使用 JavaScript 扩展二项式表达式
问题
我们需要编写一个JavaScript函数，该函数采用(ax+b)^n形式的表达式，其中a和b是整数，可以是正数或负数，x是任何单个字符变量，n是自然数。如果a=1，则变量前不会放置系数。
我们的函数应该以ax^b+cx^d+ex^f...形式的字符串形式返回扩展形式，其中a、c和e是项的系数，x是原始的单字符变量，在原始表达式中传递，b、d和f是x在每一项中被提升到的幂，并按降序排列
示例
以下是代码-
const str = '(8a+6)^4';
const trim = value => value === 1 ? '' : value === -1 ? '-' : value
const factorial = (value, total = 1) =>
value <= 1 ? total : factorial(value - 1, total * value)
const find = (str = '') => {
let [op1, coefficient, variable, op2, constant, power] = str
.match(/(\W)(\d*)(\w)(\W)(\d+)..(\d+)/)
.slice(1)
power = +power
if (!power) {
return '1'
}
if (power === 1) {
return str.match(/\((.*)\)/)[1]
}
coefficient =
op1 === '-'
? coefficient
? -coefficient
: -1
: coefficient
? +coefficient
: 1
constant = op2 === '-' ? -constant : +constant
const factorials = Array.from({ length: power + 1 }, (_,i) => factorial(i))
let result = ''
for (let i = 0, p = power; i <= power; ++i, p = power - i) {
let judge =
factorials[power] / (factorials[i] * factorials[p]) *
(coefficient * p * constant * i)
if (!judge) {
continue
}
result += p
? trim(judge) + variable + (p === 1 ? '' : `^${p}`)
: judge
result += '+'
}
return result.replace(/\+\-/g, '-').replace(/\+$/, '')
};
console.log(find(str));输出结果576a^3+1152a^2+576a