《Python程序设计与算法基础教程》——江红 余青松
第三章_上机实践
# ch3 P59_3
# *实现101-201输出所有的素数*
import math
j = 0
for m in range(101, 201):
k = int(math.sqrt(m))
for i in range(2, k + 2):
if m % i == 0:
break
if i == k + 1:
print(m, end = ' ' )
j += 1
if j % 10 == 0:
print()
# ch3 P60_4
# *输出三角形*
n = int(input("请输入图形的行数:"))
for i in range(0, n):
for j in range(0, 10- i):
print(" ", end = " ")
for j in range(0, 2 * i + 1):
print("*", end = " ")
print("\n")
# ch3 P60_5
# * 水仙花数是一个三位数,三位数各位的立方之和等于三位数本身 *
import math # 调用模块,访问math模块中*
print("三位数中所有的水仙花数为:")
for i in range(100, 1000):
n1 = i // 100 # //地板除法,求小于a与b的商的最大整数
n2 = (i % 100)//10
n3 = i % 10
if (math.pow(n1, 3) + math.pow(n2, 3) + math.pow(n3, 3) == i): # pow(x,y)返回x的y次幂的值
print(i, end= " ")
# ch3 P60_6
# * 如果一个数恰好等于它的真因子之和,则称该数为“完全数”。各个小于它的约数(真约数,列出某数的约数,去掉该数本身,剩下的就是它的真约数)的和等于它本身的自然数叫做完全数(Perfect number),又称完美数或完备数。*
# 找出1~1000之间所有的完数
print("1~1000之间所有的完数有,其因子为:")
for n in range(1, 1001):
total = 0
j = 0
factors = []
for i in range(1, n):
if (n % i == 0): # 找出n的所有约数并且出去它本身
factors.append(i) # 存入数组中
total += i
if (total == n): # 完全数的要求是所有的真约数之和为n本身
print("{0}:{1}".format(n, factors))
# ch3 P60_7
# * 求任意两个整数的最大公约数 *
m = int(input("请输入整数m:"))
n = int(input("请输入整数n:"))
while (m != n):
if (m > n):
m = m - n
else:
n = n - m
print(m)
# 上机实践
# ch3 P60_1
# * 计算1~100之和 *
total = 0
for i in range(1, 101):
total += i
print("1~100之和为:", total)
# 上机实践
# ch3 P61_5
# * 输出2000~3000之间的所有闰年 *
# * 判断闰年的条件是:年份能被4整除但不能被100整除,或者能被400整除*
j = 0
for i in range(2000, 3000):
if((i % 4 == 0 and i % 100 != 0) or i % 400 == 0):
j += 1
print(i, end = " ")
if (j % 18 == 0):
print()
# ch3 P61_6
# * 计算Sn = 1-3+5-7+9—11+。。。 *
n = int(input("请输入一个整数:"))
count = 0
Sn1 = 0
Sn2 = 0
Sn = 0
for i in range(1, n + 1):
count += 1
if (count == 1):
Sn1 += 2 * i -1
if (count == 2):
i = -i
count = 0
Sn2 += 2 * i + 1
Sn = Sn1 +Sn2
print(Sn)
# 上机实践
# ch3 P61_7
# * 计算Sn=1+1/2+1/3+... *
n = int(input("请输入一个整数:"))
Sn = 0
for i in range(1, n + 1):
An = 1 / i
Sn += An
print(Sn)
# 上机实践
# ch3 P61_8
# * 九九乘法表 *
print("***九九乘法表***")
count = 0
for i in range(1, 10):
for j in range(1, 10):
print("{}*{}={}".format(i, j, i * j), end=' ')
count += 1
if count % 9 == 0:
print()
print("***下三角九九乘法表***")
for i in range(1, 10):
for j in range(1, 10):
print("{}*{}={} ".format(i, j, i * j), end=' ')
if i == j:
break
print("")
print("***上三角九九乘法表***")
for i in range(1, 10):
for j in range(1, 10):
if j < i:
print(end=" ")
continue
print("{}*{}={} ".format(i, j, i * j), end=' ')
print("")
# 上机实践
# ch3 P61_8
# * 九九乘法表 *
print("矩阵九九乘法表:")
for i in range(1, 10):
s = ''
for j in range(1, 10):
# {2:<2} # {}叫做占位符
s += "{0:1}*{1:1}={2:2} ".format(i, j, i * j)
# s += str.format("{0:1}*{1:1}={2:<2} ", i, j, i*j) # 把后面的格式变成字符串,然后字符串的连接赋给s
print(s)
print("下三角九九乘法表")
for i in range(1, 10):
s = ''
for j in range(1, 10):
s += str.format("{0:1}*{1:1}={2:2} ", i, j, i*j)
if j == i:
break
print(s)
print("上三角九九乘法表:")
for i in range(1, 10):
s = ''
for j in range(1, 10):
if j < i:
print(end=" ")
continue
s += str.format("{0:1}*{1:1}={2:2} ", i, j, i*j)
print(s)
# 上机实践
# ch3 P61_9
# * 输入三角形三条边,判断是否可以构成三角形 *
# * 条件:1.每条边长均大于0,并且任意两边之和大于第三边
import math
A = int(input("请输入三角形的边A: "))
B = int(input("请输入三角形的边B: "))
C = int(input("请输入三角形的边C: "))
if (A + B > C and A + C > B and B + C > A):
perimeter = A + B + C
h = 1 / 2 * perimeter
area = math.sqrt(h * (h - A) * (h - B) * (h - C)) # 面积公式
print("三角形三边分别为: a = {}, b = {}, c = {}".format(A, B, C))
print("三角形的周长 = {}, 面积 = {}".format(perimeter, area))
else:
print("无法构成三角形!")
