js实现多项式累加

实现多项式累加的方法

多项式累加可以通过多种方式实现，以下是几种常见的JavaScript实现方法：

使用数组和reduce方法

将多项式的系数存储在数组中，使用reduce方法进行累加：

function addPolynomials(poly1, poly2) {
    const maxLength = Math.max(poly1.length, poly2.length);
    const result = new Array(maxLength).fill(0);

    for (let i = 0; i < poly1.length; i++) {
        result[i] += poly1[i];
    }

    for (let i = 0; i < poly2.length; i++) {
        result[i] += poly2[i];
    }

    return result;
}

// 示例：3x^2 + 2x + 1 和 4x + 5 相加
const poly1 = [1, 2, 3]; // 1 + 2x + 3x^2
const poly2 = [5, 4];    // 5 + 4x
console.log(addPolynomials(poly1, poly2)); // [6, 6, 3]

使用对象表示多项式

将多项式表示为对象，键为指数，值为系数：

function addPolynomials(poly1, poly2) {
    const result = {...poly1};

    for (const [exp, coeff] of Object.entries(poly2)) {
        result[exp] = (result[exp] || 0) + coeff;
    }

    return result;
}

// 示例：3x^2 + 2x + 1 和 4x + 5 相加
const poly1 = {0: 1, 1: 2, 2: 3}; // 1 + 2x + 3x^2
const poly2 = {0: 5, 1: 4};       // 5 + 4x
console.log(addPolynomials(poly1, poly2)); // {0: 6, 1: 6, 2: 3}

处理稀疏多项式

对于稀疏多项式，可以优化存储和计算：

function addPolynomials(poly1, poly2) {
    const terms = new Map();

    poly1.forEach(term => terms.set(term.exp, (terms.get(term.exp) || 0) + term.coeff));
    poly2.forEach(term => terms.set(term.exp, (terms.get(term.exp) || 0) + term.coeff));

    return Array.from(terms.entries())
        .map(([exp, coeff]) => ({exp, coeff}))
        .sort((a, b) => b.exp - a.exp);
}

// 示例：3x^100 + 2x + 1 和 4x^50 + 5 相加
const poly1 = [
    {exp: 0, coeff: 1},
    {exp: 1, coeff: 2},
    {exp: 100, coeff: 3}
];
const poly2 = [
    {exp: 0, coeff: 5},
    {exp: 50, coeff: 4}
];
console.log(addPolynomials(poly1, poly2));

格式化输出结果

将计算结果格式化为可读的字符串：

function polynomialToString(poly) {
    return poly.reduce((str, coeff, exp) => {
        if (coeff === 0) return str;

        const sign = coeff >= 0 ? '+' : '-';
        const absCoeff = Math.abs(coeff);
        let term = '';

        if (exp === 0) {
            term = `${absCoeff}`;
        } else {
            term = absCoeff === 1 ? `x^${exp}` : `${absCoeff}x^${exp}`;
        }

        return `${sign} ${term} ${str}`;
    }, '').trim() || '0';
}

const result = [6, 6, 3];
console.log(polynomialToString(result)); // "+ 3x^2 + 6x + 6"

这些方法可以根据实际需求选择使用，数组方法适合密集多项式，对象方法适合处理任意指数，稀疏表示适合处理高阶稀疏多项式。