Container With Most Water

The Idea

Given a row of wall heights, the water between two walls is the width times the shorter height. Start at the widest pair and always move the shorter wall inward. Moving the taller one can only lose area, so skipping it is safe.

Real-World Example

Hanging a rain tarp between two fence posts works the same way. The lower post decides how much water the tarp can hold, so raising the taller post changes nothing. You replace the short one.

The Code

def max_area(height):
    left, right = 0, len(height) - 1
    best = 0
    while left < right:
        h = min(height[left], height[right])
        best = max(best, h * (right - left))
        if height[left] < height[right]:
            left += 1        # only the shorter wall can help
        else:
            right -= 1
    return best

print(max_area([1, 8, 6, 2, 5, 4, 8, 3, 7]))   # 49

height = [4, 2, 7]
left, right = 0, 2
# water = width * the shorter wall
area = (right - left) * ___(height[left], height[right])