# Python solution with detailed explanation

• Solution

Algorithms

• Brute force solution tests every pair and computes the container with most water.
``````class Solution_BruteForce(object):
def maxArea(self, height):
"""
:type height: List[int]
:rtype: int
"""
N = len(height)
max_water = -1
for i in range(N):
for j in range(i+1,N):
max_water = max(max_water, min(height[i], height[j])*(j-i))
return max_water
``````

Two Pointer

• O(N) solution which is explained in editorial. Why the solution works needs some thought.
• Use two pointers start and end initialized at 0 and N-1
• Now compute the area implied by these pointers as (end-start) * min (height[start], height[end])
• if height[start] < height[end], start = start + 1 else end = end -1
• Why? Imagine height[start] < height[end]. Then is there any need to compare height[end-1] with height[start]? There is no way we can now get a larger area using height[start] as one of the end points. We should therefore move start.
https://discuss.leetcode.com/topic/3462/yet-another-way-to-see-what-happens-in-the-o-n-algorithm/2
``````class Solution(object):
def maxArea(self, height):
"""
:type height: List[int]
:rtype: int
"""
s, e = 0, len(height)-1
max_water = -1
while s < e:
max_water = max(max_water, (e-s)*min(height[s], height[e]))
if height[s] < height[e]:
s = s+1
else:
e = e-1
return max_water
``````

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