今年网络安全的一个小作业，简单用C++实现了下 有些粗糙 先放这儿吧 ^_^
算法描述 考完试再附上
ExEuclid简单实现/** 文件名称：myecu.cpp* 摘 要：Extend Euclid Algorithm* 作者：ld* 完成日期：25th June,2010*/#include "stdafx.h"#include #include #include #include #include using namespace std;typedef struct polyNode//多项式节点项{int coef;int power;}polyNode;void CreatePoly(vector&poly);//构造多项式void SortPolyByPower(vector&poly);//对多项式排序，按照降幂vector PolyAdd(vectorp1,vectorp2);//多项式加法vector PolySub(vectorp1,vectorp2);//多项式减法vector PolyMultiply(vectorp1,vectorp2);//多项式乘法vector PolyDiv(vector&p1,vectorp2);//多项式除法vector Eculid(vector&p1,vector&p2);//扩展欧几里得算法void SortPolyByPower(vector&poly)//OK{vector::iterator iter,tmpIter;iter = poly.begin();for (; iter != poly.end(); iter++)//按照幂数高低排序{tmpIter = iter + 1;int maxPower = (*iter).power;for (; tmpIter != poly.end(); tmpIter++){if ((*tmpIter).power > (*iter).power){iter_swap(iter,tmpIter);}}}}void CreatePoly(vector&poly)//OK{static int itemCount = 0;cout<<"Please input the itemCount of the poly:"<>itemCount; for (int t = 0; t < itemCount; t++){static polyNode tmpItem;cout<<"Please input the coef and power:"<>tmpItem.coef>>tmpItem.power;poly.push_back(tmpItem);}SortPolyByPower(poly);cout<<"原始多项式为："<::iterator iter;for ( iter = poly.begin();iter!= poly.end();iter++){cout<<"X^"<<(*iter).power<<"+";}cout< PolyAdd(vectorp1,vectorp2)//OK{vector tmpPolyAdd;vector::iterator iter1,iter2;iter1 = p1.begin();iter2 = p2.begin();if (p1.size() == 0){tmpPolyAdd.clear();tmpPolyAdd = p2;return tmpPolyAdd;}else if(p2.size() == 0){tmpPolyAdd.clear();tmpPolyAdd = p1;return tmpPolyAdd;}else{tmpPolyAdd.clear();for (; iter1 != p1.end() && iter2 != p2.end();){if ((*iter1).power > (*iter2).power){tmpPolyAdd.push_back(*iter1);iter1++;}else if ((*iter1).power == (*iter2).power){polyNode tmp;tmp.coef = ((*iter1).coef + (*iter2).coef)%2;tmp.power = (*iter1).power;if (tmp.coef != 0){tmpPolyAdd.push_back(tmp);}else;iter1++;iter2++;}else if ((*iter1).power < (*iter2).power){tmpPolyAdd.push_back(*iter2);iter2++;}}if (iter2 != p2.end()){for (;iter2 != p2.end();iter2++){tmpPolyAdd.push_back(*iter2);}SortPolyByPower(tmpPolyAdd);return tmpPolyAdd;}else if(iter1 != p1.end()){for (;iter1 != p1.end();iter1++){tmpPolyAdd.push_back(*iter1);}SortPolyByPower(tmpPolyAdd);return tmpPolyAdd;}else {SortPolyByPower(tmpPolyAdd);return tmpPolyAdd;}}}vector PolySub(vectorp1,vectorp2)//OK{vector tmpPolySub;vector::iterator iter1,iter2;iter1 = p1.begin();iter2 = p2.begin();for (; iter1 != p1.end() && iter2 != p2.end();){if ((*iter1).power > (*iter2).power){tmpPolySub.push_back(*iter1);iter1++;}else if ((*iter1).power == (*iter2).power){polyNode tmp;tmp.coef = ((*iter1).coef - (*iter2).coef)%2;tmp.power = (*iter1).power;if (tmp.coef != 