LeetCode 11. 盛最多水的容器

11. Container With Most Water

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

 解题思路：

一维数组的坐标变换 i, j

1. O(n^2) 枚举：left bar x, right bar y, (x-y)*height_diff
2. O(n) 左右边界 i, j 向中间收敛

方法一：

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

方法二： 

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