introduce the Two-Pointer framework: Place pointers at both ends of the array. Explain that the initial width is maximal, so we must increase height to improve the area.
4. Justify the movement logic: Articulate that moving the taller pointer inward cannot yield a better result because the height is capped by the shorter line. Therefore, discard the shorter line to potentially find a taller one.
5. Iterate and track: Move the pointer corresponding to the smaller value inward, update the maximum area found, and repeat until pointers meet. Emphasize the O(n) time complexity benefit.
Key Points to Cover
- Explicitly state the formula for area calculation (width * min(height1, height2))
- Demonstrate the logical proof for why moving the shorter pointer is the only valid optimization
- Correctly identify and articulate the O(n) time complexity and O(1) space complexity
- Handle edge cases such as arrays with duplicate heights or single elements gracefully
- Show confidence in explaining the trade-off between width reduction and potential height gain
Sample Answer
To solve the Container With Most Water problem efficiently, I would start by acknowledging the brute-force approach which checks every pair of lines, resulting in O(n^2) time complexity. While correct, this is inefficient for large datasets typical in Apple's high-performance environments. Instead, I propose the Two-Pointer technique to achieve O(n) time complexity.
I initialize two pointers, left at index 0 and right at the last index. The area is determined by the distance between them multiplied by the minimum height of the two lines. Since the width decreases with every step, we must hope to find a significantly taller line to compensate.
The critical insight is that if we move the pointer pointing to the taller line inward, the new height will still be limited by the shorter line, meaning the area can only decrease or stay the same. However, moving the shorter line offers a chance to encounter a taller line that could increase the overall area despite the reduced width. Therefore, at each step, I compare the heights at both pointers. If the left height is smaller, I increment the left pointer; otherwise, I decrement the right pointer. I calculate the area at each step and maintain a running maximum. This ensures we explore all potential optimal configurations without redundant checks, delivering an optimal solution.
Common Mistakes to Avoid
- Attempting to use a greedy approach that only looks at the immediate next element instead of the global pointers
- Failing to explain why moving the taller pointer is suboptimal, leading to confusion about the algorithm's correctness
- Calculating the area incorrectly by using the maximum height instead of the minimum height of the two boundaries
- Neglecting to discuss time complexity analysis after presenting the code or logic
Practice This Question with AI
Answer this question orally or via text and get instant AI-powered feedback on your response quality, structure, and delivery.