多項式的表示與相加

• 一元多項式的表示
• 一元多項式的建立
• 一元多項式相加
• 一元多項式的打印
• 完整代碼

一元多項式的表示

typedef struct ploy {double coef; //系數部分int exp; //指數部分struct ploy* next; }ploy;

一元多項式的建立

輸入的格式是 1+2x^1+2x^2這樣的格式以#結束。

ploy* create_ploy() {ploy* head,*s,*p;head = (ploy*)malloc(sizeof(ploy));head->next = NULL;s = head;char ch;int flag = 0; //記錄的是除了數字與+之外輸入的字母個數int key = 2;//標記正負p = (ploy*)malloc(sizeof(ploy));while (~scanf_s("%c", &ch,1)) {if (ch == '#')break;if (ch == '+'||ch =='-') {if (flag == 1) //表明輸入的是7x這樣的情況s->exp = 1; //x指數尾1的情況p = (ploy*)malloc(sizeof(ploy)); //建立新節點flag = 0;if (ch == '+')key = 1;elsekey = 0;}if (isdigit(ch)) {if (flag == 0) {if(key)p->coef = ch - '0';else if(key ==0)p->coef = -(ch - '0');p->exp = 0; //默認指數是-1s->next = p;s = p;}else if (flag == 2) //指數不為0s->exp = ch - '0';}else if(ch!='+'&&ch!='-')flag++;//記得加上}s->next = NULL; //最后一個結點指向空return head; }

一元多項式相加

實質是：

• 指數不同是鏈表的合并
• 指數相同，系數相加；若為0，去掉該結點；若不為0，修改結點的系數域。

ploy* add(ploy* La, ploy* Lb) {ploy* pa, * pb, * pc,*q,*head;head = (ploy*)malloc(sizeof(ploy));head->next = NULL;pc = head;pa = La->next;pb = Lb->next;while (pa && pb) {if (pa->exp == pb->exp) { //指數相同pa->coef = pa->coef + pb->coef; //系數相加if ((int)pa->coef == 0) { //系數相加為0q = pa; //刪除pa指向的結點pa = pa->next;free(q);}else //系數相加不為0{pc->next = pa;pc = pa;pa = pa->next;}q = pb; //刪除pb所指的結點pb = pb->next;free(q);}else if (pa->exp < pb->exp) {pc->next = pa;pc = pa;pa = pa->next;}//將pa所指的結點合并，pa指向下一個結點else {pc->next = pb;pc = pb;pb = pb->next;}//將pb所指的結點合并，pb指向下一個結點}//那個鏈沒有處理完，就處理if (pa)pc->next = pa; else pc->next = pb;return head; }

一元多項式的打印

void show(ploy* head) {ploy* p = head->next;while (p->next) {if (p->coef > 0.0) { //分為正負打印if (p->exp == 0)printf("+%.2lf", p->coef);else if (p->exp == 1)printf("+%.2lfx", p->coef);elseprintf("+%.2lfx^%d", p->coef, p->exp);}else {if (p->exp == 0)printf("-%.2lf", p->coef);else if (p->exp == 1)printf("-%.2lfx+", p->coef);elseprintf("-%.2lfx^%d+", p->coef, p->exp);}p = p->next;}//最后一個if(p->coef>0.0)printf("+%.2lfx^%d\n", p->coef, p->exp);elseprintf("-%.2lfx^%d\n", p->coef, p->exp);}

完整代碼

#include<stdio.h> #include<malloc.h> #include<string.h> #include<ctype.h> typedef struct ploy {double coef; //系數部分int exp; //指數部分struct ploy* next; }ploy;ploy* create_ploy() {ploy* head,*s,*p;head = (ploy*)malloc(sizeof(ploy));head->next = NULL;s = head;char ch;int flag = 0; //記錄的是除了數字與+之外輸入的字母個數int key = 2;//標記正負p = (ploy*)malloc(sizeof(ploy));while (~scanf_s("%c", &ch,1)) {if (ch == '#')break;if (ch == '+'||ch =='-') {if (flag == 1) //表明輸入的是7x這樣的情況s->exp = 1; //x指數尾1的情況p = (ploy*)malloc(sizeof(ploy)); //建立新節點flag = 0;if (ch == '+')key = 1;elsekey = 0;}if (isdigit(ch)) {if (flag == 0) {if(key)p->coef = ch - '0';else if(key ==0)p->coef = -(ch - '0');p->exp = 0; //默認指數是-1s->next = p;s = p;}else if (flag == 2) //指數不為0s->exp = ch - '0';}else if(ch!='+'&&ch!='-')flag++;//記得加上}s->next = NULL; //最后一個結點指向空return head; }ploy* add(ploy* La, ploy* Lb) {ploy* pa, * pb, * pc,*q,*head;head = (ploy*)malloc(sizeof(ploy));head->next = NULL;pc = head;pa = La->next;pb = Lb->next;while (pa && pb) {if (pa->exp == pb->exp) { //指數相同pa->coef = pa->coef + pb->coef; //系數相加if ((int)pa->coef == 0) { //系數相加為0q = pa; //刪除pa指向的結點pa = pa->next;free(q);}else //系數相加不為0{pc->next = pa;pc = pa;pa = pa->next;}q = pb; //刪除pb所指的結點pb = pb->next;free(q);}else if (pa->exp < pb->exp) {pc->next = pa;pc = pa;pa = pa->next;}//將pa所指的結點合并，pa指向下一個結點else {pc->next = pb;pc = pb;pb = pb->next;}//將pb所指的結點合并，pb指向下一個結點}//那個鏈沒有處理完，就處理if (pa)pc->next = pa; else pc->next = pb;return head; }void show(ploy* head) {ploy* p = head->next;while (p->next) {if (p->coef > 0.0) { //分為正負打印if (p->exp == 0)printf("+%.2lf", p->coef);else if (p->exp == 1)printf("+%.2lfx", p->coef);elseprintf("+%.2lfx^%d", p->coef, p->exp);}else {if (p->exp == 0)printf("-%.2lf", p->coef);else if (p->exp == 1)printf("-%.2lfx+", p->coef);elseprintf("-%.2lfx^%d+", p->coef, p->exp);}p = p->next;}//最后一個if(p->coef>0.0)printf("+%.2lfx^%d\n", p->coef, p->exp);elseprintf("-%.2lfx^%d\n", p->coef, p->exp);}int main() {ploy* head,*head1,*head2;head1 = create_ploy();getchar();head2 = create_ploy();show(head1);show(head2);head = add(head1, head2);show(head);return 0; }

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