多項式的加減乘
阿新 • • 發佈：2019-01-09
這是我學資料結構寫的第一個比較"大型"的程式，唉，還是有不足之處啊。。。
# include <stdio.h> # include <iostream.h> # include <stdlib.h> # include <malloc.h> # define OK 1 # define ERROR 0 # define OVERFLOW -1 typedef struct Polynomial { float coef; int expn; struct Polynomial *next; }Polynomial,*LinkPolyn; void Create_Polyn(LinkPolyn &L) { int i,n; LinkPolyn p,s; L = (LinkPolyn) malloc (sizeof (Polynomial)); if (!L) exit(OVERFLOW); L->next = NULL; p = L; cout<<" 請輸入您要建立多項式的項數:"; cin>>n; for (i=0; i<n; i++) { s = (LinkPolyn) malloc (sizeof (Polynomial)); p->next = s; cout<<" 請輸入第"<<i+1<<"項的係數:"; cin>>s->coef; cout<<" 請輸入第"<<i+1<<"項的指數:"; cin>>s->expn; p = s; } p->next = NULL; } void Display(LinkPolyn L) { LinkPolyn p; if (!L->next ) cout<<" 多項式的項數為0!無法顯示"<<endl; p = L->next ; while (p) { if (p->coef == 0.0) cout<<""; else if (p->expn == 0 ) cout<<p->coef ; else if (p->coef == 1 && p->expn == 1) cout<<"X"; else if (p->coef == 1 && p->expn != 1) cout<<"X^"<<p->expn; else if (p->coef == -1 && p->expn == 1) cout<<"-X"; else if (p->coef != 1 && p->expn == 1) cout<<p->coef<<"X"; else if (p->coef == -1 && p->expn != 1) cout<<"-X^"<<p->expn ; else cout<<p->coef <<"X^"<<p->expn ; if (p->next!=NULL && p->coef !=0 && p->next->coef >=0) cout<<"+"; p = p->next ; } cout<<endl; } void SortPolyn(LinkPolyn &L) { LinkPolyn p,q; int temp; float tmp; if (!L->next ) cout<<" 多項式的項數為0,無法排序!"<<endl; for(p=L->next;p; p=p->next ) for(q=L->next ;q; q=q->next) { if(p->expn < q->expn ) { temp = p->expn ; p->expn = q->expn ; q->expn = temp; tmp = p->coef ; p->coef = q->coef ; q->coef = tmp; } else if (p != q && p->expn == q->expn) { p->coef +=q->coef ; q->coef = 0; q->expn = 0; } } } void Diff_Polyn(LinkPolyn &L) { LinkPolyn p; if (!L->next ) cout<<" 多項式的項數為0,無法求導!"<<endl; p = L->next ; while (p) { p->coef *= p->expn ; p->expn -=1; p = p->next ; } } void Int_Polyn(LinkPolyn &L) { LinkPolyn p; if (!L->next ) cout<<" 多項式的項數為0,無法求積分!"<<endl; p = L->next ; while (p) { p->coef = p->coef/(p->expn+1); p->expn +=1; p = p->next ; } } int cmp (int a, int b) { if (a>b) return 1; else if (a == b) return 0; return -1; } int Add_Polyn(LinkPolyn &PA, LinkPolyn &PB) { LinkPolyn qc,qa,qb,temp; float sum; qc = PA; qa = PA->next ; qb = PB->next ; while (qa && qb) { switch(cmp(qa->expn ,qb->expn )) { case -1: qc->next = qa; qc = qa; qa = qa->next; break; case 0: sum = qa->coef + qb->coef ; if(sum !=0.0) { qa->coef = sum; qc->next = qa; qc = qa; qa = qa->next; } else { temp = qa; qa = qa->next ; free(temp); } temp = qb; qb = qb->next ; free(temp); break; case 1: qc->next = qb; qc = qb; qb = qb->next; break; } } while(qa) { qc->next = qa; qc = qa; qa = qa->next; } while(qb) { qc->next = qb; qc = qb; qb = qb->next; } free(qb); return OK; } int Sub_Polyn(LinkPolyn &PA, LinkPolyn &PB) { LinkPolyn qc,qa,qb,temp; float sum; qc = PA; qa = PA->next ; qb = PB->next ; while (qa && qb) { switch(cmp(qa->expn ,qb->expn )) { case -1: qc->next = qa; qc = qa; qa = qa->next; break; case 0: sum = qa->coef - qb->coef ; if(sum !