112 lines
3.6 KiB
Python
112 lines
3.6 KiB
Python
from fractions import Fraction
|
||
|
||
import numpy as np
|
||
import scipy as sp
|
||
|
||
|
||
def solve_equation(eq):
|
||
"""
|
||
配平化学方程式，返回配平后的化学方程式
|
||
|
||
:param eq: 化学方程式，
|
||
格式为
|
||
{
|
||
'left': [ {
|
||
'atoms': [ {'元素名称': 元素个数}, {'元素名称': 元素个数}, ... ],
|
||
'coefficient': 系数,
|
||
'pretty_name': 化学式的字符串表示
|
||
}, ... ],
|
||
'right': [ ... ]
|
||
}
|
||
:return: 配平后的化学方程式，与输入格式相同
|
||
若无法配平，则返回 None
|
||
"""
|
||
# 统计所有元素的种类
|
||
elements = set()
|
||
for each in eq['left']:
|
||
for atom in each['atoms']:
|
||
elements.add(list(atom.keys())[0])
|
||
for each in eq['right']:
|
||
for atom in each['atoms']:
|
||
elements.add(list(atom.keys())[0])
|
||
elements = list(elements)
|
||
# 构造系数矩阵
|
||
matrix = []
|
||
constant = []
|
||
for atom in elements:
|
||
# 遍历左边，左侧系数为正
|
||
row = []
|
||
for each in eq['left']:
|
||
for atom_ in each['atoms']:
|
||
if atom in atom_:
|
||
row.append(atom_[atom])
|
||
break
|
||
else:
|
||
row.append(0)
|
||
# 遍历右边，右侧系数为负
|
||
for each in eq['right']:
|
||
for atom_ in each['atoms']:
|
||
if atom in atom_:
|
||
row.append(-atom_[atom])
|
||
break
|
||
else:
|
||
row.append(0)
|
||
# 取出row中的最后一个元素，反转后加入常数项
|
||
constant.append(-row.pop())
|
||
matrix.append(row)
|
||
matrix = np.mat(matrix, int)
|
||
# 求解线性方程组
|
||
try:
|
||
result = sp.optimize.lsq_linear(matrix, constant, bounds=(0, None)).x.tolist()
|
||
except ValueError:
|
||
raise ValueError('无法配平')
|
||
|
||
# 将结果写入化学方程式，最后一个生成物的系数需要计算得到
|
||
last_substance = eq['right'][-1]
|
||
last_atom = list(last_substance['atoms'][0].keys())[0]
|
||
# 计算除最后一种生成物外的所有生成物包含last_atom的系数之和
|
||
sum_ = 0
|
||
index = 0
|
||
for each in eq['left']:
|
||
for atom in each['atoms']:
|
||
if last_atom in atom:
|
||
# 该生成物包含last_atom，则获得last_atom的总个数，等于系数*原子个数
|
||
sum_ += result[index] * atom[last_atom]
|
||
break
|
||
index += 1
|
||
for each in eq['right'][:-1]:
|
||
for atom in each['atoms']:
|
||
if last_atom in atom:
|
||
sum_ -= result[index] * atom[last_atom]
|
||
break
|
||
index += 1
|
||
result.append(sum_ / last_substance['atoms'][0][last_atom])
|
||
result = expand_to_int(*result)
|
||
for i, each in enumerate(eq['left']):
|
||
each['coefficient'] = result[i]
|
||
for i, each in enumerate(eq['right']):
|
||
each['coefficient'] = result[i + len(eq['left'])]
|
||
return eq
|
||
|
||
|
||
def expand_to_int(*args):
|
||
"""
|
||
将一系列小数同时扩大，全部转换为最接近的整数
|
||
|
||
:param args: 一系列小数
|
||
:return: 一系列整数
|
||
"""
|
||
# 将所有小数转换为分数
|
||
fractions = []
|
||
for each in args:
|
||
fractions.append(Fraction(each).limit_denominator())
|
||
# 计算所有分数的最小公倍数
|
||
lcm = 1
|
||
for each in fractions:
|
||
lcm = lcm * each.denominator // np.gcd(lcm, each.denominator)
|
||
# 将所有分数扩大为最小公倍数
|
||
result = []
|
||
for each in fractions:
|
||
result.append(each.numerator * lcm // each.denominator)
|
||
return result
|