网上有用单链表来实现多项式的加减乘，你可以参考一下，代码如下
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public class Polynomial {
private Monomial first; // 首项
//添加单项式
public void append(Monomial monomial) {
if (monomial == null) {
// do nothing
} else if (first == null) {
first = monomial;
} else {
Monomial current = first;
while (current != null) {
// Examda提示:如果指数相同，则相加
if (current.index == monomial.index) {
current.coefficient += monomial.coefficient;
break;
} else if (current.next == null) { // 否则直接扔到最后
current.next = monomial;
break;
}
current = current.next;
}
}
}
public void append(double c, int i) {
append(new Monomial(c, i));
}
public String toString() {
StringBuffer sb = new StringBuffer();
Monomial current = first;
while (current.next != null) {
sb
.append("(" + current.coefficient + "x^" + current.index
+ ") + ");
current = current.next;
}
sb.append("(" + current.coefficient + "x^" + current.index + ")");
return sb.toString();
}
// 两个多项式相加
public Polynomial add(Polynomial p2) {
Polynomial result = new Polynomial();
Monomial current = this.first;
while (current != null) {
result.append(current.coefficient, current.index); // Examda提示:注意这里
current = current.next;
}
current = p2.first;
while (current != null) {
result.append(current.coefficient, current.index);
current = current.next;
}
return result;
}
// 两个多项式相减 this- p2
public Polynomial substract(Polynomial p2) {
Polynomial result = new Polynomial();
Monomial current = this.first;
while (current != null) {
result.append(current.coefficient, current.index); // 注意这里
current = current.next;
}
current = p2.first;
while (current != null) {
result.append(-current.coefficient, current.index);
current = current.next;
}
return result;
}
/**
* this * p2
*
* @return
*/
public Polynomial multiply(Polynomial p2) {
Polynomial result = new Polynomial();
Monomial c1 = this.first;
Monomial c2 = p2.first;
while (c1 != null) {
while (c2 != null) {
result.append(c1.coefficient * c2.coefficient, c1.index
+ c2.index);
c2 = c2.next;
}
c1 = c1.next;
c2 = p2.first;
}
return result;
}
public Polynomial divide(Polynomial p2) {
// todo 实现相除
return null;
}
public static void main(String[] args) {
Polynomial p1 = new Polynomial();
p1.append(2.2, 1);
p1.append(3.3, 2);
p1.append(4.111, 7);
System.out.println("p1: " + p1);
Polynomial p2 = new Polynomial();
p2.append(2.232, 5);
p2.append(3.444, 6);
p2.append(5.777, 1);
System.out.println("p2: " + p2);
Polynomial result = p1.add(p2);
System.out.println("加: " + result);
result = p1.substract(p2);
System.out.println("减: " + result);
result = p1.multiply(p2);
System.out.println("乘: " + result);
}
}
/**
* 单项式
*/
class Monomial {
double coefficient; // 系数
int index; // 指数
Monomial next; // 后继结点