0){tmpPolySub.push_back(tmp);}else;iter1++;iter2++;}else if ((*iter1).power < (*iter2).power){tmpPolySub.push_back(*iter2);iter2++;}}if (iter2 == p2.end()){for (;iter1 != p1.end();iter1++){tmpPolySub.push_back(*iter1);}}else if(iter1 == p1.end()){for (;iter2 != p2.end();iter2++){tmpPolySub.push_back(*iter2);}}SortPolyByPower(tmpPolySub);return tmpPolySub;}vector PolyMultiply( vectorp1, vectorp2)//OK{vector tmpPolyMul;tmpPolyMul.clear();vector itemPoly;polyNode tmp;vector::iterator iter1,iter2;iter1 = p1.begin();iter2 = p2.begin();for (; iter2 != p2.end(); iter2++){for (;iter1 != p1.end(); iter1++){tmp.coef = (*iter1).coef * (*iter2).coef;tmp.power = (*iter1).power + (*iter2).power;itemPoly.push_back(tmp);}SortPolyByPower(itemPoly);iter1 = p1.begin();tmpPolyMul = PolyAdd(tmpPolyMul,itemPoly);itemPoly.clear();}SortPolyByPower(tmpPolyMul);return tmpPolyMul;}vector PolyDiv(vector&p1, vectorp2)//OK{polyNode tmpItem;vector tmpP1 = p1;vector tmpP2 = p2;static vector result;static vector ret;vector tmpMultiply;vector tmpResult;static vector rPoly;vector::iterator iter1;vector::iterator iter2;iter1 = tmpP1.begin();iter2 = tmpP2.begin();while ((*iter1).power >= (*iter2).power){for (;iter2!=tmpP2.end();iter2++){tmpItem.coef = abs((*iter1).coef / (*iter2).coef);tmpItem.power = (*iter1).power - (*iter2).power;tmpResult.push_back(tmpItem);result.push_back(tmpItem);tmpMultiply = PolyMultiply(p2,tmpResult);vector::iterator tmpIter;tmpIter = tmpMultiply.begin();tmpResult.clear();rPoly= PolySub(tmpP1,tmpMultiply);p1 = rPoly;rPoly.clear();return PolyDiv(p1,p2);}}SortPolyByPower(result);ret = result;result.clear();return ret;}vector Eculid(vector&mx,vector&bx)//OK{vector a1x;vector a2x;vector a3x;vector a3xcp;vector b1x;vector b2x;vector b3x;vector t1x;vector t2x;vector t3x;vector qx;vector gcd;vector inverse;vector::iterator iter;static polyNode tmpItem;tmpItem.coef = 1;tmpItem.power = 0;a1x.push_back(tmpItem);a3x.clear();a3x = mx;b1x.clear();tmpItem.coef = 1;tmpItem.power = 0;b2x.push_back(tmpItem);b3x = bx;do {iter = b3x.begin();if (b3x.empty()){cout<<"No inverse!!!"<else if (b3x.size() == 1 && ((*iter).coef == 1 && (*iter).power == 0)){inverse = b2x;return inverse;}a3xcp = a3x;qx = PolyDiv(a3x,b3x);a3x = a3xcp;t1x = PolySub(a1x,PolyMultiply(qx,b1x));t2x = PolySub(a2x,PolyMultiply(qx,b2x));t3x = PolySub(a3x,PolyMultiply(qx,b3x));a1x = b1x;a2x = b2x;a3x = b3x;b1x = t1x;b2x = t2x;b3x = t3x;} while (1);}int main(){vector polynomial1;vector polynomial2;vector inverse;vector ::iterator iter;vector r;CreatePoly(polynomial1);CreatePoly(polynomial2);inverse = Eculid(polynomial1,polynomial2);SortPolyByPower(inverse);iter = inverse.begin();cout<<"求得的逆为："<for (;iter!=inverse.end();iter++){cout<<"X^"<<(*iter).power<<"+"<
