11. Container With Most Water

Description of Problem

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.

Example 1:

Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
Explanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.

Example 2:

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

Constraints:

n == height.length
2 <= n <= 10^5
0 <= height[i] <= 10^4

Solution

Tags: Two Pointers

Explanation

Consider the area with most widest width. And the only reasonable move to get greater area is move a point with smaller height.

Code (Rust)

impl Solution {
    pub fn max_area(height: Vec<i32>) -> i32 {
        let (mut i, mut j) = (0, height.len() - 1);
        let mut max_area = 0;
        while i < j {
            let area = (j - i) as i32 * height[i].min(height[j]);
            max_area = max_area.max(area);
            if height[i] < height[j] {
                i+=1;
            }else {
                j-=1;
            }
        }
        return max_area;
    }
}

Complexity

n is length of height

Time Complexity

\( T(n) = O(n) \)

Auxiliary Space

\( S(n) = O(1) \)

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