# Leetcode - 11: Container With Most Water

MEDIUM
–––

## What's the question?

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.

### Let's see some examples

input.md
``````Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
``````

Instead of starting with a bruteforce solution for this problem as, we might have gone through the 2Sum and 2Sum-II problems wherein we use two pointers from the left and the right. We can use the same approach here.

We will start with a maximum area i.e. `maxArea` of `0` and then as we initialize our pointers to start and end we will calculate the area `length * height`.

Here the `length` will become `right_ptr - left_ptr` as each pole or line is at a distance of `1 unit` from each other. But now because we have two pointers we will have to choose either of the one height.

So to choose a height just imagine that if we choose a larger/bigger height out of the two then the water will start splilling from the smaller/shoter height pole so we should choose the shorter pole. Now our area formula will become `(right_ptr - left_ptr) * min(height[left_ptr], height[right_ptr])`.

Once we compute this area, if this area is larger than the current `maxArea` we can replace the current `maxArea` with the computed area. So after every left and right pointer iteration/change we can have the `maxArea` written as `maxArea = max(maxArea, (right_ptr - left_ptr) * min(height[left_ptr], height[right_ptr]))`.

## Let's code this out

maxContainerEfficient.py
``````def maxArea(height):

maxArea = 0
left_ptr = 0
right_ptr = len(height) - 1

while left_ptr < right_ptr:

maxArea = max(maxArea, (right_ptr - left_ptr) * min(height[left_ptr], height[right_ptr]))

if height[left_ptr] > height[right_ptr]:
right_ptr -= 1
elif height[right_ptr] > height[left_ptr]:
left_ptr += 1
else:
left_ptr += 1

return maxArea
``````

So that's it we did this in a single `while` loop. The logic behind updating the `left_ptr` and `right_ptr` is to move the either one when it's smaller than the other. This way we can stay at a higher ground for one pole and keep on checking with different heights of other poles.

That's it for this blog, hope you found this helpful. You can connect with me on Twitter

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