0011-container-with-most-water

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Description

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 <= 105
• 0 <= height[i] <= 104

Solution(Python)

class Solution:
    def maxArea(self, height: List[int]) -> int:
        #  height = [1,8,6,2,5,4,8,3,7]
        #            0 1 2 3 4 5 6 7 8
        #  
        #  width and height 
        #   water  = level * width
        #   level = min(left, right)
        #   width = right - left + 1
        #  maxArea 
        #  width -> 0 .. n
        #    process smallest line left < right
        #     update maxArea
        # dryrun
        # i =0 
        # j = 8
        #  -> 0 < 8
        #       1 < 7; level = 1; area = 1* 9 
        #       i = 1
        #     maxArea = 9
        #  -> 1 < 8
        #       8 > 7; level = 7; area = 7* 7 = 49
        #       j = 6
        #      maxArea = 49
        # 
        #  -> 1 < 6
        #        8 < 8; level = 8; area= 8* 6
        #      
        maxArea = 0
        i = 0
        j = len(height) - 1

        while i < j:
            if height[i] < height[j]:
                level = height[i]
                area = level * (j-i)
                i += 1
            else:
                level = height[j]
                area = level * (j-i)
                j-=1
            if area > maxArea:
                maxArea = area
        return maxArea