鸡兔同笼问题的python解法_鸡兔同笼python

方法一：通过sympy的方法进行计算

from sympy import Symbol,solve,pprint
x = Symbol('x')
y = Symbol('y')
n = Symbol('n')
m = Symbol('m')
expr1 = x + y - n
expr2 =2*x+4*y- m
solution = 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.')
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结果如下：

There are 23 chicken.
There are 12 rabbits.
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方法二：通过解析式编写函数求解
假设有$x$只鸡，$y$只兔子，我们可以列出以下方程组：
{ x + y = n 2 x + 4 y = m \left\{

$$\begin{aligned} &x+y = n \\ &2x+4y = m \\ \end{aligned}$$ \right. {​x+y=n2x+4y=m​
得到的解为：
$$\{\begin{array}{rl}& x=2n-\frac{1}{2}m\\ & y=\frac{1}{2}m-n\end{array}$$
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 - nheads
	chinum = 2*nheads - mlegs/2
	return chinum,rabnum

chicken = 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.')
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最后的结果如下：

There are 23 chicken.
There are 12 rabbits.
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