[NeetCode 150] Max Water Container

Max Water Container

You are given an integer array heights where heights[i] represents the height of the $i^{th}$ bar.

You may choose any two bars to form a container. Return the maximum amount of water a container can store.

Example 1:

Input: height = [1,7,2,5,4,7,3,6]

Output: 36

Example 2:

Input: height = [2,2,2]

Output: 4

Constraints:

2 <= height.length <= 1000
0 <= height[i] <= 1000

Solution

In a greedy strategy, a given container can have larger area when there exists a higher bar in it, beacause lower bar with shorter distance will definitely have smaller area. Also, for a given container, when we shrink the length between its endpoints, they area might become large only when we move the shorter bar.

Therefore, we can first take the 0 and n-1 bar as the endpoints, and move the shorter bar every time to gain a maximum.

Code

class Solution:
    def maxArea(self, heights: List[int]) -> int:
        ans = 0
        le = 0
        ri = len(heights)-1
        while le < ri:
            ans = max(ans, min(heights[le], heights[ri])*(ri-le))
            if heights[le] < heights[ri]:
                le += 1
            else:
                ri -= 1
        return ans