系统学习编程笔记（十一）

计算机科学和 Python 编程导论

第三讲-简单算法 Lecture 3 - Simple Algorithms

ProblemSet1: 使用for循环打印以下内容
print "Hello!"
print 10
print 8
print 6
print 4
print 2

# There are always many ways to solve a programming problem. Here is one:
print "Hello!"
for num in range(0, 10, 2):
    print 10 - num

# Here is another:
print "Hello!"
for num in range(10, 0, -2):
    print num

ProblemSet2:编写一个从1加到end的for循环。答案中比较巧妙的是将total初始化为end，这样可以少做一次加运算。

# Here is another:
total = end
for next in range(end):
    total += next
print total

将浮点数表示成二进制

# lecture 3.4, slide 4

x = float(raw_input('Enter a decimal number between 0 and 1: '))

p = 0
while ((2**p)*x)%1 != 0:
    print('Remainder = ' + str((2**p)*x - int((2**p)*x)))
    p += 1

num = int(x*(2**p))

result = ''
if num == 0:
    result = '0'
while num > 0:
    result = str(num%2) + result
    num = num/2

for i in range(p - len(result)):
    result = '0' + result

result = result[0:-p] + '.' + result[-p:]
print('The binary representation of the decimal ' + str(x) + ' is ' + str(result))

使用便利贴展示了二分查找的强大~~~~

ProblemSet：In this problem, you'll create a program that guesses a secret number!

low = 0; high=100
print('Please think of a number between %d and %d !'% (low,high))
# 第一处修改，增加变量
guessed = False
#while True:    
while not guessed:    #第二处修改，使用变量去控制循环
    guess = (low+high)/2
    print('Is your secret number %d ?'% guess)
    ans = input("Enter 'h' to indicate the guess is too high. Enter 'l' to indicate the\
 guess is too low. Enter 'c' to indicate I guessed correctly. ")
    if ans=='h':
        high=guess
    elif ans=='l':
        low = guess
    elif ans=='c':
        print('Game over. Your secret number was: %d'% guess)
        #break;
        guessed = True  #第三处修改，尽量避免用break来中断循环
    else:
        print('Sorry, I did not understand your input.')
        #continue        #第四处修改，这是多余的语句。

 Newton-Raphson方法求解：迭代算法，之前的例子都是采用穷举法，而这里利用数学特性来进行猜测，效率非常高。

# Lecture 3.7, slide 3

# Newton-Raphson for square root

epsilon = 0.01
y = 24.0
guess = y/2.0

while abs(guess*guess - y) >= epsilon:
    guess = guess - (((guess**2) - y)/(2*guess))
    print(guess)
print('Square root of ' + str(y) + ' is about ' + str(guess))