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/********************** 输入文件格式有变化。 **************************/
/*
创建多项式A:
4
-1 4
8.75 3
0.5556666 2
1234.456 1
A(x) = -x^4 + 8.75x^3 + 0.555667x^2 + 1234.46x
创建多项式B:
1
6007.0012 0
B(x) = 6007
运算符 : +-*
C(x) = -x^4 + 8.75x^3 + 0.555667x^2 + 1234.46x + 6007
D(x) = -x^4 + 8.75x^3 + 0.555667x^2 + 1234.46x - 6007
E(x) = -6007x^4 + 52561.3x^3 + 3337.89x^2 + 7.41538e+06x
A(2) = 2525.13B(2) = 6007
C(2) = 8532.14
D(2) = -3481.87
E(2) = 1.51685e+07
请按任意键继续. . .
*/
#include <iostream>
#include <cmath>
using namespace std;
#define EPS 1E-6
typedef struct item {
double coefficient;
int power;
struct item *next;
} *POLYNOMIAL,*pItem;
POLYNOMIAL Create() { // 创建多项式
pItem head,p;
double coe;
int pwr,iterms,i;
head = p = new item;
cin >> iterms; // 读入多项式的项数
for(i = 0; i < iterms; ++i) {
cin >> coe >> pwr;
p->next = new item;
p->next->coefficient = coe;
p->next->power = pwr;
p = p->next;
}
p->next = NULL;
return head;
}
void Sort(POLYNOMIAL head) { // 按幂次降排序
pItem pt,q,p = head;
while(p->next) {
q = p->next;
while(q->next) {
if(p->next->power < q->next->power) {
pt = p->next;
p->next = q->next;
q->next = p->next->next;
p->next->next = pt;
}
else q = q->next;
}
p = p->next;
}
}
void Show(POLYNOMIAL head) { // 显示
POLYNOMIAL p = head->next;
int flag = 1;
if(p == NULL) return;
while(p) {
if(flag) {
if(fabs(p->coefficient) >= EPS) {
if(p->power == 0) cout << p->coefficient;
else if(p->power == 1) {
if(p->coefficient == 1.0) cout << "x ";
else if(p->coefficient == -1.0) cout << "-x ";
else cout << p->coefficient << "x ";
}
else if(p->coefficient == 1.0) cout << "x^" << p->power << " ";
else if(p->coefficient == -1.0) cout << "-x^" << p->power << " ";
else cout << p->coefficient << "x^" << p->power << " ";
flag = 0;
}
}
else if(p->coefficient > 0.0 && fabs(p->coefficient) >= EPS) {
if(p->power == 0) cout << "+ " << p->coefficient << " ";
else if(p->power == 1) {
if(p->coefficient == 1.0) cout << "+ x ";
else cout << "+ " << p->coefficient << "x ";
}
else if(p->coefficient == 1.0) cout << "+ x^" << p->power << " ";
else cout << "+ " << p->coefficient << "x^" << p->power << " ";
}
else if(p->coefficient < 0.0 && fabs(p->coefficient) >= EPS) {
if(p->power == 0) cout << "- " << -p->coefficient << " ";
else if(p->power == 1) {
if(p->coefficient == -1.0) cout << "- x ";
else cout << "- " << -p->coefficient << "x ";
}
else if(p->coefficient == -1.0) cout << "- " << "x^" << p->power << " ";
else cout << "- " << -p->coefficient << "x^" << p->power << " ";
}
p = p->next;
}
cout << endl;
}
double Power(double x,int n) {
double value = 1.0;
int i;
for(i = 0; i < n; ++i) value *= x;
return value;
}
double Value(POLYNOMIAL head,double x) { // 多项式求值
POLYNOMIAL p;
double value = 0.0;
for(p = head->next; p; p = p->next)
value += p->coefficient * Power(x,p->power);
return value;
}
POLYNOMIAL Copy(POLYNOMIAL A) {
POLYNOMIAL head,t,p;
head = t = new item;
for(p = A->next; p; p = p->next) {
t->next = new item;
