能否完美拼成矩形

题目：给定一个N行4列的二维数组matrix,表示N个每条边不是平行于X轴就是平行于Y轴的矩形，想知道所有的矩形能否组成一个大的完美矩形。完美矩形是指拼出的整体图案是矩形，既不缺任何块，也没有重合的部分。

思路：1、每一个小矩形的面积累加起来必须是等于大矩形的面积  2、除大矩形的四个顶点只出现一次之外，其它任何小矩形的顶点都必须出现偶数次。

def isRectangleCover(matrix):
    
    import sys
    
    if len(matrix) == 0 or len(matrix[0]) == 0:
        return False
    
    mostLeft = sys.maxsize
    mostRight = -sys.maxsize
    mostDown = sys.maxsize
    mostUp = -sys.maxsize
    map_ = {}
    
    area = 0
    
    for rect in matrix:
        mostLeft = min(rect[0],mostLeft)
        mostDown = min(rect[1],mostDown)
        mostRight = max(rect[2],mostRight)
        mostUp = max(rect[3],mostUp)
        
        area += (rect[2]-rect[0]) * (rect[3] - rect[1])
        
        leftDown = rect[0] + '_' + rect[1]
        leftUp = rect[0] + '_' + rect[3]
        rightDown = rect[2] + '_' + rect[1]
        rightUp = rect[2] + '_' + rect[3]
        
        if !map_.add(leftDown):
            map.remove(leftDown)
            
        if !map_.add(leftUp):
            map.remove(leftUp)

        if !map_.add(rightDown):
            map.remove(rightDown)

        if !map_.add(rightUp):
            map.remove(rightUp)
                        
    if(mostLeft + '_' + mostDown not in map_ or 
       mostLeft + '_' + mostUp not in map_ or 
       mostRight + '_' + mostDown not in map_ or
       mostRight + '_' + mostUp not in map_ or
      len(map_)!=4):
        return False
    
    return area == (mostRight - mostLeft) * (mostUp - mostDown)