feat: largest rectangle

pkg/largest_rectangle_in_histogram/main.go

@@ -0,0 +1,60 @@
+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
+}