python 练习题

　　python是一个功能很强大的语言，他可以解决各种在数学问题，下面我分享一些练习题供大家参考：

有关正态分布的问题：

 # -*- coding: cp936 -*-
 import math
 a=0
 u=0
 x=0
 while 1:
     a =int(input("please input a :"))
     ifa<0:
        print "请重新输入："
     elifa>0:
        break;
 u = int(input("please intput u :"))
 x = int(input("please intput x :"))
 fs =(1/math.sqrt(2*math.pi)*a)*math.exp(0.5*(math.pow(((x-u)/a),2)))
 print "this fs is :%.2f"%fs;

关于平抛运动矢量位移：

 v0 =10
 g= 9.81
 #t = int(input("please input a time:"))
 #h = v0*t+0.5*g*t**2
 #print "this h is :%.2f"%h;

 while 1:
     h =int(input("please input a hight:"))
     #h =v0*t+0.5*g*t**2
     t1=(-v0+(v0**2-4*0.5*g*(-h))**0.5)/(2*0.5*g)
     t2=(-v0-(v0**2-4*0.5*g*(-h))**0.5)/(2*0.5*g)
     ift1>0:
        print "this time1 is:%.2f"%t1;
     ift2>0:
        print "this time2 is :%.2f"%t2;

python的函数式编程

　　判断一个数是不是质数：

  >>>f = lambda x:not reduce(lambda x,y:x or y,[x%i==0 for i inrange(2,x)])
 >>> f(97)
 True
 >>> f(96)
 False  

　　求最大公约数：

 >>> f = lambdam,n:[i for i in range(min(m,n),0,-1) if m%i==0 and n%i==0][0]
 >>> f(123,77)
 1
 >>> f(125,100)
 25

计算给定数字的阶乘：

 >>> f = lambdax:reduce(lambda x,y:x*y,[i for i in range(1,x+1)])
 >>> f(5)
 120

 >>> zip3 = lambdal1,l2,l3:[(l1[i],l2[i],l3[i]) for i in range(len(l1))]
 >>>zip3([1,2,3],['a','b','c'],[1j,2j,3j])
 [(1, 'a', 1j), (2, 'b', 2j), (3, 'c', 3j)]

python的reduce函数的应用：

 >>> f = lambdal:reduce(lambda x,y:x*y,l)
 >>> f(l)
 0
 >>>f([1,2,2,3,4])
 48

蒙特卡洛近似求解

　　1.求圆周率：

 import random
 import math
 def round_(num):
     i=0
    number=0.0
     whilei<num:
        x = random.random()
        y = random.random()

        y_=s(x)
        if y<=y_:
            number+=1
        i+=1
     return4*number/num
 def s(a):
     returnmath.sqrt(1-math.pow(a,2))

　　2.求面积：

 import random
 def f(num):
     i=0
     s=0.0
     while i<num:
         x = random.random()
         #print x
         y = random.random()
         y_=ft(x)
         if y<=y_:
             s+=1
         i+=1
     return s/num

 def ft(a) :
     return a*a