LeetCode-in-All

11. Container With Most Water

Medium

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.

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

Example 3:

Input: height = [4,3,2,1,4]

Output: 16

Example 4:

Input: height = [1,2,1]

Output: 2

Constraints:

• n == height.length
• 2 <= n <= 105
• 0 <= height[i] <= 104

Solution

defmodule Solution do
  @spec max_area(height :: [integer]) :: integer
  def max_area(height) do
    left = 0
    right = length(height) - 1

    height
    |> List.to_tuple()
    |> solve(left, right, 0)
  end

  def solve(_, l, r, ans) when l == r, do: ans
  def solve(height, l, r, ans) do
    lh = elem(height, l)
    rh = elem(height, r)

    ans = max(min(lh, rh) * (r - l), ans)
    cond do
      lh >= rh -> solve(height, l, r - 1, ans)
      lh < rh -> solve(height, l + 1, r, ans)
    end
  end
end

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