Container With Most Water

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Leetcode

Medium

Arrays

Two Pointers

Geometry

Google

Container With Most Water

Find two vertical lines that form a container holding the maximum amount of water.

Acceptance 96%

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Problem Statement

You are given an array of non-negative integers where each value represents the height of a vertical line drawn at that index. Choose any two lines together with the x-axis to form a container.

Return the maximum amount of water the container can hold.

The water contained by two lines at positions $i$ and $j$ is determined by:

the distance between them, and
the shorter of the two heights.

So the area is:

$\text{area} = (j - i) \times \min(h[i], h[j])$

Find the largest possible area over all valid pairs.

Input Format

An integer array height of length n
height[i] is the height of the vertical line at index i

Output Format

Return a single integer: the maximum container area

Constraints

$2 \le n$
$0 \le height[i]$
Use 64-bit arithmetic if your language may overflow on large products

Examples

Sample cases returned by the problem API.

Example 1

Input

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

Output

Explanation

The best pair is the lines at indices 1 and 8 with heights 8 and 7. The width is 7, so the area is 7 × 7 = 49.

Example 2

Input

height = [1,1]

Output

Explanation

Only one pair exists. The width is 1 and the limiting height is 1, so the area is 1.

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