Container With Most Water

Problem

You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the i-th 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.

You may not slant the container.

Input / Output Format

Input: Array height of non-negative integers. Output: Integer — maximum container area.

Examples

Example 1

Input: height = [1,8,6,2,5,4,8,3,7] Output: 49 Explanation: Pick lines at index 1 (height 8) and index 8 (height 7). Width = 7, height = min(8,7) = 7. Area = 49.

Example 2

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

Approach Hints

• Two Pointers — Start l=0, r=n-1. Area = (r-l) * min(height[l], height[r]). Track max. Move whichever pointer points at the smaller line inward — moving the taller line can only reduce or hold area constant.
• Why moving the smaller line works: Area is bounded by the shorter line. Moving the taller side cannot increase min(...) and reduces width.
• Time: O(n). Space: O(1).