265 lines
5.6 KiB
C++
265 lines
5.6 KiB
C++
#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include <string.h>
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#include <ctype.h>
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typedef struct node {
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int coef;
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int exp;
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int root;
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struct node* rlink;
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struct node* llink;
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} node;
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node *head, *tail, *current, *prev, *temp ,*head_root , *current_root , *tail_root;
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void init_f() {
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head = (node *)malloc(sizeof(node));
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tail = (node *)malloc(sizeof(node));
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head->rlink = tail;
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tail->llink = head;
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head_root = (node *)malloc(sizeof(node));
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tail_root = (node *)malloc(sizeof(node));
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head_root->rlink = tail_root;
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tail_root->llink = head_root;
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}
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void read_poly(char str[] ){
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int argCount ;
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while (1) {
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node* newNode = (node*)malloc(sizeof(node));
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argCount = sscanf(str, "%dx^%d%s", &newNode->coef, &newNode->exp, str);
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if (argCount >= 2) { // 成功讀取係數和指數
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newNode->llink = tail->llink;
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newNode->rlink = tail;
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tail->llink->rlink = newNode;
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tail->llink = newNode;
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if (argCount == 2) {
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break ;
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}
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} else {
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if(!isdigit(newNode->coef)){
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newNode->exp = 0;
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newNode->llink = tail->llink;
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newNode->rlink = tail;
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tail->llink->rlink = newNode;
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tail->llink = newNode;
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break ;
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}else{
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// printf("newNode->coef = %d\n",newNode->coef);
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// printf("isdigit(newNode->coef) = %d",isdigit(newNode->coef));
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free(newNode);
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break ;
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}
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}
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}
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}
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void compact(char str[]){ /* 移除str當中的空白，使變得緊實 */
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int i, j;
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for (i = j = 0; str[i]; i++, j++) {
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for (; str[i]==' '; i++);
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str[j] = str[i];
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}
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str[j] = '\0';
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printf("\n移除空白後的字串：%s",str);
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}
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void clear_node(){
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// 釋放記憶體
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current = head->rlink;
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while (current != tail) {
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temp = current;
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current = current->rlink;
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free(temp);
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}
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current_root = head_root->rlink;
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while (current_root != tail_root) {
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temp = current_root;
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current_root = current_root->rlink;
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free(temp);
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}
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free(head);
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free(tail);
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free(head_root);
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free(tail_root);
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}
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void show( int n, int mode){
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int i;
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if(mode == 0){
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printf("\n方程式p(x)= ");
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current = head->rlink;
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while (current != tail) {
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if(abs(current->coef)>1){
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printf("%s%d", current->coef > 1? "":"\b",current->coef);
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}else if(current->coef == -1){
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printf("%s", current->exp == 0? "\b-1":"\b-");
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}
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switch(current->exp){
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case 0:
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if(current->coef == 1 ) printf("1+");
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else printf("+");
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break;
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case 1:
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printf("x+");
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break;
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default:
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printf("x^%d+",current->exp);
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}
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current = current->rlink;
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}
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printf("\b ");
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}else { /* mode==1，顯示所得解 */
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current_root = head_root->rlink;
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while(current_root != tail_root){
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printf("%d ",current_root->root);
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current_root = current_root->rlink;
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}
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}
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}
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int findRoot() /* 找根，所得解存入q[]，回傳根的個數 */
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{
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current_root = head_root->rlink;
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int r, c = 0, i, j, k, sum;
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int sign[2] = {1,-1};
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current = tail->llink;
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r = abs(current->coef); /* 取出最低階項之係數 */
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if (current->exp != 0) { /* 最低階項的指數 >= 1，則0為可能解 */
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if ((i = current->exp) > 0) {
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node* newNode = (node*)malloc(sizeof(node));
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newNode->root = 0; /* 最低階項的指數設為i */
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newNode->llink = tail_root->llink;
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newNode->rlink = tail_root;
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tail_root->llink->rlink = newNode;
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tail_root->llink = newNode;
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c = 1;
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}
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current = head->rlink;
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while(current!=tail){
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current->exp -= i; /* 所有項次的指數減去i */
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current = current->rlink;
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}
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}
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// r = abs(p[2*p[0]]); /* 取出最低階項之係數 */
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for (i = 1; i <= r; i++) { /* 考慮能整除r的因數i，須注意正負號 */
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if (r%i != 0) continue; /* 不能整除r的i將略過，繼續考慮下一個i */
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for (j = 0; j < 2; j++) { /* j為0，代表考慮+i的情境；j為1，代表考慮-i的情況 */
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for (sum = 0, current = head->rlink ; current!= tail ; current = current->rlink) /* 計算每一項的結果值(係數*x^指數)並累加到sum之中 */
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sum += current->coef *(int)(pow(sign[j]*i,current->exp));
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if (sum == 0) {
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node* newNode = (node*)malloc(sizeof(node));
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newNode->root = sign[j]*i; /* bingo! 發現合乎條件的整數根，將其寫入q陣列 */
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newNode->llink = tail_root->llink;
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newNode->rlink = tail_root;
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tail_root->llink->rlink = newNode;
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tail_root->llink = newNode;
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c = 1;
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}
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}
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}
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return c;
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}
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void sort(){
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//若沒有資料或只有一筆資料
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if (head->rlink == tail || head->rlink->rlink == tail) {
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return;
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}
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int flag = 1;
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while(flag){
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flag = 0;
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current = head->rlink;
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while(current->rlink != tail){
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temp = current->rlink;
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if(current->exp < temp->exp ){
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temp->llink = current->llink;
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current->rlink = temp->rlink;
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temp->rlink->llink = current;
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temp->rlink = current;
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current->llink->rlink = temp;
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current->llink = temp;
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flag = 1;
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}
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else{
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current = current->rlink;
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}
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}
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}
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}
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int main() {
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char str[100];
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int poly_num ,c , high;
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init_f();
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printf("\n*** 解多項式之整數根 ***\n\n輸入多項式 ==> ");
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if (fgets(str, sizeof(str), stdin) == NULL) {
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printf("輸入錯誤！\n");
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return 1;
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}
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compact(str);
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read_poly(str);
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sort();
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current = head->rlink;
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high= current->exp;
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show(c,0);
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c = findRoot();
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if (c > 0) {
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printf("\n\n解得整數根為：");
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show(c,1);
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}
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else
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printf("\n\n整數根不存在\n");
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clear_node();
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return 0;
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}
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