在 Java 中，可以使用数组或链表来表示多项式，然后通过遍历多项式的每一项，将相同指数的项相加得到最终结果。
以下是一种使用链表表示多项式的实现方式：
public class PolynomialNode { int coefficient; int exponent; PolynomialNode next; public PolynomialNode(int coefficient, int exponent) { this.coefficient = coefficient; this.exponent = exponent; this.next = null; }}public class Polynomial { private PolynomialNode head; public Polynomial() { this.head = null; } public void addTerm(int coefficient, int exponent) { PolynomialNode newNode = new PolynomialNode(coefficient, exponent); if (head == null) { head = newNode; } else { PolynomialNode current = head; PolynomialNode previous = null; while (current != null && current.exponent > exponent) { previous = current; current = current.next; } if (current != null && current.exponent == exponent) { current.coefficient += coefficient; } else { newNode.next = current; if (previous != null) { previous.next = newNode; } else { head = newNode; } } } } public Polynomial add(Polynomial polynomial) { Polynomial result = new Polynomial(); PolynomialNode node1 = this.head; PolynomialNode node2 = polynomial.head; while (node1 != null && node2 != null) { if (node1.exponent > node2.exponent) { result.addTerm(node1.coefficient, node1.exponent); node1 = node1.next; } else if (node1.exponent < node2.exponent) { result.addTerm(node2.coefficient, node2.exponent); node2 = node2.next; } else { int sum = node1.coefficient + node2.coefficient; if (sum != 0) { result.addTerm(sum, node1.exponent); } node1 = node1.next; node2 = node2.next; } } while (node1 != null) { result.addTerm(node1.coefficient, node1.exponent); node1 = node1.next; } while (node2 != null) { result.addTerm(node2.coefficient, node2.exponent); node2 = node2.next; } return result; } public String toString() { StringBuilder sb = new StringBuilder(); PolynomialNode current = head; boolean isFirstTerm = true; while (current != null) { if (current.coefficient != 0) { if (current.coefficient > 0 && !isFirstTerm) { sb.append("+"); } sb.append(current.coefficient); if (current.exponent > 1) { sb.append("x^").append(current.exponent); } else if (current.exponent == 1) { sb.append("x"); } isFirstTerm = false; } current = current.next; } return sb.toString(); }}使用示例：
public class Main { public static void main(String[] args) { Polynomial polynomial1 = new Polynomial(); polynomial1.addTerm(3, 4); polynomial1.addTerm(2, 3); polynomial1.addTerm(5, 2); polynomial1.addTerm(1, 0); Polynomial polynomial2 = new Polynomial(); polynomial2.addTerm(1, 3); polynomial2.addTerm(4, 2); polynomial2.addTerm(2, 1); polynomial2.addTerm(3, 0); Polynomial result = polynomial1.add(polynomial2); System.out.println("Polynomial 1: " + polynomial1); System.out.println("Polynomial 2: " + polynomial2); System.out.println("Result: " + result); }}输出结果：
Polynomial 1: 3x^4+2x^3+5x^2+1Polynomial 2: x^3+4x^2+2x+3Result: 3x^4+3x^3+9x^2+2x+4