IntroductionToComputerScienceAndProgramming/Lec06.py at master · CyberSpaceXYZ/IntroductionToComputerScienceAndProgramming · GitHub

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# MIT600《计算机科学及编程导论》（2008年秋季）样码
# 第六讲
# 翻译制作：ocourse.org
# 课程讨论版：http://ocourse.org/bbs/forum.php?mod=forumdisplay&fid=29
# by yoeo24

def squareRootBi(x, epsilon):
    """Assume x >= 0 and epsilon > 0
       Return y s.t. y*y is within epsilon of x"""
    #假设x>=0且ε>0，返回y，使得y*y在x的ε内
    assert x >= 0, 'x必须为非负数，而不是' + str(x)
    assert epsilon > 0, 'ε必须为正数，而不是' + str(epsilon)
    low = 0
    high = max(x,1.0)
    #high = max(x,1)
    guess = (low + high)/2.0
    ctr = 1
    while abs(guess**2 - x) > epsilon and ctr <= 100:
        #print 'low:', low, 'high:', high, 'guess:', guess
        if guess**2 < x:
            low = guess
        else:
            high = guess
        guess = (low + high)/2.0
        ctr += 1
    assert ctr <=100, '循环计数次数超出范围'
    print 'Bi方法，循环数', ctr, '估值', guess
    return guess

def testBi():
    print '     squareRoot(4, 0.0001)'
    squareRootBi(4, 0.0001)
    print '     squareRoot(9, 0.0001)'
    squareRootBi(9, 0.0001)
    print '     squareRoot(2, 0.0001)'
    squareRootBi(2, 0.0001)
    print '     squareRoot(0.25, 0.0001)'
    squareRootBi(0.25, 0.0001)

def squareRootNR(x, epsilon):
    """Assume x >= 0 and epsilon > 0
       Return y s.t. y*y is within epsilon of x"""
    #假设x>=0且ε>0，返回y，使得y*y在x的ε内
    assert x >= 0, 'x必须为非负数，而不是' + str(x)
    assert epsilon > 0, 'ε必须为正数，而不是' + str(epsilon)
    x = float(x)
    guess = x/2.0
    #guess = 0.001
    diff = guess**2 -x
    ctr = 1
    while abs(diff) > epsilon and ctr <= 100:
        #print '差值:', diff, '猜想值:', guess
        guess = guess - diff/(2.0*guess)
        diff = guess**2 - x
        ctr += 1
    assert ctr <=100, '循环计数次数超出范围'
    print 'NR方法，循环数', ctr, '估值', guess
    return guess

def compareMethods():
    print '     squareRoot(2, 0.01)'
    squareRootBi(2, 0.01)
    squareRootNR(2, 0.01)
    raw_input()
    print '     squareRoot(2, 0.0001)'
    squareRootBi(2, 0.0001)
    squareRootNR(2, 0.0001)
    raw_input()
    print '     squareRoot(2, 0.000001)'
    squareRootBi(2, 0.000001)
    squareRootNR(2, 0.000001)
    raw_input()
    print '     squareRoot(123456789, 0.0001)'
    #注意，此处上下数字不等，我只按照屏幕上的录下来，请大家自行更改
    squareRootBi(123456789, 0.0001)
    squareRootNR(123456789, 0.0001)
    raw_input()
    print '     squareRoot(123456789, 0.0000001)'
    squareRootBi(123456789, 0.0000001)
    squareRootNR(123456789, 0.0000001)
    raw_input()
    print '     squareRoot(2736336100, 0.0001)'
    squareRootBi(2736336100, 0.0001)
    squareRootNR(2736336100, 0.0001)
    raw_input()

def showLists():
    Techs = ['MIT', 'Cal Tec']
    print Techs
    raw_input()
    Ivys = ['Harvard', 'Yale', 'Brown']
    print Ivys
    raw_input()
    Univs = []
    Univs.append(Techs)
    print Univs
    raw_input()
    Univs.append(Ivys)
    print Univs
    raw_input()
    for e in Univs:
        print e
        for c in e: print c
    raw_input()
    Univs = Techs + Ivys
    print Univs
    raw_input()
    Univs.remove('Harvard')
    print Univs