python算法（一）

python算法（一）

一、求数x的因子

　　

x=100
divisors=()#初始化空的元组
for i in range(1,x):
    if x%i==0:
        divisors=divisors+(i,)
        print divisors

二、求数x各个数位之和

 

sumdigits=0
for c in str(1952):
    sumdigits +=int(c)
    print sumdigits
print sumdigits

三、鸡兔同笼以及变形

　　1.有鸡兔两种，共有x个头，y只脚，求解鸡兔各有几只？

def slove(num_heads,num_legs):
    for chicken_num in range(0,num_heads+1):
        pig_num =num_heads-chicken_num
        top_legs=pig_num*4+chicken_num*2
        if top_legs==num_legs:
            return [chicken_num,pig_num]
    return [None,None]

def barnYard():
    heads=int(raw_input("Enter the number of heads: "))
    legs=int (raw_input("Enter the number of legs: "))
    chicken,pig=slove(heads,legs)
    if chicken==None:
        print "不可解"
    else:
        print "the number of chicken is:",chicken
        print "the number of pig is:",pig

barnYard()

2.有鸡兔，蜘蛛一共三种，共有x个头，y只脚，求解鸡兔，蜘蛛各有几只？

def slove1(num_heads,num_legs):
    for spider_num in range(0,num_heads+1):
        for chicken_num in range(0,num_heads-spider_num):
            pig_num =num_heads-chicken_num-spider_num
            top_legs=pig_num*4+chicken_num*2+spider_num*8
            if top_legs==num_legs:
                return [chicken_num,pig_num,spider_num]
    return [None,None,None]

def barnYard1():
    heads=int(raw_input("Enter the number of heads: "))
    legs=int (raw_input("Enter the number of legs: "))
    chicken,pig,spider=slove1(heads,legs)
    if chicken==None:
        print "不可解"
    else:
        print "the number of chicken is:",chicken
        print "the number of pig is:",pig
        print "the number of spider is",spider

barnYard1()

3.2中的问题或许不只有一个解答，依次输出符合要求的解答

def slove2(num_heads,num_legs):
    solutionFound=False
    for spider_num in range(0,num_heads+1):
        for chicken_num in range(0,num_heads-spider_num):
            pig_num =num_heads-chicken_num-spider_num
            top_legs=pig_num*4+chicken_num*2+spider_num*8
            if top_legs==num_legs:
                print "the number of chicken is:", chicken_num
                print "the number of pig is:", pig_num
                print "the number of spider is", spider_num
                solutionFound=True
    if not solutionFound:
        print "不可解"


def barnYard2():
    heads=int(raw_input("Enter the number of heads: "))
    legs=int (raw_input("Enter the number of legs: "))
    slove2(heads,legs)

barnYard2()

四、递归判断字符串是否为回文

解法一：

def isPlalindrome(s):
    if len(s)<=1:
        return True
    else :
        return s[0]==s[-1] and isPlalindrome(s[1:-1])

解法二：

def isPlalindrome1(s,indent):
    print indent, 'hisPalindromel called with', s
    if 1 >= len(s):
         print indent, 'About to return True from base case',s
         return True
    else:
        ans= s[0] == s[-1] and isPlalindrome1(s[1:-1], indent + indent)
        print indent, 'About to return ',ans
    return ans

isPlalindrome1("abccba",1)

五、斐波那契数列

def fib(x):
    sum=1;
    if x==1 or x==0:
        return 1;
    else:
        return fib(x-1)+fib(x-2)

print fib(4)

六、求数x平方根

1.二分法求解

def squrtRootBi(x,epsilon):
    assert x>=0,"x must be positive"+str(x)
    assert epsilon>0,"epsilon must be positive"+str(epsilon)
    low=0
    #high=x
    high=max(x,1.0)
    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,"not perfect square number!"
    print "times of Iteration:",ctr," guess",guess
    return guess

def testBi():
    squrtRootBi(4,0.0001)
    squrtRootBi(2, 0.0001)
    squrtRootBi(0.25, 0.0001)

testBi()

2.牛顿迭代法求解

def squrtRootNR(x,epsilon):
    assert x >= 0, "x must be positive" + str(x)
    assert epsilon > 0, "epsilon must be positive" + 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, "not perfect square number!"
    print "times of Iteration:", ctr, " guess", guess
    return guess

def testBi1():
    squrtRootNR(4,0.0001)
    squrtRootNR(2, 0.0001)
    squrtRootNR(0.25, 0.0001)

testBi1()