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python之"math.floor(x)"和 "int(x)"是否在 Python 中对正实数产生不同的结果

2025年05月04日11qq号

我在 Python shell 上检查了几个例子,它们似乎吐出相同的数字。但是在一个应该对大量数字进行近似的程序中,它们显然会产生不同的结果。

我正在尝试编写一个小程序来模拟物体在矩形平面上的运动。为此,我必须编写一个名为“RectangularRoom”的类,它接受宽度和高度并创建一个网格:

class RectangularRoom(object): 
""" 
A RectangularRoom represents a rectangular region containing clean or dirty 
tiles. 
 
A room has a width and a height and contains (width * height) tiles. At any 
particular time, each of these tiles is either clean or dirty. 
""" 
def __init__(self, width, height): 
    """ 
    Initializes a rectangular room with the specified width and height. 
 
    Initially, no tiles in the room have been cleaned. 
 
    width: an integer > 0 
    height: an integer > 0 
    """ 
    self.width = width 
    self.height = height 
    self.room_coordinates = [] 
    for m in range(self.width): 
        for n in range(self.height): 
            self.room_coordinates.append((m,n)) 
    self.cleaned = [] 
def cleanTileAtPosition(self, pos): 
    """ 
    Mark the tile under the position POS as cleaned. 
 
    Assumes that POS represents a valid position inside this room. 
 
    pos: a Position 
    """ 
    self.cleaned.append((int(pos.getX()), int(pos.getY()))) 
 
def isTileCleaned(self, m, n): 
    """ 
    Return True if the tile (m, n) has been cleaned. 
 
    Assumes that (m, n) represents a valid tile inside the room. 
 
    m: an integer 
    n: an integer 
    returns: True if (m, n) is cleaned, False otherwise 
    """ 
    assert type (m)== int and type (n) == int 
    return (m,n) in self.cleaned 
 
def getNumTiles(self): 
    """ 
    Return the total number of tiles in the room. 
 
    returns: an integer 
    """ 
    return self.width*self.height 
 
def getNumCleanedTiles(self): 
    """ 
    Return the total number of clean tiles in the room. 
 
    returns: an integer 
    """ 
    return len(self.cleaned) 
 
def getRandomPosition(self): 
    """  
    Return a random position inside the room. 
 
    returns: a Position object. 
    """ 
    return Position (random.randrange(0 , self.width), random.randrange(0 , self.height)) 
 
def isPositionInRoom(self, pos): 
    """ 
    Return True if pos is inside the room. 
 
    pos: a Position object. 
    returns: True if pos is in the room, False otherwise. 
    """ 
    return (int(pos.getX()), int(pos.getY())) in self.room_coordinates 

如您所见,我使用 int() 方法和随机生成器“random.randrange”实现了它。

在解决方案中,老师使用 math.floor() 函数和随机生成器 random.random() 实现了这个类:

class RectangularRoom(object): 
""" 
A RectangularRoom represents a rectangular region containing clean or dirty 
tiles. 
 
A room has a width and a height and contains (width * height) tiles. At any 
particular time, each of these tiles is either clean or dirty. 
""" 
def __init__(self, width, height): 
    """ 
    Initializes a rectangular room with the specified width and height. 
 
    Initially, no tiles in the room have been cleaned. 
 
    width: an integer > 0 
    height: an integer > 0 
    """ 
    self.width = width 
    self.height = height 
    self.tiles = {} 
    for x in range(self.width): 
        for y in range(self.height): 
            self.tiles[(x, y)] = False 
 
def cleanTileAtPosition(self, pos): 
    """ 
    Mark the tile under the position POS as cleaned. 
 
    Assumes that POS represents a valid position inside this room. 
 
    pos: a Position 
    """ 
    x = math.floor(pos.getX()) 
    y = math.floor(pos.getY()) 
    self.tiles[(x, y)] = True 
 
def isTileCleaned(self, m, n): 
    """ 
    Return True if the tile (m, n) has been cleaned. 
 
    Assumes that (m, n) represents a valid tile inside the room. 
 
    m: an integer 
    n: an integer 
    returns: True if (m, n) is cleaned, False otherwise 
    """ 
    return self.tiles[(m, n)] 
 
def getNumTiles(self): 
    """ 
    Return the total number of tiles in the room. 
 
    returns: an integer 
    """ 
    return self.width * self.height 
 
def getNumCleanedTiles(self): 
    """ 
    Return the total number of clean tiles in the room. 
 
    returns: an integer 
    """ 
    return sum(self.tiles.values()) 
 
def getRandomPosition(self): 
    """ 
    Return a random position inside the room. 
 
    returns: a Position object. 
    """ 
    return Position(random.random() * self.width, 
                    random.random() * self.height) 
 
def isPositionInRoom(self, pos): 
    """ 
    Return True if pos is inside the room. 
 
    pos: a Position object. 
    returns: True if pos is in the room, False otherwise. 
    """ 
    return ((0 <= pos.getX() < self.width) 
            and (0 <= pos.getY() < self.height)) 

令人惊讶的是,这两段代码产生了完全不同的结果。我想知道为什么会这样。 int() 和 floor() 对正数应该有相同的效果,这两个随机函数似乎产生相似的数字。

请您参考如下方法:

嗯,我不知道你问题的答案 - 我怀疑他们返回的是完全相同的东西。但是,我认为您的解决方案存在问题,可能会解释输出:

在“cleanTileAtPosition”中

self.cleaned.append((int(pos.getX()), int(pos.getY()))) 

在“getNumCleanedTiles”中

return len(self.cleaned) 

此代码似乎允许多次清洁瓷砖。这不是您的教师代码所做的,因为磁贴只能设置为“True”一次。

(顺便说一句,因为 random.randrange 返回一个整数.. 整数转换应该什么都不做!)

编辑:另外 - 我认为类型差异值得考虑。但是您所有的类型都是“整数”,所以这应该不是问题。