3.6 编写将两个多项式相加的函数。不要毁坏输入数据。用一个链表实现。
我的想法是 先将两个多项式按照exponent(次方)进行排序,相同次方的进行合并,再将这两个多项式进行相加。
多项式的结构体定义如下:
struct Node{ int coefficient; int exponent; Position next;};具体函数实现方法如下:
首先是排序算法:
/* 冒泡排序多项式,按照项的次数从小到大排序 */void MPSort( Position h , int size ){ Position p; for( int i = 0; i < size-1; i++ ) { p = h->next; while( p != NULL && p->next != NULL ) { if ( p->exponent > p->next->exponent ) { Swap2Position( h, p, p->next ); //交换两个结点 } else if ( p->exponent == p->next->exponent ) { Union2Position( p, p->next ); //合并两个结点 } else { p = p->next; //指针移到下一个结点 } } } return;} /* 交换两个相邻的结点 */void Swap2Position( Position h, Position p1, Position p2 ){ Position p0; p0 = FindPRevious( h, p1 ); p1->next = p2->next; p2->next = p1; p0->next = p2; return;} /* 合并两个次数相同的结点 */void Union2Position( Position p1, Position p2 ){ if ( p1->exponent == p2->exponent ) { p1->coefficient = p1->coefficient + p2->coefficient; p1->next = p2->next; free( p2 ); }}接着是多项式相加的算法 (按照次数升序排序的)/* 将两个以排好序(升序)的多项式相加 */Position Add2Polynomial( Position h1, Position h2 ){ int size; Position h; Position p1, p2; p1 = h1->next; p2 = h2->next; h = ( Position )malloc(sizeof(struct Node)); h->next = NULL; while ( p1 != NULL && p2 != NULL ) { if ( p1->exponent < p2->exponent ) { InsertPolynomial( h, p1->coefficient, p1->exponent ); //将p1指向的结点插入到新的多项式中 p1 = p1->next; size++; } else if ( p1->exponent > p2->exponent ) { InsertPolynomial( h, p2->coefficient, p2->exponent ); //将p2指向的结点插入到新的多项式中 p2 = p2->next; size++; } else { InsertPolynomial( h, p1->coefficient + p2->coefficient, p1->exponent ); //将两个结点的系数相加 然后插入到新的多项式中 p1 = p1->next; p2 = p2->next; size++; } } while ( p1 != NULL ) { InsertPolynomial( h, p1->coefficient, p1->exponent ); p1 = p1->next; size++; } while ( p2 != NULL ) { InsertPolynomial( h, p2->coefficient, p2->exponent ); p2 = p2->next; size++; } //排序 MPSort( h, size ); return h;}中间的插入算法:void InsertPolynomial( Position h, int coefficient, int exponent ){ Position tmpCell; tmpCell = ( Position )malloc(sizeof(struct Node)); tmpCell->coefficient = coefficient; tmpCell->exponent = exponent; tmpCell->next = h->next; h->next = tmpCell;}
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