LeetCode 11. Container With Most Water

11. Container With Most Water

Difficulty: Medium

Given n non-negative integers $a_1, a_2…a_n$, where each represents a point at coordinate $(i, a_i)$. n vertical lines are drawn such that the two endpoints of line i is at $(i, a_i)$ and $(i, 0)$. Find two lines, which together with x-axis forms a container, such that the container contains the most water.

Note: You may not slant the container and n is at least 2.

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:

1 2	Input: [1,8,6,2,5,4,8,3,7] Output: 49

Solution

Language: Java

$O(n^2)$算法

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

$O(n)$算法

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