11. Container With Most Water Leetcode JavaScript (JS) Solution

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

Solution

Bruteforce solution with O(n2) time complexity

 // brute force solution O(n2) time complexity
var maxArea = function(height) {
    let biggestarea = 0;
    for(let i = 0; i<height.length; i++){
        for(let j = i+1; j<height.length;j++){
            let smallerheight = (height[i] > height[j])?height[j]:height[i];
            let area =  Math.abs(smallerheight)*Math.abs(i-j);
            if(area > biggestarea){
                biggestarea = area;
            }
        }
    }
    return biggestarea;
};

Optimal solution with O(n) complexity

// optimal solution with O(n) time complexity
var maxArea = function(height) {
    let biggestarea = 0;
    let left = 0; let right = height.length -1;
    while(left < right){
        
        let smallerheight = (height[left] > height[right])?height[right]:height[left];
        let area =  Math.abs(smallerheight)*Math.abs(left-right);
        if(area > biggestarea){
                biggestarea = area;
            }
        if(height[left] < height[right]){
            left++;
        }
        else{
            right--;
        }
    }
    return biggestarea;
};