{"id":980,"date":"2010-11-15T16:03:27","date_gmt":"2010-11-15T16:03:27","guid":{"rendered":"http:\/\/pchero21.com\/?p=980"},"modified":"2010-11-15T16:03:27","modified_gmt":"2010-11-15T16:03:27","slug":"lec-6-mit-6-00-introduction-to-computer-science-and-programming-fall-2008","status":"publish","type":"post","link":"http:\/\/pchero21.com\/?p=980","title":{"rendered":"Lec 6 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008"},"content":{"rendered":"

6: Bisection Methods, Newton\/Raphson, Introduction to Lists
\n <\/span><\/h1>\n

<\/p>\n

def squareRootBi(x, epsilon):
    “””Assumes x >= 0 and epsilon > 0
    Return y s.t. y * y is within epsilon of x”””
    assert x >= 0, ‘x must be non-negative, not’ + str(x)
    assert epsilon > 0, ‘epsilon must be positive, not’ + str(epsilon)
    low = 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, ‘Iteration count exceeded’
    print ‘Bi method. Num. iteratins:’, ctr, ‘Estimate:’, guess
    return guess<\/p>\n

def squareRootNR(x, epsilon):
    “””Assumes x >= 0 and epsilon > 0
    Return y s.t. y * y is within epsilon of x”””
    assert x >= 0, ‘x must be non-negative, not’ + str(x)
    assert epsilon > 0, ‘epsilon must be positive, not’ + 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 ‘Error:’, diff, ‘guess:’, guess
        guess = guess – diff \/ (2.0 * guess)
        diff = guess ** 2 – x
        ctr += 1
    assert ctr <= 100, ‘Iteration count exceeded’
    print ‘NR method. Num. iterations:’, ctr, ‘Estimate:’, guess
    return guess<\/p>\n

squareRootBi(9, 0.001)<\/p>\n

squareRootBi(4, 0.001)<\/p>\n

squareRootBi(2, 0.001)<\/p>\n

squareRootBi(0.25, 0.001)<\/p>\n

squareRootBi(4, 0.00001)
squareRootNR(4, 0.00001)<\/p>\n

squareRootBi(123, 0.00001)
squareRootNR(123, 0.00001)<\/p>\n

squareRootBi(123456789, 0.00001)
squareRootNR(123456789, 0.00001)<\/p>\n

Techs = [‘MIT’, ‘Cal Tech’]
print Techs<\/p>\n

Ivys = [‘Harvard’, ‘Yale’, ‘Brown’]
print Ivys
Univs = []
Univs.append(Techs)
print Univs
Univs.append(Ivys)
raw_input()
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()
Ivys.remove(‘Harvard’)
print Univs
Ivys[1] = -1
print Ivys<\/p>\n

L1 = [1, 2, 3]
L2 = L1
L1[0] = 4
print L2
def f(L):
    L[0] = 4
L1 = [1, 2, 3]
L2 = [1, 2, 3]
L3 = L1
print L1 == L2
f(L1)
print L1 == L2
print L1
print L2
print L3<\/p>\n

L1 = [1, 2, 3]
L2 = L1[:]  # make a copy of L1<\/p><\/blockquote>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

6: Bisection Methods, Newton\/Raphson, Introduction to Lists def squareRootBi(x, epsilon):    “””Assumes x >= 0 and epsilon > 0    Return y s.t. y * y is within epsilon of x”””    assert x >= 0, ‘x must be non-negative, … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[27],"tags":[259,293],"_links":{"self":[{"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/posts\/980"}],"collection":[{"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/pchero21.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=980"}],"version-history":[{"count":0,"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/posts\/980\/revisions"}],"wp:attachment":[{"href":"http:\/\/pchero21.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=980"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pchero21.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=980"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pchero21.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=980"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}