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.
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
n == height.length
2 <= n <= 3 * 104
0 <= height[i] <= 3 * 104
Solutions (Click to expand)
A container can be represented as two points in the array, i and j, that can hold at the most the the minimum height of the two pointers, min(height[i], height[j]), times the length between the pointers, j - 1
Here we can see that the amount of water that we can hold is largely deterministic by the height of the shorter of the two pointers. If we want a larger volume we would need to replace the shorter edge with an edge that is closer to the larger edge and has a height that makes up for the loss in distance and makes for a larger resulting volume.
Now our new volume is the shorter of the two pointers * the length between the two pointers.
This would go one until the two pointers meet, j - i = 0, and we can't hold anymore water
Time: O(N) where N is the length of the array
Space: O(1)