1 九九乘法表

print("........ Multiplication Table")

# Display the number title

print(" |", end = '')

for j in range(1, 10):

....print(" ", j, end = '')

print() # Jump to the new line

print("-----------------------------------------")

# Display table body

for i in range(1, 10):

....print(i, "|", end = '')

....for j in range(1, 10):

........# Display the product and align properly

........if i >= j:

............print(format(i * j, '4d'), end = '')

....print()# Jump to the new line

output:

也可以写成：

for i in range(1, 10):

....print(' ')

....for j in range(1, i+1):

........print("%d*%d=%d" % (j, i, i*j),end=" ")

output:

2 最大公约数

2.1 使用简单循环

# Prompt the user to enter two integers

a = eval(input("Enter first integer: "))

b = eval(input("Enter second integer: "))

gcd = 1

k = 2

while k <= a/2 and k <= b/2:

.... if a % k == 0 and b % k == 0:

........ gcd = k

.... k += 1

print("The greatest common divisor for",

.... a, "and", b, "is", gcd)

output:

Enter first integer: 125

Enter second integer: 2525

The greatest common divisor for 125 and 2525 is 25

2.2 也可以用辗转相除法：

a = eval(input("Enter first integer: "))

b = eval(input("Enter second integer: "))

def gcd(x,y):

....while(x%y != 0):

........g = x%y

........x = y

........y = g

....return g

print("The greatest common divisor for",

....a, "and", b, "is", gcd(a,b))

3 蒙特卡罗模拟求pi

假设一个矩形的面积是4，矩形内切圆的半径是1，算出圆的面积也是π。

在正方形内随机产生一个点，这个点落在圆内的概率为：

圆面积/矩形面积 = π/4

import random

NUMBER_OF_TRIALS = 1000000 # Constant，要随机产生一千万个点

numberOfHits = 0

for i in range(NUMBER_OF_TRIALS):

....x = random.random() * 2 - 1

....y = random.random() * 2 - 1

....if x * x + y * y <= 1:

........numberOfHits += 1

pi = 4 * numberOfHits / NUMBER_OF_TRIALS

print("PI is", pi)

注意两个知识点：

随机函数random()的返回值：0 <= random() <1.0

圆方程：x² +y ² = 1

output1:

PI is 3.140228

try again:

PI is 3.141368

4 自然数内的前50个素数，每行显示10个

output:

也可以写成函数的形式：

5 十进制转与16进制的相互转换

5.1 十进制转16进制

output:

Enter a decimal number: 1000

The hex number for decimal 1000 is 3E8

5.2 十六进制转十进制

output:

Enter a hex number: 3e8

The decimal value for hex number 3e8 is 1000

附代码1

NUMBER_OF_PRIMES = 50 # Number of primes to display

NUMBER_OF_PRIMES_PER_LINE = 10 # Display 10 per line

count = 0 # Count the number of prime numbers

number = 2 # A number to be tested for primeness

print("The first 50 prime numbers are")

while count < NUMBER_OF_PRIMES: # Repeatedly find prime numbers

....isPrime = True #Is the current number prime?

....divisor = 2

....while divisor <= number / 2:

........if number % divisor == 0:

# If true, the number is not prime

............isPrime = False # Set isPrime to false

............break # Exit the for loop

........divisor += 1

....if isPrime: # Display the prime number and increase the count

........count += 1 # Increase the count

........print(format(number, '5d'), end = '')

........if count % NUMBER_OF_PRIMES_PER_LINE == 0:

# Display the number and advance to the new line

............print() # Jump to the new line

....number += 1 # Check if the next number is prime

附代码2

def isPrime(number):................# Check whether number is prime

....divisor = 2

....while divisor <= number / 2:

........if number % divisor == 0: # If true, number is not prime............

............return False............# number is not a prime

........divisor += 1

....return True.................... # number is prime

def printPrimeNumbers(numberOfPrimes):

....NUMBER_OF_PRIMES = 50........ # Number of primes to display

....NUMBER_OF_PRIMES_PER_LINE = 10 # Display 10 per line

....count = 0.................... # Count the number of prime numbers

....number = 2.................... # A number to be tested for primeness

....

....while count < numberOfPrimes: # Repeatedly find prime numbers

....................................# Print the prime number and increase the count

........if isPrime(number):

............count += 1............ # Increase the count

............print(number, end = " ")

............if count % NUMBER_OF_PRIMES_PER_LINE == 0:

....................................# Print the number and advance to the new line

................print()

....................................# Check if the next number is prime

........number += 1

def main():

....print("The first 50 prime numbers are")

....printPrimeNumbers(50)

main()............................ # Call the main function

附代码3

....................# Convert a decimal to a hex as a string

def decimalToHex(decimalValue):

....hex = ""

....while decimalValue != 0:

........hexValue = decimalValue % 16

........hex = toHexChar(hexValue) + hex

........decimalValue = decimalValue // 16

....

....return hex

....................# Convert an integer to a single hex digit in a character

def toHexChar(hexValue):

....if 0 <= hexValue <= 9:

........return chr(hexValue + ord('0'))

....else:.................................... # 10 <= hexValue <= 15

........return chr(hexValue - 10 + ord('A'))

def main():

....................# Prompt the user to enter a decimal integer

....decimalValue = eval(input("Enter a decimal number: "))

....print("The hex number for decimal",

........decimalValue, "is", decimalToHex(decimalValue))

main()........................................ # Call the main function

附代码4：

def main():

........................# Prompt the user to enter a hex number

....hex = input("Enter a hex number: ").strip()

....decimal = hexToDecimal(hex.upper())

....if decimal == None:

........print("Incorrect hex number")

....else:

........print("The decimal value for hex number",

............hex, "is", decimal)

def hexToDecimal(hex):

....decimalValue = 0

....for i in range(len(hex)):

........ch = hex[i]

........if 'A' <= ch <= 'F' or '0' <= ch <= '9':

............decimalValue = decimalValue * 16 +

................hexCharToDecimal(ch)

........else:

............return None

....return decimalValue

def hexCharToDecimal(ch):

....if 'A' <= ch <= 'F':

........return 10 + ord(ch) - ord('A')

....else:

........return ord(ch) - ord('0')

main()................ # Call the main function

－End－