public Monomial() {
}
public Monomial(double c, int i) {
this.coefficient = c;
this.index = i;
}
}
除以上功能外，还有乘法和除法的计算和导数计算呢。
这是我以前做的数据结构课程设计。希望能帮上你的忙。
#includestdio.h
#includemalloc.h
typedef struct Polynomial{
float coef;
int expn;
struct Polynomial *next;
}*Polyn,Polynomial; //Polyn为结点指针类型
void Insert(Polyn p,Polyn h){
if(p-coef==0) free(p); //系数为0的话释放结点
else{
Polyn q1,q2;
q1=h;q2=h-next;
while(q2p-expnq2-expn){ //查找插入位置
q1=q2;
q2=q2-next;
}
if(q2p-expn==q2-expn){ //将指数相同相合并
q2-coef+=p-coef;
free(p);
if(!q2-coef){ //系数为0的话释放结点
q1-next=q2-next;
free(q2);
}
}
else{ //指数为新时将结点插入
p-next=q2;
q1-next=p;
}
}
}//Insert
Polyn CreatePolyn(Polyn head,int m){//建立一个头指针为head、项数为m的一元多项式
int i;
Polyn p;
p=head=(Polyn)malloc(sizeof(struct Polynomial));
head-next=NULL;
for(i=0;im;i++){
p=(Polyn)malloc(sizeof(struct Polynomial));//建立新结点以接收数据
printf("请输入第%d项的系数与指数:",i+1);
scanf("%f %d",p-coef,p-expn);
Insert(p,head); //调用Insert函数插入结点
}
return head;
}//CreatePolyn
void DestroyPolyn(Polyn p){//销毁多项式p
Polyn q1,q2;
q1=p-next;
q2=q1-next;
while(q1-next){
free(q1);
q1=q2;//指针后移
q2=q2-next;
}
}
void PrintPolyn(Polyn P){
Polyn q=P-next;
int flag=1;//项数计数器
if(!q) { //若多项式为空，输出0
putchar('0');
printf("\n");
return;
}
while (q){
if(q-coef0flag!=1) putchar('+'); //系数大于0且不是第一项
if(q-coef!=1q-coef!=-1){//系数非1或-1的普通情况
printf("%g",q-coef);
if(q-expn==1) putchar('X');
else if(q-expn) printf("X^%d",q-expn);
}
else{
if(q-coef==1){
if(!q-expn) putchar('1');
else if(q-expn==1) putchar('X');
else printf("X^%d",q-expn);
}
if(q-coef==-1){
if(!q-expn) printf("-1");
else if(q-expn==1) printf("-X");
else printf("-X^%d",q-expn);
}
}
q=q-next;
flag++;
}//while
printf("\n");
}//PrintPolyn
int compare(Polyn a,Polyn b){
if(ab){
if(!b||a-expnb-expn) return 1;
else if(!a||a-expnb-expn) return -1;
else return 0;
}
else if(!ab) return -1;//a多项式已空，但b多项式非空
else return 1;//b多项式已空，但a多项式非空
}//compare
Polyn AddPolyn(Polyn pa,Polyn pb){//求解并建立多项式a+b，返回其头指针
Polyn qa=pa-next;
Polyn qb=pb-next;
Polyn headc,hc,qc;
hc=(Polyn)malloc(sizeof(struct Polynomial));//建立头结点
hc-next=NULL;
headc=hc;
while(qa||qb){
qc=(Polyn)malloc(sizeof(struct Polynomial));
switch(compare(qa,qb)){
case 1:
{
qc-coef=qa-coef;
qc-expn=qa-expn;
qa=qa-next;
break;
}
case 0:
{
qc-coef=qa-coef+qb-coef;
qc-expn=qa-expn;
qa=qa-next;
qb=qb-next;
break;
}
case -1:
{
qc-coef=qb-coef;
qc-expn=qb-expn;
qb=qb-next;
break;
}
}//switch
if(qc-coef!=0){
qc-next=hc-next;
hc-next=qc;
hc=qc;
}
else free(qc);//当相加系数为0时，释放该结点
}//while
return headc;
}//AddPolyn
Polyn SubtractPolyn(Polyn pa,Polyn pb){//求解并建立多项式a+b，返回其头指针
Polyn h=pb;
Polyn p=pb-next;
Polyn pd;
while(p){ //将pb的系数取反
p-coef*=-1;
p=p-next;
}
pd=AddPolyn(pa,h);
for(p=h-next;p;p=p-next) //恢复pb的系数
p-coef*=-1;
return pd;
