Container With Most Water

At first I was thinking about using the same strategy as the one we used in Largest Rectangle in Histogram, or Trapping Rain Water. But none of them worked. The difference between this problem and Largest Rectangle in Histogram is that in the latter, the rectangles should be adjacent to each other (see the following figure, the largest rectangle should be among 1 to 5).

Largest Rectangle in Histogram

In this problem, we only deal with lines. So the containers can be any rectangles formed by elements from 0 to 6 . For any element i in the array, the largest element will the the farthest element j from i that has num[j] > num[i].

Container with Most Water

public int maxArea(int[] height) {
        if (height == null)
            throw new NullPointerException("Null array!");
        if (height.length < 2)
            return 0;
        int left = 0;
        int right = height.length - 1;
        int maxArea = 0;
        while (left < right) {
            int h = Math.min(height[left], height[right]);
            maxArea = Math.max(maxArea, h * (right - left));
            if (height[left] < height[right])
                left++;
            else
                right--;
        }
        return maxArea;
    }