计算机导论课第二次作业

10205102406 edited 2 年前

1、略

2、

def sqr(x):
    x = abs(x)
    res = 0
    for i in range(x):
        res += x
    return res

def cube(x):
    t = sqr(x)
    res = 0
    for i in range(abs(x)):
        res += t
    if x > 0:
        return res
    else:
        return -res

def quad(x):
    if x == 0:
        return 0
    else:
        return int(sqr(x)/(1/sqr(x)))

print(sqr(5), sqr(-5))
print(cube(5), cube(-5))
print(quad(5), quad(-5))

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3、

def factor(n):
    res = n
    for i in range(2,n):
        res *= i
    return res

def combination(n, k):
    return int(factor(n)/(factor(n-k)*factor(k)))

print(factor(4))
print(combination(4, 2))

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4、因为3/x不是整除,会有小数点,x太大的时候因为浮点数精度不足就把3/x当成0了,所以3/x+1就是1啦,但是x不够大的时候3/x就没有被当做0,还有一点点,所以3/x+1就大于1,而不是等于1啦。

5、

print(2**10)
print(2**20)
print(2**30)
print(2**40)
print(2**50)

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6、

def square_root_1():
    c = 10
    i = 0
    g = 0

    while (g+1)**2 < c:
        g+=1

    while (abs(g*g-c) > 0.0001):
        g += 0.00001
        i = i+1
        print("% d:g = %.5f" % (i,g))

square_root_1()

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7、

def square_root_2():
    i = 0
    c = 0.9
    m_max = c if c>1 else 1
    m_min = 0
    g = (m_min + m_max)/2
    while(abs(g*g-c) > 0.00000000001):
        if(g*g<c):
            m_min = g
        else:
            m_max = g
        g = (m_min + m_max)/2
        i = i+1
        print("%d:%.13f" % (i,g))

square_root_2()

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8、

x = 1
c = 0
i = 1.5
while abs(x-i) > 0.1**12:
    x = i
    if x**3+x**2-10 > 0:
        i = x - 0.5 ** (c+2)
    else:
        i = x + 0.5 ** (c+2)
    c+=1
print("二分法结果为%.12f,共迭代%d次"%(i,c))

x = 1
c = 0
i = 1.5
while abs(x-i) > 0.1**12:
    x = i
    i = x-(x**3+x**2-10)/(3*x**2+2*x)
    c+=1
print("牛顿法结果为%.12f,共迭代%d次"%(i,c))

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9、

A = [[1,2,6],
     [2,4,12]]

D = A[0][0]*A[1][1] - A[0][1]*A[1][0] 
Dx = A[0][2]*A[1][1] - A[0][1]*A[1][2]
Dy = A[0][0]*A[1][2] - A[0][2]*A[1][0]

if D == 0:
    if Dx == 0 and Dy == 0: 
        print("方程有无穷解")
    else:
        print("方程无解")
else:
    print("方程有解:x = %f, y = %f" %(Dx/D, Dy/D)) 

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10、

s = "I am  a   Chinese    "
res = []

word = ""
for i in s:
    if i == ' ':
        if word:
            res.insert(0, word)
            word = ""
    else:
        word += i
if word:
    res.insert(0, word)

print(res)

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11、

s = "ABABA"
if s == s[::-1]:
    print(True)
else:
    print(False)

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12、略

编辑者:姜博远
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