}//SubtractPolyn
float ValuePolyn(Polyn head,float x){//输入x值，计算并返回多项式的值
Polyn p;
int i;
float sum=0,t;
for(p=head-next;p;p=p-next){
t=1;
for(i=p-expn;i!=0;){
if(i0){t/=x;i++;}//指数小于0，进行除法
else{t*=x;i--;}//指数大于0，进行乘法
}
sum+=p-coef*t;
}
return sum;
}//ValuePolyn
Polyn Derivative(Polyn head){//求解并建立a的导函数多项式，并返回其头指针
Polyn q=head-next,p1,p2,hd;
hd=p1=(Polyn)malloc(sizeof(struct Polynomial));//建立头结点
hd-next=NULL;
while(q){
if(q-expn!=0){ //该项不是常数项时
p2=(Polyn)malloc(sizeof(struct Polynomial));
p2-coef=q-coef*q-expn;
p2-expn=q-expn-1;
p2-next=p1-next;//连接结点
p1-next=p2;
p1=p2;
}
q=q-next;
}
return hd;
}//Dervative
Polyn MultiplyPolyn(Polyn pa,Polyn pb){//求解并建立多项式a*b，返回其头指针
Polyn hf,pf;
Polyn qa=pa-next;
Polyn qb=pb-next;
hf=(Polyn)malloc(sizeof(struct Polynomial));//建立头结点
hf-next=NULL;
for(;qa;qa=qa-next){
for(qb=pb-next;qb;qb=qb-next){
pf=(Polyn)malloc(sizeof(struct Polynomial));
pf-coef=qa-coef*qb-coef;
pf-expn=qa-expn+qb-expn;
Insert(pf,hf);//调用Insert函数以合并指数相同的项
}
}
return hf;
}//MultiplyPolyn
void DevicePolyn(Polyn pa,Polyn pb){//求解并建立多项式a*b，返回其头指针
Polyn hf,pf,af,temp1,temp2,q;
Polyn qa=pa-next;
Polyn qb=pb-next;
hf=(Polyn)malloc(sizeof(struct Polynomial));//建立头结点,存储商
hf-next=NULL;
pf=(Polyn)malloc(sizeof(struct Polynomial));//建立头结点，存储余数
pf-next=NULL;
temp1=(Polyn)malloc(sizeof(struct Polynomial));
temp1-next=NULL;
temp2=(Polyn)malloc(sizeof(struct Polynomial));
temp2-next=NULL;
temp1=AddPolyn(temp1,pa);
while(qa!=NULLqa-expn=qb-expn){
temp2-next=(Polyn)malloc(sizeof(struct Polynomial));
temp2-next-coef=(qa-coef)/(qb-coef);
temp2-next-expn=(qa-expn)-(qb-expn);
Insert(temp2-next,hf);
pa=SubtractPolyn(pa,MultiplyPolyn(pb,temp2));
qa=pa-next;
temp2-next=NULL;
}
pf=SubtractPolyn(temp1,MultiplyPolyn(hf,pb));
pb=temp1;
printf("商是：");
PrintPolyn(hf);
printf("余数是：");
PrintPolyn(pf);
}//DevicePolyn
int main(){
int m,n,flag=0;
float x;
Polyn pa=0,pb=0,pc,pd,pe,pf;//定义各式的头指针，pa与pb在使用前付初值NULL
printf("请输入a的项数:");
scanf("%d",m);
pa=CreatePolyn(pa,m);//建立多项式a
printf("请输入b的项数:");
scanf("%d",n);
pb=CreatePolyn(pb,n);//建立多项式a
//输出菜单
printf("**********************************************\n");
printf("操作提示：\n\t1.输出多项式a和b\n\t2.建立多项式a+b\n\t3.建立多项式a-b\n");
printf("\t4.计算多项式a在x处的值\n\t5.求多项式a的导函数\n\t6.建立多项式a*b\n");
printf("\t7.建立多项式a/b\n\t8.退出\n**********************************************\n");
for(;;flag=0){
printf("执行操作");
scanf("%d",flag);
if(flag==1){
printf("多项式a：");PrintPolyn(pa);
printf("多项式b：");PrintPolyn(pb);continue;
}
if(flag==2){
pc=AddPolyn(pa,pb);
printf("多项式a+b：");PrintPolyn(pc);
DestroyPolyn(pc);continue;
}
if(flag==3){
pd=SubtractPolyn(pa,pb);
printf("多项式a-b：");PrintPolyn(pd);
DestroyPolyn(pd);continue;
}
if(flag==4){
printf("输入x的值：x=");
scanf("%f",x);
printf("多项式a的值%g\n",ValuePolyn(pa,x));continue;
