Container With Most Water

Problem

You are given an integer array height of length n. 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.

Examples

The brute-force approach

Try every pair of lines. For each pair (i, j), the area is min(height[i], height[j]) × (j - i). Track the maximum across all pairs.

max_area = 0

for i in range(len(height)):
    for j in range(i + 1, len(height)):      # ← all pairs
        area = min(height[i], height[j]) * (j - i)
        max_area = max(max_area, area)

return max_area

Checking every pair is O(n²), for 1000 lines that's 500,000 pair checks. The key insight is that you can eliminate huge chunks of pairs without checking them, because moving toward the center from the taller side can never improve the area.

Spotting the pattern

This is a Two Pointers problem. The key question to ask yourself:

Starting from both ends, which pointer should I move inward to have a chance of finding a larger container?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.