Python 入门（七）函数

什么是函数

我们知道圆的面积计算公式为：

S = πr²

当我们知道半径r的值时，就可以根据公式计算出面积。假设我们需要计算3个不同大小的圆的面积：

r1 = 12.34

r2 = 9.08

r3 = 73.1

s1 = 3.14 * r1 * r1

s2 = 3.14 * r2 * r2

s3 = 3.14 * r3 * r3

当代码出现有规律的重复的时候，你就需要当心了，每次写3.14 * x * x不仅很麻烦，而且，如果要把3.14改成3.14159265359的时候，得全部替换。

有了函数，我们就不再每次写s = 3.14 * x * x，而是写成更有意义的函数调用 s = area_of_circle(x)，而函数 area_of_circle 本身只需要写一次，就可以多次调用。

抽象是数学中非常常见的概念。举个例子：

计算数列的和，比如：1 + 2 + 3 + ... + 100，写起来十分不方便，于是数学家发明了求和符号∑，可以把1 + 2 + 3 + ... + 100记作：

100

∑n

n=1

这种抽象记法非常强大，因为我们看到∑就可以理解成求和，而不是还原成低级的加法运算。

而且，这种抽象记法是可扩展的，比如：

100

∑(n²+1)

n=1

还原成加法运算就变成了：

(1 x 1 + 1) + (2 x 2 + 1) + (3 x 3 + 1) + ... + (100 x 100 + 1)

可见，借助抽象，我们才能不关心底层的具体计算过程，而直接在更高的层次上思考问题。

写计算机程序也是一样，函数就是最基本的一种代码抽象的方式。

Python不但能非常灵活地定义函数，而且本身内置了很多有用的函数，可以直接调用。

任务

此节没有任务，进入下一节继续学习。

调用函数

Python内置了很多有用的函数，我们可以直接调用。

要调用一个函数，需要知道函数的名称和参数，比如求绝对值的函数 abs，它接收一个参数。

可以直接从Python的官方网站查看文档：

http://docs.python.org/2/library/functions.html#abs

也可以在交互式命令行通过 help(abs) 查看abs函数的帮助信息。

调用 abs 函数：

>>> abs(100)

100

>>> abs(-20)

20

>>> abs(12.34)

12.34

调用函数的时候，如果传入的参数数量不对，会报TypeError的错误，并且Python会明确地告诉你：abs()有且仅有1个参数，但给出了两个：

>>> abs(1, 2)

Traceback (most recent call last):

  File "<stdin>", line 1, in <module>

TypeError: abs() takes exactly one argument (2 given)

如果传入的参数数量是对的，但参数类型不能被函数所接受，也会报TypeError的错误，并且给出错误信息：str是错误的参数类型：

>>> abs('a')

Traceback (most recent call last):

  File "<stdin>", line 1, in <module>

TypeError: bad operand type for abs(): 'str'

而比较函数 cmp(x, y) 就需要两个参数，如果 x<y，返回 -1，如果 x==y，返回 0，如果 x>y，返回 1：

>>> cmp(1, 2)

-1

>>> cmp(2, 1)

1

>>> cmp(3, 3)

0

Python内置的常用函数还包括数据类型转换函数，比如 int()函数可以把其他数据类型转换为整数：

>>> int('123')

123

>>> int(12.34)

12

str()函数把其他类型转换成 str：

>>> str(123)

'123'

>>> str(1.23)

'1.23'

任务

sum()函数接受一个list作为参数，并返回list所有元素之和。请计算 1*1 + 2*2 + 3*3 + ... + 100*100。

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编写函数

在Python中，定义一个函数要使用 def 语句，依次写出函数名、括号、括号中的参数和冒号:，然后，在缩进块中编写函数体，函数的返回值用 return 语句返回。

我们以自定义一个求绝对值的 my_abs 函数为例：

def my_abs(x):

    if x >= 0:

        return x

    else:

        return -x

请注意，函数体内部的语句在执行时，一旦执行到return时，函数就执行完毕，并将结果返回。因此，函数内部通过条件判断和循环可以实现非常复杂的逻辑。

如果没有return语句，函数执行完毕后也会返回结果，只是结果为 None。

return None可以简写为return。

任务

请定义一个 square_of_sum 函数，它接受一个list，返回list中每个元素平方的和。

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" 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返回多值

