多項式合并

思路

• 多項式合并

  P1 = 5 + 2x + 8x ^8 +3x^16

  P2 = 6x + 16x^6 - 8x^8

  P = P1 + P2 = 5 + 8x + 16x^6 + 3x^16

• 使用帶頭結點的單向不循環鏈表

• 每個節點分為三個部分，系數項，指數項，指針域

• 結構體表示為

  struct node_st {int exponent;int coefficient;struct node_st *next; };

• 定義兩個指針p,q,分別指向多項式P1，P2第一個有效節點

• 在定義一個指針r,保存合并結果，p的前驅指向不確定，r表示p的前驅，r可以指向p,也可以指向q

• 比較p指向節點的指針項與q指向節點的指針項

  • p->exponent == q->exponent

    指數項不變，系數項相加

    • 若系數之和為零

    p = p->next;
    q = q->next;

    • 若系數之和不為零

      r->next = p;
      r = p;

      p = p->next;
      q = q->next;

  • p->exponent > q->exponent

    r->next = q;
    r = q;
    q = q->next;

  • p->exponent < q->exponent

    r->next = p;

    r= p;

    p = p->next;

代碼

main.c(負責測試)

#include<stdio.h> #include<stdlib.h> #include "polynomial.h" int main() {//p1,p2表示多項式struct node_st *p1 = NULL, *p2 = NULL;//數組中第一個元素為系數，第二個元素為指數int arr1[][2] = { {5,0},{3,16},{8,8},{2,1} };int arr2[][2] = { {16,6},{-8,8},{6,1} };p1 = poly_create(arr1,4);if (p1 == NULL){return -1;}p2 = poly_create(arr2,3);if (p2 == NULL){return -1;}poly_show(p1);poly_show(p2);poly_union(p1, p2);poly_show(p1);poly_destroy(p1);poly_destroy(p2);return 0; }

polynomial.c(負責函數定義)

#include<stdio.h> #include<stdlib.h> #include "polynomial.h"struct node_st* poly_create(int arr[][2],int row) {struct node_st *ps = NULL,*prenode = NULL,*curnode = NULL;struct node_st *newnode = NULL;int i = 0;//生成頭結點ps = (struct node_st*)malloc(sizeof(struct node_st));if (ps == NULL){return NULL;}ps->next = NULL;for (i = 0; i < row; i++){prenode = ps;curnode = ps->next;//按照指數從小到大的順序插入有效節點while ((curnode != NULL) && (curnode->exponent < arr[i][1])){prenode = curnode;curnode = curnode->next; }//生成新節點newnode = (struct node_st*)malloc(sizeof(struct node_st));if (newnode == NULL){return NULL;}newnode->coeffitient = arr[i][0];newnode->exponent = arr[i][1];newnode->next = prenode->next;prenode->next = newnode;}return ps; }void poly_show(struct node_st* ps) {struct node_st *p = ps->next;printf("%3s\t%3s\n", "系數", "指數");while (p){printf("%3d\t%3d\n", p->coeffitient, p->exponent);p = p->next; } }//多項式合并,p2向p1上合并,p1保存合并后的結果 void poly_union(struct node_st *p1, struct node_st *p2) {struct node_st *p = p1->next;struct node_st *q = p2->next;struct node_st *r = p1,*temp=NULL;while (p&&q){if (p->exponent > q->exponent){temp = (struct node_st*)malloc(sizeof(struct node_st));if (temp == NULL){return;}temp->coeffitient = q->coeffitient;temp->exponent = q->exponent;temp->next = q->next;r->next = temp;r = temp;q = q->next;}else if (p->exponent < q->exponent){r->next = p;r = p;p = p->next;}else if (p->exponent == q->exponent){p->coeffitient += q->coeffitient;if (p->coeffitient){r->next = p;r = p;}p = p->next;q = q->next;}}if (p == NULL){r->next = q;}if (q == NULL){r->next = p;}}void poly_destroy(struct node_st* ps) {struct node_st *cur = ps->next,*next = NULL;while (cur){next = cur->next;free(cur);cur = next; }free(ps);ps = NULL; }

polynomial.h(負責函數聲明)

#ifndef POLYNOMIAL_H__ #define POLYNOMIAL_H__ struct node_st {int coeffitient;int exponent;struct node_st *next; }; struct node_st* poly_create(int arr[][2], int row); void poly_show(struct node_st* ps); void poly_destroy(struct node_st* ps); void poly_union(struct node_st *p1, struct node_st *p2); #endif

運行結果

總結

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