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

(define/contract (max-area height)
  (-> (listof exact-integer?) exact-integer?)
    
    (define h (list->vector height))
    (define (helper left right)
        (cond [(>= left right) 0]
              [else (let ([area (* (min (vector-ref h left) (vector-ref h right)) (- right left))])
                        (max area
                            (if (< (vector-ref h left) (vector-ref h right))
                                (helper (add1 left) right)
                                (helper left (sub1 right)))))]))
                                
    (helper 0 (sub1 (vector-length h)))
  )

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