=0.0) { qa->coef = sum; qc->next = qa; qc = qa; qa = qa->next; } else { temp = qa; qa = qa->next ; free(temp); } temp = qb; qb = qb->next ; free(temp); break; case 1: qb->coef =-qb->coef ; qc->next = qb; qc = qb; qb = qb->next; break; } } while(qa) { qc->next = qa; qc = qa; qa = qa->next; } while(qb) { qb->coef =-qb->coef ; qc->next = qb; qc = qb; qb = qb->next; } free(qb); return OK; } int Mul_Polyn(LinkPolyn pa,LinkPolyn pb,LinkPolyn &pc) { LinkPolyn qa,qb,qc,s; pc = (LinkPolyn) malloc (sizeof (Polynomial)); pc->next = NULL; qc = pc; for(qa=pa->next;qa;qa=qa->next) { for(qb=pb->next;qb;qb=qb->next) { s = (LinkPolyn) malloc (sizeof (Polynomial)); qc->next = s; s->coef=qa->coef*qb->coef; s->expn=qa->expn+qb->expn; qc = s; } } qc->next = NULL; SortPolyn(pc); return OK; } int main (void) { char i; LinkPolyn L; LinkPolyn PA,PB,PC; cout<<endl; cout<<" ********************************************************"<<endl; cout<<" | 歡迎使用本系統! |"<<endl; cout<<" | 製作人:風塵三俠 |"<<endl; cout<<" | 1:建立一個多項式 2:對一個多項式求導 |"<<endl; cout<<" | 3:對一個多項式求積分 4:兩個多項式相加 |"<<endl; cout<<" | 5:兩個多項式相減 6:兩個多項式相乘 |"<<endl; cout<<" | 7:幫助 8:退出 |"<<endl; cout<<" ********************************************************"<<endl; cout<<endl; do { cout<<" 請選擇您要執行的操作:"; cin>>i; switch (i) { case '1': Create_Polyn(L); SortPolyn(L); cout<<" 您建立的多項式是: F(X) = "; Display(L); break; case '2': cout<<" 對一個多項式求導前請先建立一個多項式!"<<endl; Create_Polyn(L); SortPolyn(L); cout<<" 您建立的多項式是: F(X) = "; Display(L); Diff_Polyn(L); cout<<" 求導後的多項式是: F'(X) = "; Display(L); break; case '3': cout<<" 對一個多項式求積分前請先建立一個多項式!"<<endl; Create_Polyn(L); SortPolyn(L); cout<<" 您建立的多項式是: F(X) = "; Display(L); Int_Polyn(L); cout<<" 積分後的多項式是: F'(X) = "; Display(L); break; case '4': cout<<" 請先建立兩個多項式!"<<endl; cout<<" 建立第一個多項式!"<<endl; Create_Polyn(PA); SortPolyn(PA); cout<<" 您建立的第一個多項式是: F(X) = "; Display(PA); cout<<" 建立第二個多項式!"<<endl; Create_Polyn(PB); SortPolyn(PB); cout<<" 您建立的第二個多項式是: G(X) = "; Display(PB); cout<<" 兩個多項式相加後：F(X) + G(X) = "; Add_Polyn(PA, PB); Display(PA); break; case '5': cout<<" 請先建立兩個多項式!"<<endl; cout<<" 建立第一個多項式!"<<endl; Create_Polyn(PA); SortPolyn(PA); cout<<" 您建立的第一個多項式是: F(X) = "; Display(PA); cout<<" 建立第二個多項式!"<<endl; Create_Polyn(PB); SortPolyn(PB); cout<<" 您建立的第二個多項式是: G(X) = "; Display(PB); cout<<" 兩個多項式相減後：F(X) - G(X) = "; Sub_Polyn(PA, PB); Display(PA); break; case '6': cout<<" 請先建立兩個多項式!"<<endl; cout<<" 建立第一個多項式!"<<endl; Create_Polyn(PA); SortPolyn(PA); cout<<" 您建立的第一個多項式是: F(X) = "; Display(PA); cout<<" 建立第二個多項式!"<<endl; Create_Polyn(PB); SortPolyn(PB); cout<<" 您建立的第二個多項式是: G(X) = "; Display(PB); cout<<" 兩個多項式相乘後：F(X) * G(X) = "; Mul_Polyn(PA, PB,PC); Display(PC); break; case '7': cout<<" 建立多項式! "<<endl; cout<<" 先輸入多項式的項數，要輸入自然數!"<<endl; cout<<" 可以輸入重複的項，先輸入係數，再輸入指數!"<<endl; cout<<" 係數可以是任意的數字，指數要輸入自然數!"<<endl; break; case '8': cout<<" 謝謝使用,再見!"<<endl; exit(OVERFLOW); break; default: { cout<<" 您的輸入有誤，請重新輸入!"<<endl; break; } } }while (i != 8); return 0; }