PAT A1009 Product of Polynomials

PAT A1009 Product of Polynomials

题目描述：

 　　This time, you are supposed to find A×B where A and B are two polynomials.

 

　　Input Specification:
　　Each input file contains one test case. Each case occupies 2 lines, and each line contains the information of a polynomial:
　　K N​1​​ a​N​1​​​​ N​2​​ a​N​2​​​​ ... N​K​​ a​N​K​​​​
　　where K is the number of nonzero terms in the polynomial, N​i​​ and a​N​i​​​​ (i=1,2,⋯,K) are the exponents and coefficients, respectively. It is given that 1≤K≤10, 0≤N​K​​<⋯<N​2​​<N​1​​≤1000.

 

　　Output Specification:
　　For each test case you should output the product of A and B in one line, with the same format as the input. Notice that there must be NO extra space at the end of each line. Please be accurate up to 1 decimal place.

 

　　Sample Input:
　　2 1 2.4 0 3.2
　　2 2 1.5 1 0.5

 

　　Sample Output:
　　3 3 3.6 2 6.0 1 1.6

 

参考代码：

参考1：

/****************************************************
PAT A1009 Product of Polynomials
****************************************************/
#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <cmath>

using namespace std;

struct Term {
    int Exponent = 0;
    double Coefficient = 0.0;
};

bool cmp(Term A, Term B) {
    return A.Exponent > B.Exponent;
}

//整理得到的方程
void ArrangePoly(vector<Term>& poly) {
    //合并指数相同项
    for (vector<Term>::iterator itr = poly.begin() + 1; itr != poly.end(); ++itr) {
        if (itr->Exponent == (itr - 1)->Exponent) {
            (itr - 1)->Coefficient += itr->Coefficient;
            itr = poly.erase(itr);
            itr--;
        }
    }

    //移除系数绝对值小于0.1（包括0）项
    for (vector<Term>::iterator itr = poly.begin(); itr != poly.end(); ++itr) {
        if (itr->Coefficient == 0 || fabs(itr->Coefficient) < 0.1) {
            itr = poly.erase(itr);
            itr--;
        }
    }
}

//计算两个方程相乘之后的新方程
vector<Term> GetPolynomial(const vector<Term> poly1, const vector<Term> poly2) {
    Term temp;
    vector<Term> poly3;

    for (int i = 0; i < poly1.size(); ++i) {
        for (int j = 0; j < poly2.size(); ++j) {
            temp.Exponent = poly1[i].Exponent + poly2[j].Exponent;
            temp.Coefficient = poly1[i].Coefficient * poly2[j].Coefficient;

            poly3.push_back(temp);
        }
    }

    //结果按照指数从大到小的顺序排列，以便后续的处理
    sort(poly3.begin(), poly3.end(), cmp);
    ArrangePoly(poly3);

    return poly3;
}

int main() {
    int N1 = 0, N2 = 0;

    cin >> N1;
    vector<Term> func1(N1);
    for (int i = 0; i < N1; ++i)
        cin >> func1[i].Exponent >> func1[i].Coefficient;

    cin >> N2;
    vector<Term> func2(N2);
    for (int i = 0; i < N2; ++i)
        cin >> func2[i].Exponent >> func2[i].Coefficient;

    vector<Term> func3(GetPolynomial(func1, func2));

    func3.size() == 0 ? cout << '0' : cout << func3.size() << ' ';
    for (int i = 0; i < func3.size(); ++i) {
        cout << setiosflags(ios::fixed) << setprecision(0) << func3[i].Exponent << ' ';
        cout << setiosflags(ios::fixed) << setprecision(1) << func3[i].Coefficient;
        if (i != func3.size() - 1) cout << ' ';
    }

    return 0;
}

 参考2：这套代码纯粹是为了复习map的使用然后自己记录一下，虽然也通过了所有测试但是不推荐食用。

/****************************************************
PAT A1009 Product of Polynomials
****************************************************/
#include <iostream>
#include <iomanip>
#include <cmath>
#include <map>

using namespace std;

//自定义的map按key从大到小比较函数
struct cmpKey {
    bool operator()(const int key1, const int key2) const {
        return key1 > key2;
    }
};

int main() {
    double coe = 0.0;
    int k = 0, exp = 0;

    map<int, double, cmpKey> func;
    map<int, double, cmpKey> resoult;

    //录入第一个函数
    cin >> k;
    for (int i = 0; i < k; ++i) {
        cin >> exp >> coe;
        func[exp] = coe;
    }

    cin >> k;
    for (int i = 0; i < k; ++i) {
        cin >> exp >> coe;

        //将获取的第二个函数的因子与第一个函数的因子分别相乘
        for (map<int, double>::iterator it = func.begin(); it != func.end(); ++it) {
            if (resoult.find(exp + it->first) != resoult.end()) {
                resoult[exp + it->first] += coe * it->second;
            }
            else {
                resoult[exp + it->first] = coe * it->second;
            }
        }
    }

    //移除系数绝对值小于0.1（结果中系数只保留1位小数）的因子
    for (map<int, double>::iterator it = resoult.begin(); it != resoult.end(); ++it) {
        if (fabs(it->second) < 0.1) resoult.erase(it);
    }

    //输出结果
    int printTime = 0;  //帮助判断是否输出空格；map中迭代器不能执行“-”的操作，不能使用it != mapName.end() - 1判断是否输出空格
    resoult.size() == 0 ? cout << '0' : cout << resoult.size() << ' ';
    for (map<int, double>::iterator it = resoult.begin(); it != resoult.end(); ++it) {
        cout << it->first << ' ';
        cout << setiosflags(ios::fixed) << setprecision(1) << it->second;
        if (printTime++ != resoult.size() - 1) cout << ' ';
    }

    return 0;
}

 

注意事项：

　　1：参考代码2主要是复习map的使用，涉及的知识有map自定key的排序；map的遍历，仅仅是为了记录不推荐使用.

　　2：后续会补上另外一种方法。