函数可以返回多个值吗？答案是肯定的。

比如在游戏中经常需要从一个点移动到另一个点，给出坐标、位移和角度，就可以计算出新的坐标：

# math包提供了sin()和 cos()函数，我们先用import引用它：

import math

def move(x, y, step, angle):

    nx = x + step * math.cos(angle)

    ny = y - step * math.sin(angle)

    return nx, ny

这样我们就可以同时获得返回值：

>>> x, y = move(100, 100, 60, math.pi / 6)

>>> print x, y

151.961524227 70.0

但其实这只是一种假象，Python函数返回的仍然是单一值：

>>> r = move(100, 100, 60, math.pi / 6)

>>> print r

(151.96152422706632, 70.0)

用print打印返回结果，原来返回值是一个tuple！

但是，在语法上，返回一个tuple可以省略括号，而多个变量可以同时接收一个tuple，按位置赋给对应的值，所以，Python的函数返回多值其实就是返回一个tuple，但写起来更方便。

任务

一元二次方程的定义是：ax² + bx + c = 0

请编写一个函数，返回一元二次方程的两个解。

注意：Python的math包提供了sqrt()函数用于计算平方根。

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" 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递归函数

在函数内部，可以调用其他函数。如果一个函数在内部调用自身本身，这个函数就是递归函数。

举个例子，我们来计算阶乘 n! = 1 * 2 * 3 * ... * n，用函数 fact(n)表示，可以看出：

fact(n) = n! = 1 * 2 * 3 * ... * (n-1) * n = (n-1)! * n = fact(n-1) * n

所以，fact(n)可以表示为 n * fact(n-1)，只有n=1时需要特殊处理。

于是，fact(n)用递归的方式写出来就是：

def fact(n):

    if n==1:

        return 1

    return n * fact(n - 1)

上面就是一个递归函数。可以试试：

>>> fact(1)

1

>>> fact(5)

120

>>> fact(100)

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000L

如果我们计算fact(5)，可以根据函数定义看到计算过程如下：

===> fact(5)

===> 5 * fact(4)

===> 5 * (4 * fact(3))

===> 5 * (4 * (3 * fact(2)))

===> 5 * (4 * (3 * (2 * fact(1))))

===> 5 * (4 * (3 * (2 * 1)))

===> 5 * (4 * (3 * 2))

===> 5 * (4 * 6)

===> 5 * 24

===> 120

递归函数的优点是定义简单，逻辑清晰。理论上，所有的递归函数都可以写成循环的方式，但循环的逻辑不如递归清晰。

使用递归函数需要注意防止栈溢出。在计算机中，函数调用是通过栈（stack）这种数据结构实现的，每当进入一个函数调用，栈就会加一层栈帧，每当函数返回，栈就会减一层栈帧。由于栈的大小不是无限的，所以，递归调用的次数过多，会导致栈溢出。可以试试计算 fact(10000)。

任务

汉诺塔 (http://baike.baidu.com/view/191666.htm) 的移动也可以看做是递归函数。

我们对柱子编号为a, b, c，将所有圆盘从a移到c可以描述为：

如果a只有一个圆盘，可以直接移动到c；

如果a有N个圆盘，可以看成a有1个圆盘（底盘） + (N-1)个圆盘，首先需要把 (N-1) 个圆盘移动到 b，然后，将 a的最后一个圆盘移动到c，再将b的(N-1)个圆盘移动到c。

请编写一个函数，给定输入 n, a, b, c，打印出移动的步骤：

move(n, a, b, c)

