from collections import namedtuple
from functools import partial


def remove_overlapping(rectangles):
    def overlap(a, b):
        return compute_intersection(a, b) > 0

    def does_not_overlap(rect, rectangles):
        return not any(overlap(rect, r2) for r2 in rectangles if not rect == r2)

    rectangles = list(map(xywh_to_vec_rect, rectangles))
    rectangles = filter(partial(does_not_overlap, rectangles=rectangles), rectangles)
    rectangles = map(vec_rect_to_xywh, rectangles)
    return rectangles


def remove_included(rectangles):
    def included(a, b):
        return b.xmin >= a.xmin and b.ymin >= a.ymin and b.xmax <= a.xmax and b.ymax <= a.ymax

    def is_not_included(rect, rectangles):
        return not any(included(r2, rect) for r2 in rectangles if not rect == r2)

    rectangles = list(map(xywh_to_vec_rect, rectangles))
    rectangles = filter(partial(is_not_included, rectangles=rectangles), rectangles)
    rectangles = map(vec_rect_to_xywh, rectangles)
    return rectangles


Rectangle = namedtuple("Rectangle", "xmin ymin xmax ymax")


def make_box(x1, y1, x2, y2):
    keys = "x1", "y1", "x2", "y2"
    return dict(zip(keys, [x1, y1, x2, y2]))


def compute_intersection(a, b):

    dx = min(a.xmax, b.xmax) - max(a.xmin, b.xmin)
    dy = min(a.ymax, b.ymax) - max(a.ymin, b.ymin)

    return dx * dy if (dx >= 0) and (dy >= 0) else 0


def has_no_parent(hierarchy):
    return hierarchy[-1] <= 0


def xywh_to_vec_rect(rect):
    x1, y1, w, h = rect
    x2 = x1 + w
    y2 = y1 + h
    return Rectangle(x1, y1, x2, y2)


def vec_rect_to_xywh(rect):
    x, y, x2, y2 = rect
    w = x2 - x
    h = y2 - y
    return x, y, w, h