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