例如，输入 move(2, 'A', 'B', 'C')，打印出：

A --> B
A --> C
B --> C

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6rmY4tMxtbxglwKbrVYHGwmhbssdrgLhLjVWHLOAHGQ7caLA5Wi8NcDQC0o1sNFgerAQAYh241WBysBgBgHLrVYHGwWpzCrG4MAPYiWeWN6YWtdCTBUbAaAIBpiJV4w3phF3AdSPOtxlwNALQjVuINXgeyQFZb2mv1upmWy2KuVtHaLw0AckamvrNmfy5WW66/6zaOsi0CyVytgtUAyoRMfTevv1oBr6vd3Gt33u3dzLi0cfHmamndQSvuspDuMlexpmtZVsxK2X9qt1IAMAqZ+m5eL+zCzdWW9lq9dn0p84L9xZurpXUHDa90HP66kjxXG2W1pP2P6jIKAOYgU9+NnKtlfUvmYeRptY0jb1Fjg62WDyndQaNtQkMdaioTWC1h/6NXQwYAU5Cp72ZfVxv/XdlGkp/VwiYz2Gr5zdWG50mz269jZxpDkststZS1/7EagPmIlXiD74HM9MYMg8nNahtHoVbLHo17xlktH1KsE52rRcFqAOVBrMQb3Au7ENfVEudthllN51xt6Fpa/C1DEgq2d+d5WA2gEEhWeZX3HLK2iAVWy4f0OzVSG4omdwENTlru357dfo3VAAqBoopfhrC2SBxjn1cDgPKgWw0WB6sBABiHbjVYHKwWh7kaAGhHtxosDlYDADAO3WqwOFgNAMA4dKvB4mA1AADj0K0Gi4PVAACMQ7jQq3s4jOfVsFqchd3j9u689mGYxeJOu3vgpP2otbOgfYQAahEu9CoXhCz12iI399rh5bIGKx2X2mrOQS+tfI/P1edP7l68WH2g/9eRYoTVqhWn0ek1avoHCaAQ4UKvcm7UL3Mv7Jt77UwmK7zVas3ucX1xqp0sr168WHt+Z7VEVpupztdbnaaje5AACpGs8l6DNMF9ph0l02ZYLcePlNPoNHd32t1Or3vgOAe9bqfnn/VadF/v9LrBjGFh97gXOi0W/bbW9LaPnWlc2D2Ozzncau4eMXzQNK4+f7L6YMZ127RWC8Y55UzIafjT8Umd7f45+H/Uw38OzsHlfzgAFiNZ5XOx2piHKNp1NZus1useOG6hb+0s+FOHxZ12UKnn6y1PVGmvV2vNrj+rCH9dSZ5wuHV8UK8zzEimttp8veXPjWrNIQFn+6Ob3jeL3j8p/H3GRSswzQUwGMkq7/kjq3XohT2W1YLraiavbuw03LLuecWTVnx2FcwYYobzDBGdUkTeHhFhJfRicObNG8blA5aYqw3/+hO8V0g2sTOQCTOz8D8dAIqHZJVXPz3yD5R1G7v7q8XYOMomtlw/UmlWi5f7mMAatZmouhZ2j+Mt5SJnMocuHaVbbf4Xu3/+8ncDfvvj2ICnt1psqBMK45LrYZPuJ+l84xTqBTAfsRKvfm6UaedFttp37x12eocbdlktfa5WmanWmt0Dx70m5yRuEMWouVp0MJMLI/GXmnA/l8/VuGEEiotYiacXdl5WW66/63aO7lt2BjJatePXn5xGp+nUmpH6G7uWFibtupqc1dy7Tsa59SP8gIFzEJ+rjb+f6ny9lb7l+PuJ/Dkk/hlyXQ2KjViJz8EiJX5ebbn+bsKH1YyxWtUrzYmn6RZ32ikv+m8JV+fUeyDjwxgx1AeP7168CBNxm3e3y3i/sn+O1Ik/GJ5hPwOxJd8DOfZ+0v/QBnAPJBQcmfoevZym4uoaa4tMjvYPmQpUTzhGzpws3w+nH6HQKKr4ZQhW04vI2iJJDO7+mFohpu1nhrVFoBToVoPFwWq6YR3IbLAOJJQC3WqwOFgNAMA4dKvB4mA1AADj0K0Gi4PVAACMQ7caLA5WAwAwDt1qsDhYTZAbD5+evn+6Pad/JKO59ujt5snbJWXjVL1/gOIjXOjN6IXtv0XpU2v5Wy14FrtwXUOzWe3249PXzg0tQ13b3zzZn7N3/wCFR7jQG7ACZOLG9lttaa/V6zbuFXWulg27rbZ+a8RsDKsBTIlwoVe8YH9514HcOMq8UJYmq914+PT02cr6s8bp+8bp+8abh7ODH805b147N+acN+8bp+8bgZb8V94/Xr90P8HGPpF3JSPW1VOItf3Nk/Nba+oOIdB9FMBWJKu8Mb2wVY9hcJQcrXa/0WvX9w69UtWuLxlttfeN02cr1YorIe+84kBI7rez269Dwhv8dMhqEZmFfpppribW1VOUue07J+d3Hl1XsHOZ7qMAtiJZ5Y3phV1Iq4XW6Te5E81gjuV/u/4sbKbgylnwukui1YL9rOyHr7pNfgbSqNZi67dOzjc/XxfeLUvyQ8mRrPLG9MIupNXC87PYt/ZYLf1soUKryXT1TOf60hfnmycDQucV016PbSB8x6NU91EAW5Gs8uqXyfcPNOUGMsPIea4WulXEHqvNbr9u7N+eqVa0WU2qq6cwys5ASnUfBbAVsRJvUi/s4lnt6sZRt/Nu7+bHV7/78dWbe23/a8OtdvtxcDeHoNWiJzNHI9bVU5Dsd4tIdR8FKD5iJZ5e2IqfVws1Ds2iNC1WS7xBMcVq0e2Dt4yyWuRdl94DKdfVU4aRd/anIdV9FKDwiJV4emGztkhlpjp0Xc10bJnZ2DJOAO3I1Pfo5TQVV9emWVtEcBiR/WO1JOyxmmA3TsYJYAyKKn4ZgtUSscdqAFBEdKvB4mA1AADj0K0Gi4PVAACMQ7caLA5WAwAwDt1qsDhYDQDAOHSrweJgNd0sxB8+04FFK1Qt7rRZ9RiKj241WJwcrba01wqvZJjxQWztHzI1hBcNmZirz5/cvXix+mDyPVhkNfeBdJ4QgIIjU98Vd53u0ws7zMZRaP3+slpNYGX65dWLF2vP76yWyGru09xNR/swANQhVuJzWMuj1L2wA7ItbZy31ZxGp7m70+52et0Dx1290D/rtei+HuneubB7HF4IKvpt0O0zdqZxYfc4Pudw7eIecZzFpa4+f7L6YMZ12/RW83+1qU7xiXU3HdU11Dmg+xoUGrESn8vqxmVeB3LAzb12pomaBqv1ugeOv26hP5WJrCU/X295okp7vVprdv1ZRfjrSvKEw/XKoF5nmJFIWK3jnwud4hSfWHfTy7qG0oANio1YiWfN/lyslnmipsFq7d35wCuetOKzq2DGEDNcaH392BzOf3tis5XomcDxO87IzNUSfi+RP8YJ3nuptML/dAAoHmIlPq/mav1S9lcLTdQyLthvitXiZTomsEZtJqquWKvPoTOZQ5ey0q02/4vdP3/5uwG//XFswOZYTaa76RjX+YxpMgegArESn3GultbzOu31EYfL+lOp5G+1WO9Qq6yWPlerzFRrze6B416TcxI3iFLIuZpUd9PLu4ZywwgUG7ESn0t/tTF3XkyrTTZRM8Vq0Wobv27kNDpNp9aM+CB2LS1M2nU1OauN36UzctyhMY+/H7Huppf2rOG6GhQbsRKfl9XKel1taa810UTNGKtVvdKceHptcaed8qL/lrAtUu+BjA9jxFAfPL578SJMxG1jd+lMH2S2/Uh2Nx3ZNZR7IKHgiJV4emGztkieqJ5wSHXpNHE/nH6EQiNW4g1+Xk3VeLCaVkTWFklCqkunafuZYW0RKAUy9d3stUVUjKeP1fRjxDqQFsE6kFAKFFX8MgSrAQAYh241WBysBgBgHLrVYHGwGgCAcehWg8XBagAAxqFbDRYHqwEAGIduNVicnK12vxEsEmhwJxoAAK3oVoPFydNqy/V33dbesvtt1qWztH/IAAByQ6a+G/m82sTvGnfnOVotuq7x0l6rd7iB1QAAhhAr8YatLaJ0JIOd53kG8uZe2zvxeL/RC+ZtWA0AIIxYiTesF7a/fYHWFrl36F5Xy7rGsfYPGQBAboiVeJN6YYe3LIjVNo66ncFZx/uNXrdzdB+rAQAMI1biTeqFHd6sEFZb2muF73uMfYvVAAA8xEq8Sb2wY9sUYM3+6LW0e4cd7hYBAEhCrMSb1Avb30ztbZn5dw3leTUAgNGIlXiTemH3c7nOx9oiAADGIVbi6YWN1QAAtCNW4g17Xg2rYTUAKCMy9d2wtUViI1E0MKwGAGAcsoW+VMFqAADGoVsNFgerAQAYh241WBysBgBgHLrVYHGw2mUs7B63d+eV7Pzao7ebJ2+X5lRtX8jjLu60WzsLKv53ABiEbjVYnJyttlx/5z2FnWURSH1Wcw563QNn6PXZxa9e3L14snhzuv2v7W+e7M/FX7++9MV5cvVP3l7guNcevd08OfcYOrSy41YrM9XK+i3/0F9sX7t8e6fR6TVqav+/A2hGtxosjq6uoZEOosZardbsHtcXh16/+vzJ3TePVxVZbW77zhfbc4/e3nl0faztJY577dHbzc/Xg69jR1FntbntOyfnwW86t30r/FunHXe+3uo0Hdn/1wBGoVsNFifn1Y1DCz/eO5y8F7bT6DR3d9rdTq974DgHvW6n55+VWnRf7/S6wb/oF3aPe6HTVtFva01v+9iZxoXd46Q5wc07axdPFm8uC1gtiYFg5rbvxCYuKglbrTq3fUfEYWMw9/l5cNwsOAc9zkNCkZGs8iqfWptsh2qXo8zParHljKfphe00Or3ugeMKqbWzsLjTds8TLu60g9nVfL3liSrt9Wqt2fX/1R/+upI2IZhd/OrF2vPZakWR1a4vfXF+a22mWlm/JXEpa0zic7WJTDPFL5udlGk0QEEQK/E5rOVR4l7Y9xtBs1D3AtsUVmvvzgfi8aQVn10F/6KPGc67VBb9J3/k7RER+jx4fPerO1crM6qsFponzX1+nnASUg3R62o5TdTcK2oTWi38TxOA4iFW4g1bB9LfvhD91T4Or9nfrt+bbq6WaDXvdW/LmMAatZmouhZ2j4MeAi6RM5nx+0TCJlNitcg8aW0/fveEMobOQOYzTZzCakP/rwEKhUx9V98pdIJj+Q3bVI1E25399w4n74Wdfa5WmanWmt0Dx70m5yRuECVhrvbg8d2LF3HeLMt9lN27H89H3Y6ohuhZxylODGZk4utq3DACBUemvudotfEPV1CrZWwZOq7VoiqqNaM3gDiNTtOpNSMai11LC3NJ3UyYq7n3rUxx03nsWtr1pS/GOgk59XEnnKtNf9zq2v7miHsgR8B1NSg2MvV9oiteiT2v016f4Ijh1Y2zDm+c5Gq1jSPvRF+Wux+zWK3qldqkexrd2yMTX/TfEtZYyj2QA5LOQHp3r0z4OR465Xjt0duxTkJOedxLn1dTdtxqZXBzf/LzaulwDyQUHJn6bupcTW0bAdYWGUHWCcF8vaXlAeEyHpfTj1BoZOq7edfV8uj3htVGkrK2yDCDG09yL/FlO+4Ma4tAKRAr8YbdA0nXUO1WU7oOJEwA60BCKRAr8fTCxmoAANqRrPL0wsZqAAB6kS30pQpWAwAwDt1qsDhYDQDAOHSrweJgNQAA49CtBouD1QAAjEO3GiwOVgMAMA7darA4WA0AwDh0q8HiYDUAAOOQqe8qu2D7hzBtVFgNAMA4xEo8a4tgNQAA7YiVePVWy7RnrIbVAKCMiJX4XKw25s7z6SGA1QAAjEOsxCu+rhY71pQbyAwDqwEAmIZYic84V0vreZ32+ojDZf2pVLAaAIBxiJX4XPqrjblzrIbVAKCkiJX4vKzGdTWsBgCQiliJpxc2VgMA0I5YiTf4eTVV48FqAACmIVPfzV5bRMV4+lgNAMBAFFX8MgSrAQAYh241WBysBgBgHLrVYHGwGgCAcehWg8XBagAAxqFbDRYHqwEAGIduNVgcrAYAYBy61WBxsBoAgHEIF3oDOqv1c3l+ro/VAAAMRLjQ6+6slrgxa4vo/5wBAOSDcKFX3F9tsnUgsZr+zxkAQD5IVnmvQZrgPtOOkmkzrKb/cwYAkA+SVT4Xq415CK6rYTUAKCOSVd7zh/Ze2H3malgNAMqJZJVXPz3yD5R1G/qrAQCUArESr35ulGnnWA2rAUAZESvx9MLGagAA2hEr8TlYhOfVsBoAwGhk6nv0cpqKq2usLYLVAAAuR1HFL0OwGgCAcehWg8XBagAAxqFbDRYHqwEAGIduNVgcrG9QFJwAAAI/SURBVAYAYBy61WBxsBoAgHHoVoPFwWoAAMahWw0WB6sBABiHcKE3oxe2/xalT61hNQAA4xAu9AasAJm4MVYDACgFwoVe8YL9rAOJ1QAARiFZ5Y3pha16DIOjYDUAANOQrPLG9MLGalgNAEqKZJU3phc2VsNqAFBSJKu8+mXy/QNNuYHMMLAaAIBpiJV4k3phYzWsBgAlRazE0wsbqwEAaEesxNMLG6sBAGhHpr5HL6epuLo2zdoigsOI7B+rAQCYhqKKX4ZgNQAA49CtBouD1QAAjEO3GiwOVgMAMA7darA4WA0AwDh0q8HiYDUAAOPQrQaLg9UAAIxDtxosDlYDADAOmfquuOt0n17YWA0AYBzESnwOa3nQCxurAQCMRqzE57K6MetAYjUAgFGIlXjW7MdqAADaESvxeTVX69NfDasBAKQhVuIzztXSel6nvT7icFl/KhWsBgBgHGIlPpf+amPuHKthNQAoKWIlPi+rcV0NqwEApCJW4umFjdUAALQjVuINfl5N1XiwGgCAacjUd7PXFlExnj5WAwAwEEUVvwzBagAAxqFbDRYHqwEAGIduNVgcrAYAYBy61WBxsBoAgHHoVoPFwWoAAMahWw0WB6sBABiHbjVYHKwGAGAcutVgcbAaAIBx6FaDxcFqAADGoVsNFgerAQAYh241WBysBgBgHLrVYHGwGgCAcehWg8XBagAAxqFbDRYHqwEAGIduNVgcrAYAYBy61WBxsBoAgHF4JfqrvX/Z+yryBbkk/w8ECxXjRDmmqgAAAABJRU5ErkJggg==" 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定义默认参数

