s0084_largest_rectangle_in_histogram

84. Largest Rectangle in Histogram

Hard

Given an array of integers heights representing the histogram's bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.

Example 1:

Input: heights = [2,1,5,6,2,3]

Output: 10

Explanation: The above is a histogram where width of each bar is 1.

The largest rectangle is shown in the red area, which has an area = 10 units.

Example 2:

Input: heights = [2,4]

Output: 4

Constraints:

• 1 <= heights.length <= 105
• 0 <= heights[i] <= 104

Solution

(define/contract (largest-rectangle-area heights)
  (-> (listof exact-integer?) exact-integer?)
  (let* ((n (length heights))
         (heights-vec (list->vector (append heights '(0))))
         (stack '())
         (max-area 0))
    
    (for ([i (in-range (add1 n))])
      (let loop ()
        (when (and (not (null? stack))
                   (<= (vector-ref heights-vec i) (vector-ref heights-vec (car stack))))
          (let* ((top (car stack))
                 (new-stack (cdr stack))
                 (height (vector-ref heights-vec top))
                 (width (if (null? new-stack) i (- i (car new-stack) 1)))
                 (area (* height width)))
            (set! max-area (max max-area area))
            (set! stack new-stack)
            (loop))))
      (set! stack (cons i stack)))

    max-area))