0011 - Container With Most Water

0011 - Container With Most Water

Given n non-negative integers a1, a2, ..., an , where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of the line i is at (i, ai) and (i, 0). Find two lines, which, together with the x-axis forms a container, such that the container contains the most water.

Notice that you may not slant the container.

Examples

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.

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

Input: height = [4,3,2,1,4] Output: 16

Input: height = [1,2,1] Output: 2

Constraints

n == height.length 2 <= n <= 105 0 <= height[i] <= 104

Java Solution

Brute Force (Exceeds Time Limit)

class Solution {
    public int maxArea(int[] height) {
        int max = 0;
        
        for(int i = 0; i < height.length; i++) {
            for(int j = i + 1; j < height.length; j++) {
                max = Math.max((j-i) * Math.min(height[i], height[j]), max);
            }
        }
        
        return max;
    }
}

Two Pointer

class Solution {
    public int maxArea(int[] height) {
        int max = 0;
        int left = 0;
        int right = height.length - 1;
        
        while(left < right) {
            max = Math.max(max, Math.min(height[right], height[left]) * (right - left));
            if(height[left] < height[right]) left++;
            else right--;
        }
        return max;
    }
}