算法:

1、建立空表Lc

2、遍历La、Lb表(未到末尾):

(1)如果系数相同,系数相加

(2)如果系数不同:若La的系数小,把La加入Lc中;若Lb系数小,把Lb加入Lc中

3、有一个表已经遍历结束,把还有元素的表加入到Lc中

#include<iostream>
using namespace std;
#define MAXSIZE 100
#define OK 1
#define OVERFLOW -2

typedef struct{
	float coef;
	int expn;
}polyElem;
typedef struct{
	polyElem *elem;
	int length;
}SqList; 

//初始化
int InitList(SqList &L){
	L.elem=new polyElem[MAXSIZE];
	if(!L.elem) return OVERFLOW;
	L.length=0;
	return OK;
} 
//创建
void CreatList(SqList &L,int n){
	for(int i=0;i<n;i++){
		cin>>L.elem[i].coef>>L.elem[i].expn;
		L.length++;
	}
} 
//显示元素
void Show(SqList L){
	for(int i=0;i<L.length;i++){
		cout<<'('<<'('<<L.elem[i].coef<<','<<L.elem[i].expn<<')'<<')'<<' ';
	}
	cout<<endl;
} 

//稀疏多项式运算
void CalculatePoly(SqList La,SqList Lb,SqList &Lc){
	int La_len=La.length;
	int Lb_len=Lb.length;
	Lc.elem=new polyElem[La_len+Lb_len];
	Lc.length=0;
	
	polyElem *pa=La.elem;
	polyElem *pb=Lb.elem;
	polyElem *pc=Lc.elem;
	
	polyElem *pa_last=La.elem+La.length-1;
	polyElem *pb_last=Lb.elem+Lb.length-1;


	while(pa<=pa_last&&pb<=pb_last){      //La、Lb不为空,遍历La,Lb 
		if(pa->expn == pb->expn){//指数相同
		int coefSum=pa->coef+pb->coef; 
		if(coefSum!=0)
		{
			pc->expn=pa->expn;   //指数不变 
			pc->coef=coefSum;  //系数相加 
			pc++;
			Lc.length++;	
		}   
			pa++;
			pb++;
		}
		else{
			if(pa->expn<pb->expn){  //La的系数小 
				pc->expn=pa->expn;
				pc->coef=pa->coef;
				pa++;
				pc++;
				Lc.length++;
			}
			else{      //Lb的系数小 
				pc->expn=pb->expn;
				pc->coef=pb->coef;
				pb++;pc++;
				Lc.length++;
			}
		}
	}
	while(pa<=pa_last){      //La还有元素
		pc->coef=pa->coef;
		pc->expn=pa->expn;
		pc++;pa++;
		Lc.length++;
	} 
	while(pb<=pb_last){     //Lb还有元素
		pc->coef=pb->coef;
		pc->expn=pb->expn;
		pc++;pb++;
		Lc.length++;
	}

} 

int main(){
	SqList La,Lb,Lc;
	InitList(La);
	InitList(Lb);
	CreatList(La,4);
	CreatList(Lb,3);
	cout<<"La:";
	Show(La);
	cout<<"Lb:";
	Show(Lb);
	
	CalculatePoly(La,Lb,Lc);
	cout<<"Lc:";
	Show(Lc);

	return 1;
}

运行结果

y1=7+3x+9x^8+5x^{^{17}}

y2=8x+22x^7-9x^8

 

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