c語言數(shù)據(jù)結(jié)構(gòu)實(shí)現(xiàn)-一元多項(xiàng)式的基本運(yùn)算

c語言數(shù)據(jù)結(jié)構(gòu)實(shí)現(xiàn)——一元多項(xiàng)式的基本運(yùn)算在C語言中，一元多項(xiàng)式的表示與運(yùn)算是常見的數(shù)據(jù)結(jié)構(gòu)操作之一。一元多項(xiàng)式由一系列具有相同變量的單項(xiàng)式組成，每個(gè)單項(xiàng)式由系數(shù)和指數(shù)組成。本文將介紹如何使用C語言實(shí)現(xiàn)一元多項(xiàng)式的基本運(yùn)算，包括多項(xiàng)式的創(chuàng)建、求和、差、乘積等操作。首先，我們需要定義一個(gè)結(jié)構(gòu)體來表示單項(xiàng)式。每個(gè)單項(xiàng)式由一個(gè)系數(shù)和一個(gè)指數(shù)組成，我們可以將其定義如下：```cstructterm{floatcoefficient;//系數(shù)intexponent;//指數(shù)};typedefstructtermTerm;```接下來，我們可以定義一個(gè)結(jié)構(gòu)體來表示一元多項(xiàng)式。一元多項(xiàng)式由一系列單項(xiàng)式組成，可以使用一個(gè)動(dòng)態(tài)數(shù)組來存儲(chǔ)這些單項(xiàng)式。```cstructpolynomial{Term*terms;//單項(xiàng)式數(shù)組intnum_terms;//單項(xiàng)式數(shù)量};typedefstructpolynomialPolynomial;```現(xiàn)在，我們可以開始實(shí)現(xiàn)一元多項(xiàng)式的基本運(yùn)算了。1.創(chuàng)建一元多項(xiàng)式要?jiǎng)?chuàng)建一元多項(xiàng)式，我們需要輸入每個(gè)單項(xiàng)式的系數(shù)和指數(shù)。我們可以使用動(dòng)態(tài)內(nèi)存分配來創(chuàng)建一個(gè)適應(yīng)輸入的單項(xiàng)式數(shù)組。```cPolynomialcreate_polynomial(){Polynomialpoly;printf("請輸入多項(xiàng)式的項(xiàng)數(shù)：");scanf("%d",&poly.num_terms);poly.terms=(Term*)malloc(poly.num_terms*sizeof(Term));for(inti=0;i<poly.num_terms;i++){printf("請輸入第%d個(gè)單項(xiàng)式的系數(shù)和指數(shù)：",i+1);scanf("%f%d",&poly.terms[i].coefficient,&poly.terms[i].exponent);}returnpoly;}```2.求兩個(gè)一元多項(xiàng)式的和兩個(gè)一元多項(xiàng)式的和等于對應(yīng)指數(shù)相同的單項(xiàng)式系數(shù)相加的結(jié)果。我們可以實(shí)現(xiàn)一個(gè)函數(shù)來計(jì)算兩個(gè)一元多項(xiàng)式的和，并返回一個(gè)新的一元多項(xiàng)式。```cPolynomialadd_polynomials(Polynomialpoly1,Polynomialpoly2){Polynomialsum;inti=0,j=0,k=0;sum.num_terms=poly1.num_terms+poly2.num_terms;sum.terms=(Term*)malloc(sum.num_terms*sizeof(Term));while(i<poly1.num_terms&&j<poly2.num_terms){if(poly1.terms[i].exponent>poly2.terms[j].exponent){sum.terms[k]=poly1.terms[i];i++;}elseif(poly1.terms[i].exponent<poly2.terms[j].exponent){sum.terms[k]=poly2.terms[j];j++;}else{sum.terms[k].coefficient=poly1.terms[i].coefficient+poly2.terms[j].coefficient;sum.terms[k].exponent=poly1.terms[i].exponent;i++;j++;}k++;}while(i<poly1.num_terms){sum.terms[k]=poly1.terms[i];i++;k++;}while(j<poly2.num_terms){sum.terms[k]=poly2.terms[j];j++;k++;}returnsum;}```3.求兩個(gè)一元多項(xiàng)式的差和求和類似，兩個(gè)一元多項(xiàng)式的差等于對應(yīng)指數(shù)相同的單項(xiàng)式系數(shù)相減的結(jié)果。我們可以實(shí)現(xiàn)一個(gè)函數(shù)來計(jì)算兩個(gè)一元多項(xiàng)式的差，并返回一個(gè)新的一元多項(xiàng)式。```cPolynomialsubtract_polynomials(Polynomialpoly1,Polynomialpoly2){Polynomialdiff;inti=0,j=0,k=0;diff.num_terms=poly1.num_terms+poly2.num_terms;diff.terms=(Term*)malloc(diff.num_terms*sizeof(Term));while(i<poly1.num_terms&&j<poly2.num_terms){if(poly1.terms[i].exponent>poly2.terms[j].exponent){diff.terms[k]=poly1.terms[i];i++;}elseif(poly1.terms[i].exponent<poly2.terms[j].exponent){diff.terms[k].coefficient=-poly2.terms[j].coefficient;diff.terms[k].exponent=poly2.terms[j].exponent;j++;}else{diff.terms[k].coefficient=poly1.terms[i].coefficient-poly2.terms[j].coefficient;diff.terms[k].exponent=poly1.terms[i].exponent;i++;j++;}k++;}while(i<poly1.num_terms){diff.terms[k]=poly1.terms[i];i++;k++;}while(j<poly2.num_terms){diff.terms[k].coefficient=-poly2.terms[j].coefficient;diff.terms[k].exponent=poly2.terms[j].exponent;j++;k++;}returndiff;}```4.求兩個(gè)一元多項(xiàng)式的乘積兩個(gè)一元多項(xiàng)式的乘積等于對應(yīng)指數(shù)相加的單項(xiàng)式系數(shù)相乘的結(jié)果。我們可以實(shí)現(xiàn)一個(gè)函數(shù)來計(jì)算兩個(gè)一元多項(xiàng)式的乘積，并返回一個(gè)新的一元多項(xiàng)式。```cPolynomialmultiply_polynomials(Polynomialpoly1,Polynomialpoly2){Polynomialproduct;inti,j,k;product.num_terms=poly1.num_terms*poly2.num_terms;product.terms=(Term*)malloc(product.num_terms*sizeof(Term));k=0;for(i=0;i<poly1.num_terms;i++){for(j=0;j<poly2.num_terms;j++){product.terms[k].coefficient=poly1.terms[i].coefficient*poly2.terms[j].coefficient;product.terms[k].exponent=