# 上机实践
# ch3 P61_10
# * 输入x,根据如下公式,计算分段函数y的值 *
import math
x = float(input("请输入x: "))
if x >= 0:
y = (x ** 2 - 3 * x)/(x + 1) + 2 * math.pi + math.sin(x)
else:
y = math.log((-5 * x), math.e) + 6 * math.sqrt(math.fabs(x) + math.e ** 4) - (x + 1) ** 3
print("方法三: x ="+ str(x) + " y = " + str(y))
# 上机实践
# ch3 P61_11
# * 输入x,根据如下公式,计算分段函数y的值 *
import math
while (1):
a = float(input("请输入系数a: "))
b = float(input("请输入系数b: "))
c = float(input("请输入系数c: "))
if (a == 0 and b == 0):
print("此方程无解!")
elif (a == 0 and b != 0):
x = -c / b
print("此方程有一个实根: ", x)
elif (b ** 2 - 4 * a * c == 0):
x1 = x2 = -b / (2 * a)
print("此方程有两个相同实根: {}和{}".format(x1, x2))
elif (b ** 2 - 4 * a * c > 0):
x1 = - b / (2 * a) + (math.sqrt(b ** 2 - 4 * a * c) / (2 * a))
x2 = - b / (2 * a) - (math.sqrt(b ** 2 - 4 * a * c) / (2 * a))
print("此方程有两个不等实根:{}和{}".format(x1, x2))
else:
print("此方程有两个共轭复根:{0}+{1}i和{0}-{1}i".format(- b / (2 * a), (math.sqrt(4 * a * c - b ** 2) / (2 * a))))
# 上机实践
# ch3 P61_12
# * 输入x,根据如下公式,计算分段函数y的值 *
import math
j = 1
whileCount = 1
n = int(input("请输入非负整数n:"))
while (n < 0):
n = int(input("请输入非负整数n:"))
x = n # 再用x指代输入的n,防止在后面的操作中n的数值已经发生变化了
if (n == 0):
print("0! = 1")
else:
for i in range(1, n + 1):
j *= i
print(" for循环:{}! = {}".format(n, j))
while (n):
whileCount *= n
n -= 1
print("while循环:{}! = {}".format(x, whileCount))
s = i = 1
while (i <= x):
s *= i
i += 1
print("while循环:{}! = {}".format(x, s))
# 上机实践
# ch3 P61_13
# * 编写程序,产生两个0~100之间(包含0和1000)的随机整数a和b *
# * 求这两个整数的最大公约数和最小公倍数 *
# * 方法:辗转相除法求最大公约数 *
import random
a = random.randint(0, 100)
b = random.randint(0, 100)
print("整数1 = {}, 整数2 = {}".format(a, b))
if a > b: # 1.对于已知的两个正整数m、n,使得m>n。
m = a
n = b
else:
m = b
n = a
r = m % n # 2.m除以n得余数r
while r != 0:
m = n
n = r
r = m % n # 若r != 0,则令m = n,n = r,继续相除得到新的余数r。
# 若仍然r != 0,则重复此过程,直到r = 0 为止。最后的m就是最大公约数。
m = n
leastCommonMultiple = int(a * b / m) # 最小公倍数就是已知的两个正整数之积除以最大公约数的商
print("最大公约数 = {}, 最小公倍数 = {}".format(m, leastCommonMultiple))