定义函数的时候，还可以有默认参数。

例如Python自带的 int() 函数，其实就有两个参数，我们既可以传一个参数，又可以传两个参数：

>>> int('123')

123

>>> int('123', 8)

83

int()函数的第二个参数是转换进制，如果不传，默认是十进制 (base=10)，如果传了，就用传入的参数。

可见，函数的默认参数的作用是简化调用，你只需要把必须的参数传进去。但是在需要的时候，又可以传入额外的参数来覆盖默认参数值。

我们来定义一个计算 x 的N次方的函数:

def power(x, n):

    s = 1

    while n > 0:

        n = n - 1

        s = s * x

    return s

假设计算平方的次数最多，我们就可以把 n 的默认值设定为 2：

def power(x, n=2):

    s = 1

    while n > 0:

        n = n - 1

        s = s * x

    return s

这样一来，计算平方就不需要传入两个参数了：

>>> power(5)

25

由于函数的参数按从左到右的顺序匹配，所以默认参数只能定义在必需参数的后面：

# OK:

def fn1(a, b=1, c=2):

    pass

# Error:

def fn2(a=1, b):

    pass

任务

请定义一个 greet() 函数，它包含一个默认参数，如果没有传入，打印 'Hello, world.'，如果传入，打印 'Hello, xxx.'

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" 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定义可变参数

如果想让一个函数能接受任意个参数，我们就可以定义一个可变参数：

def fn(*args):

    print args

可变参数的名字前面有个 * 号，我们可以传入0个、1个或多个参数给可变参数：

>>> fn()

()

>>> fn('a')

('a',)

>>> fn('a', 'b')

('a', 'b')

>>> fn('a', 'b', 'c')

('a', 'b', 'c')

可变参数也不是很神秘，Python解释器会把传入的一组参数组装成一个tuple传递给可变参数，因此，在函数内部，直接把变量 args 看成一个 tuple 就好了。

定义可变参数的目的也是为了简化调用。假设我们要计算任意个数的平均值，就可以定义一个可变参数：

def average(*args):

    ...

这样，在调用的时候，可以这样写：

>>> average()

0

>>> average(1, 2)

1.5

>>> average(1, 2, 2, 3, 4)

2.4

任务

请编写接受可变参数的 average() 函数。

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" 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