python – 最大矩形算法实现

我正在尝试用Python实现Maximum Rectangle Algorithm from Dr. Dobbs(清单4).它主要起作用,但是一个特定情况会给出错误的结果,我无法弄清楚原因.

这是我的源代码：

from collections import namedtuple

Point = namedtuple('Point',('X','Y'))

#Y      0  1  2      X
arr = [[0,],#0
       [1,#1
       [0,1,#2
       ]

def area(ll,ur):
    if (ll.X < 0) or (ll.Y < 0) or (ur.X < 0) or (ur.Y < 0):
        return 0.
    return ((ur.X - ll.X) + 1) * ((ur.Y - ll.Y) + 1)

def update_cache(a,c,x):
    M = len(a[0])
    N = len(a)
    for y in range(M):
        if a[x][y] == 0:
            c[y] = c[y] + 1
        else:
            c[y] = 0

def mrp(a):
    best_ll = Point(-1,-1)
    best_ur = Point(-1,-1)
    M = len(a[0]) 
    N = len(a)
    c = [0 for x in range(M + 1)]
    stack = []
    for x in range(N-1,-1,-1):

        update_cache(a,x)        
        width = 0
        for y in range(M + 1):
            if c[y] > width:
                stack.append((y,width))                
                width = c[y]
            if c[y] < width:
                while True:
                    y0,w0 = stack.pop()
                    if (width * (y - y0)) > area(best_ll,best_ur):
                        best_ll = Point(x,y0)
                        best_ur = Point(x + width - 1,y - 1)
                    width = w0
                    if (c[y] >= width):
                        break
                width = c[y] 
                if width == 0:
                    stack.append((y0,width))
    return best_ll,best_ur

这是结果：

>>> mrp(arr)
(Point(X=0,Y=0),Point(X=1,Y=2))

正如你所看到的,第一点是错误的,但我无法弄清楚它出错的地点和原因.更改arr会给出正确的结果.

编辑：我注意到与文章相比,我已经更改了数组的值.这会更改update_cache中的比较. 0 =清除,1 =保留.我正在寻找结果(Point(X = 0,Y = 1),Point(X = 1,Y = 2)).