鸡兔同笼问题的python解法

方法一：通过sympy的方法进行计算

from sympy import Symbol,solve,pprintx = Symbol('x')y = Symbol('y')n = Symbol('n')m = Symbol('m')expr1 = x + y - nexpr2 =2*x+4*y- msolution = solve((expr1,expr2),(x,y),dict=True)chicken = solution[0][x].subs({n:35,m:94})rabbits = solution[0][y].subs({n:35,m:94})print(f'There are {chicken} chicken.')print(f'There are {rabbits} rabbits.')

结果如下：

There are 23 chicken.There are 12 rabbits.

方法二：通过解析式编写函数求解

假设有xxx只鸡，yyy只兔子，我们可以列出以下方程组：

{x+y=n2x+4y=m\left\{ \begin{aligned} &x+y = n \\ &2x+4y = m \\ \end{aligned} \right. {​x+y=n2x+4y=m​

得到的解为：

{x=2n−12my=12m−n\left\{ \begin{aligned} &x = 2n-\frac{1}{2}m \\ &y = \frac{1}{2}m-n \\ \end{aligned} \right. ⎩⎪⎨⎪⎧​​x=2n−21​my=21​m−n​

据此，我们可以写出以下函数进行该问题的求解：

def chicken_and_rabbits(nheads,mlegs):rabnum = mlegs/2 - nheadschinum = 2*nheads - mlegs/2return chinum,rabnumchicken = int(chicken_and_rabbits(35,94)[0])rabbits = int(chicken_and_rabbits(35,94)[1])print(f'There are {chicken} chicken.')print(f'There are {rabbits} rabbits.')

最后的结果如下：

There are 23 chicken.There are 12 rabbits.

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