《python》编程导论 第1/2/3/4章

前几章比较简单，本文纯粹是为了对基本概念做个记录，顺便码一下。

第三章

3.3 近似解和二分查找

3.3.1 平方根迭代近似解

x=25
epsilon = 0.01 
step = epsilon**2
numGuesses = 0
ans = 0
while abs(ans**2-x) >= epsilon and ans <= x:
    ans += step
    numGuesses += 1
print(f'numGuesses ={numGuesses}')
if abs(ans**2 - x) >= epsilon:
    print(f'Failed on square root of {x}')
else:
    print(f'{ans} is close to square root of {x}')

3.3.1 平方根二分查找近似解

x=25
epsilon = 0.01 
low = 0
high = max(1,x)
numGuesses = 0
ans = (high + low)/2
while abs(ans**2-x) >= epsilon:
    print(f'low = {low},high = {high}')
    numGuesses += 1
    if ans**2 < x:
        low = ans 
    else:
        high = ans
    ans = (high + low)/2
print(f'numGuesses = {numGuesses}')
print(f'{ans} is close to square root of {x}')

3.4 关于浮点数

浮点数都是高精度的近似值

x = 0
for i in range(10):
    x += 0.1
if x == 1:
    print(f'{x} = 1')
else:
    print(f'{x} is not 1.0')

3.5 牛顿-拉弗森法

求解多项式

epsilon = 0.01
k = 25
guess = k/2
while abs(guess*guess - k) >= epsilon:
    guess -= (((guess**2)-k)/(2*guess))
print(f'Square root of {k} is about {guess}')

4.2 规范（测试用例）

def findRoot(x,power,epsilon):
    '''二分法找平方根'''
    if x <0 and power%2==0:
        return None
    low = min(-1,x)
    high = max(1,x)
    ans = (high + low)/2
    while abs(ans**power-x) >= epsilon:
        if ans**power < x:
            low = ans 
        else:
            high = ans
        ans = (high + low)/2
    return ans

def testFindRoot():
    epsilon=0.0001
    
    for x in [0.25,-0.25,2,-2,8,-8]:
        for power in range(1,4):
            print(f'Testing x ={str(x)} and power = {power}')
            result=findRoot(x,power,epsilon)
            if result == None:
                print(' No root')
            else:
                print(f'  {result**power}~={x}')

4.3 递归

4.3.1 阶乘

def factR(n):
    if n == 1:
        return n
    else:
        return n*factR(n-1)

4.3.2 斐波那契

def fib(n):
    if n==0 or n==1:
        return 1
    else:
        return fib(n-1)+fib(n-2)
def testFib(n):
    for i in range(n+1):
        print(f'fib of {i} = {fib(i)}')

4.3.3 回文检测

def isPalindrome(s):
    '''回文检测，忽略点符号、空格、大小写'''
    def toChars(s):
        s=s.lower()
        letters=''
        for c in s:
            if c in 'abcdefghijklmnopqrestuvwxyz':
                letters=letters+c
        return letters
    
    def isPal(s):
        print(f'isPal called with {s}')
        if len(s)<=1:
            print('About to return Ture from base case')
        else:
            answer=s[0]==s[-1] and isPal(s[1:-1])
            print(f'About to return {answer} for {s}')
            return answer
        
    return isPal(toChars(s))

def testIsPalindrome():
    print('Try dogGod')
    print(isPalindrome('dogGod'))
    print('Try doGood')
    print(isPalindrome('doGood'))

4.4 全局变量

用于打印函数内循环变量，查找错误点，还是不错的

def fib(x):
    global numFibcalls
    
    numFibcalls+=1
    if x==0 or x==1:
        return 1
    else:
        return fib(x-1)+fib(x-2)
    
def testFib(n):
    for i in range(n+1):
        global numFibcalls
        numFibcalls=0
        print(f'fib of {i} = {fib(i)}')
        print(f'fib called {numFibcalls} times')