1465. Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts

class Solution:
    def maxArea(self, h: int, w: int, hh: List[int], ww: List[int]) -> int:
        """tc O(NlgN)  sc O(1)
        1. sort height and width  
        2. find max height and and max width, note the edge width and edge height  
        3. get the max area = max_height * max_width
        """
        M = 10**9+7
        hh.sort()
        ww.sort()
        max_h, max_w = max(hh[0],h-hh[-1]), max(ww[0],w-ww[-1])
        
        for i in range(1,len(hh)):
            height = hh[i]- hh[i-1]
            max_h = max(max_h,height)
        
        for j in range(1,len(ww)):
            width = ww[j]- ww[j-1]
            max_w = max(max_w,width)
            
        return max_w * max_h %M