package largest_rectangle_in_histogram

type Box struct {
	Start  int
	Height int
}

// Calculates the size of the box, from its starting point upto (and NOT
// including) a certain point.
func (b Box) Size(upto int) int {
	return (upto - b.Start) * b.Height
}

func LargestRectangleArea(heights []int) int {
	// This is a stack, containing all boxes that haven't been completed yet. Each
	// box contains two integers. The first is the starting index, and the second
	// is the height of the box.
	boxes := []Box{}
	// The accumulation of the biggest box so far.
	biggest := 0
	// Add a number that is guaranted to be lower than any other. This will pop out
	// any boxes left in the stack at the end of the program.
	heights = append(heights, -1)

	for i, height := range heights {
		// This is the farthest index back where the eventual new box can start.
		// Everytime we pop a box off the top of the stack, this means every item
		// from the start of the box until now is > the current height. So, we can
		// extend that box at least that far back.
		farthest := i

		for len(boxes) > 0 {
			top := boxes[len(boxes)-1]

			// The boxes are implicitly ordered by height. When one gets the top box,
			// all below must have a <= height.
			//
			// If the very top box has a height <= to the current height, that means
			// all boxes left will carry over into the next iteration, so we can continue.
			if top.Height < height {
				break
			}

			// Since this box is taller than the current height, it ends here.
			// We calculate its size, and accumulate it in the `biggest` variable.
			biggest = max(biggest, top.Size(i))

			// Remove it from the stack.
			boxes = boxes[:len(boxes)-1]

			// Push the starting point of the box farther back.
			farthest = top.Start
		}

		// A box is always created for each new height.
		boxes = append(boxes, Box{Start: farthest, Height: height})
	}

	return biggest
}