t->next->coefficient = p->coefficient;
t->next->power = p->power;
t = t->next;
}
t->next = NULL;
return head;
}
POLYNOMIAL Additive(POLYNOMIAL A, POLYNOMIAL B) { // 多项式加
POLYNOMIAL head,p,q,t;
head = Copy(A);
for(p = B; p->next; p = p->next) {
q = head;
while(q->next) {
if(p->next->power == q->next->power) {
q->next->coefficient += p->next->coefficient;
if(fabs(q->next->coefficient) <= EPS) {
t = q->next;
q->next = t->next;
free(t);
}
break;
}
q = q->next;
}
if(q->next == NULL) {
q->next = new item;
q->next->coefficient = p->next->coefficient;
q->next->power = p->next->power;
q->next->next = NULL;
}
}
Sort(head);
return head;
}
POLYNOMIAL Subtract(POLYNOMIAL A, POLYNOMIAL B) { // 多项式减
POLYNOMIAL head,p,q,t;
head = Copy(A);
for(p = B; p->next; p = p->next) {
q = head;
while(q->next) {
if(p->next->power == q->next->power) {
q->next->coefficient -= p->next->coefficient;
if(fabs(q->next->coefficient) <= EPS) {
t = q->next;
q->next = t->next;
free(t);
}
break;
}
q = q->next;
}
if(q->next == NULL) {
q->next = new item;
q->next->coefficient = -p->next->coefficient;
q->next->power = p->next->power;
q->next->next = NULL;
}
}
Sort(head);
return head;
}
POLYNOMIAL Multiplication(POLYNOMIAL A, POLYNOMIAL B) { // 多项式乘
POLYNOMIAL head,t,p,q;
head = t = new item;
for(p = A->next; p; p = p->next) { // 完成相乘过程
for(q = B->next; q; q = q->next) {
t->next = new item;
t->next->coefficient = p->coefficient * q->coefficient;
t->next->power = p->power + q->power;
t = t->next;
}
}
t->next = NULL;
Sort(head); // 排序
p = head;
while(p->next) { // 合并同类项
q = p->next;
while(q->next) {
if(p->next->power == q->next->power) {
p->next->coefficient += q->next->coefficient;
t = q->next;
q->next = t->next;
free(t);
}
else q = q->next;
}
p = p->next;
}
return head;
}
void FreeMemory(POLYNOMIAL head) {
POLYNOMIAL q,p = head;
while(p) {
q = p;
p = q->next;
delete q;
}
}
int main() {
char ops[3];
POLYNOMIAL A,B,C = NULL,D = NULL,E = NULL;
cout << "创建多项式A:\n";
A = Create();
Sort(A);
cout << "A(x) = ";Show(A);
cout << "创建多项式B:\n";
B = Create();
Sort(B);
cout << "B(x) = ";Show(B);
cout << "运算符 : ";
fflush(stdin);
gets(ops);
for(int i = 0; ops[i]; ++i) {
switch(ops[i]) {
case '+' : C = Additive(A,B);
cout << "C(x) = ";
Show(C);
break;
case '-' : D = Subtract(A,B);
cout << "D(x) = ";
Show(D);
break;
case '*' : E = Multiplication(A,B);
cout << "E(x) = ";
Show(E);
break;
default : cout << "不能识别运算符 : " << ops[i] << endl;
}
}
cout << "A(2) = " << Value(A,2.0) << endl;
cout << "B(2) = " << Value(B,2.0) << endl;
if(C) cout << "C(2) = " << Value(C,2.0) << endl;
if(D) cout << "D(2) = " << Value(D,2.0) << endl;
if(E) cout << "E(2) = " << Value(E,2.0) << endl;
FreeMemory(A);
FreeMemory(B);
FreeMemory(C);
FreeMemory(D);
FreeMemory(E);
return 0;
}
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这个题目已经很清楚了，基本没有算法的问题了
注意一下最后面提到的输出格式就ok了，比如判定下数字1，还有有效长度截取
程序逻辑本身就是两重循环，遍历所有输入后，做一次数据归并即可
注意一下最后面提到的输出格式就ok了，比如判定下数字1，还有有效长度截取
程序逻辑本身就是两重循环，遍历所有输入后，做一次数据归并即可
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