package container_with_most_water

func MaxArea(height []int) int {
	if len(height) < 2 {
		return 0
	}

	start := 0
	end := len(height) - 1

	// Let:
	// - A = the smaller side,
	// - B = the larger side.
	//
	// Notice that:
	// - Any container with A cannot have a height larger than `min(A, B)`.
	// - Any container with A cannot have a width larger than `B - A`.
	//
	// Because of this, all solutions containing A cannot be larger than `area`.
	area := (end - start) * min(height[start], height[end])

	// Futhermore, we can completely ignore A.
	//
	// The maximum area will either be the current `area`, or some other two
	// lines in the subset without A.
	var subset []int
	if height[start] < height[end] {
		subset = height[start+1:]
	} else {
		subset = height[:end]
	}

	// We can now evaluate the problem space in the subset, and compute the
	// maximum area.
	return max(area, MaxArea(subset))
}