}
if(flag==5){
pe=Derivative(pa);
printf("多项式a的导函数：");PrintPolyn(pe);
DestroyPolyn(pe);continue;
}
if(flag==6){
pf=MultiplyPolyn(pa,pb);
printf("多项式a*b：");PrintPolyn(pf);
DestroyPolyn(pf);continue;
}
if(flag==7){
DevicePolyn(pa,pb);
continue;
}
if(flag==8) break;
if(flag1||flag8) printf("Error!!!\n");continue;
}//for
DestroyPolyn(pa);
DestroyPolyn(pb);
return 0;
}
public class Test {
public static void main(String[] args) {
try{
LinkList list1 = new LinkList();
LinkList list2 = new LinkList();
LinkList list3 = null;
list1.addAt(0, new Item(1, 5));
list1.addAt(1, new Item(-1.5, 3));
list1.addAt(2, new Item(1, 1));
list2.addAt(0, new Item(0.5, 5));
list2.addAt(1, new Item(0.5, 4));
list2.addAt(2, new Item(1.5, 3));
list2.addAt(3, new Item(3, 0));
list3 = mergeLinkList(list1, list2);
System.out.println("一元多项式的相加过程：");
list1.listAll();
System.out.println(" + ");
list2.listAll();
System.out.println(" = ");
list3.listAll();
}
catch(Exception e){
e.printStackTrace();
}
}
/**
* 一元多项式的一般项类
*/
class Item{
private double coef; //一元多项式的一般项的系数
private int exp; //一元多项式的一般项的指数
public Item(){
this.coef = 0.0;
this.exp = 0;
}
public Item(double coef, int exp){
this.coef = coef;
this.exp = exp;
}
public double getCoef(){
return this.coef;
}
public void setCoef(double coef){
this.coef = coef;
}
public int getExp(){
return this.exp;
}
public void setExp(int exp){
this.exp = exp;
}
}
/**
* 链表结点类
*/
class Node{
private Item data;
private Node next; //链表结点的指针域，指向直接后继结点
public Node(){
data = null;
next = null;
}
public Node(Item data, Node next){
this.data = data;
this.next = next;
}
public Item getData(){
return this.data;
}
public void setData(Item data){
this.data = data;
}
public Node getNext(){
return this.next;
}
public void setNext(Node next){
this.next = next;
}
}
/**
* 链表类
*/
class LinkList{
private Node head = null; //头结点指针
private int size = 0;
public LinkList(){
head = new Node();
size = 0;
}
//在i位置插入元素elem
public boolean addAt(int i, Item elem) {
if(i 0 || i size){
return false;
}
Node pre,curr;
int pos;
for(pre=head; i0 pre.getNext()!=null; i--,pre=pre.getNext());
curr = new Node(elem, pre.getNext());
pre.setNext(curr);
size++;
return true;
}
//删除i位置的元素
public boolean removeAt(int i) {
if(i 0 || i = size){
return false;
}
Node pre,curr;
for(pre=head; i0 pre.getNext()!=null; i--,pre=pre.getNext());
curr = pre.getNext();
pre.setNext(curr.getNext());
size--;
return true;
}
java是一种可以撰写跨平台应用软件的面向对象的程序设计语言。Java 技术具有卓越的通用性、高效性、平台移植性和安全性，广泛应用于PC、数据中心、游戏控制台、科学超级计算机、移动电话和互联网，同时拥有全球最大的开发者专业社群。
矩阵规模如何?
如果矩阵比较小 (~10), 可以直接按照定义来计算, P[x] = det( x*I - A); 其中det是一个矩阵的行列式; 可以按照定义直接迭代求;
如果矩阵比较大(100), 可以先求特征值, 然后构造矩阵特征多项式 P[x] = (x-x1)*(x-x2)... (x-xn), 其中xi为矩阵的第i个特征值.
