多项式方面的应用（多项式用结构体来实现）

最近在数据结构学习中，学到了多项式方面的应用，因此，特意记录下，以后可以用

#include<iostream>
#include<cstdlib>
#include<cmath>
#include<stdio.h>
#include<algorithm>
#include<fstream>
using namespace std;
#define P 0.0000001
typedef struct {
	double coef;
	int exp;
}polynomial;
bool comp(polynomial p1, polynomial p2) {
	return p1.exp > p2.exp;
}
void Zero(int n, polynomial poly[]) {
	int i;
	for (i = 0; i < n; i++) {
		poly[i].coef = 0;
		poly[i].exp = 0;
	}
}
bool IsZero(polynomial poly[], int n) {
	int i;
	for (i = 0; i < n; i++)
	if (fabs(poly[i].coef - 0)>P)
		return false;
	return true;
}
double Coef(polynomial poly[], int exp, int n) {
	int i;
	for (i = 0; i < n; i++) {
		if (poly[i].exp == exp &&fabs(poly[i].coef - 0)>P)
			return poly[i].coef;
	}
	return 0;
}
int Lead_Exp(polynomial poly[], int n) {
	int max = 0;
	for (int i = 0; i < n; i++)
	if (poly[i].exp >= max)
		max = poly[i].exp;
	return max;
}
void Attach(polynomial poly[], double coef, int n, int exp) {
	for (int i = 0; i < n; i++) {
		if (poly[i].exp == exp)
			return;
	}
	poly[n].coef = coef;
	poly[n].exp = exp;
}
void  Remove(polynomial poly[], int exp, int n) {
	for (int i = 0; i<n; i++) {
		if (poly[i].exp == exp)
		{
			poly[i].exp = 0;
			poly[i].coef = 0;
		}
	}
}
void SingleMult(polynomial poly[], double coef, int exp, int n) {
	for (int i = 0; i<n; i++) {
		if (poly[i].coef != 0) {
			poly[i].coef *= coef;
			poly[i].exp += exp;
		}
	}
}
int Add(polynomial poly1[], int n1, polynomial poly2[], int n2) {
	int i, k = 0, j;
	for (i = 0; i<n2; i++) {
		bool flag = false;
		for (j = 0; j<n1; j++) {
			if (poly1[j].exp == poly2[i].exp) {
				flag = true;
				poly1[j].coef += poly2[i].coef;
				break;
			}
		}
		if (flag == false) {
			poly1[n1 + k] = poly2[i];
			k++;
		}
	}
	n1 += k;
	return n1;
}
int   Mult(polynomial poly1[], int n1, polynomial poly2[], int n2, polynomial poly3[]) {
	int k = 0;
	for (int i = 0; i<n1; i++) {
		for (int j = 0; j<n2; j++) {
			poly3[k].exp = poly1[i].exp + poly2[j].exp;
			poly3[k].coef = poly1[i].coef*poly2[j].coef;
			k++;
		}
	}
	for (int i = 0; i < k; i++) {
		for (int j = i + 1; j < k; j++) {
			if (poly3[i].exp == poly3[j].exp) {
				poly3[i].coef += poly3[j].coef;
				poly3[j].exp = poly3[j].coef = 0;
			}
		}
	}
	return k;
}
void Print(polynomial poly[], int n) {
	if (n == 1) {
		if (fabs(poly[0].coef - 1) < P) {
			if (poly[0].coef < 0)
				cout << "-";
			else
				cout << " ";
		}
		else
			cout << poly[0].coef;
		if (poly[0].exp == 0)
			cout << " ";
		else if (poly[0].exp == 1)
			cout << "x";
		else
			cout << "x^" << poly[0].exp;
	}
	else for (int i = 0; i<n; i++) {
		if (i == 0) {
			if (fabs(poly[i].coef - 1) < P)
			{
				if (poly[i].coef < 0)
					cout << "-";
				else
					cout << " ";
			}
			else
				cout << poly[i].coef;
			if (poly[i].exp == 1)
				cout << "x";
			else
				cout << "x^" << poly[i].exp;
		}
		else if (i == n - 1){
			if (poly[i].exp == 0) {
				if (poly[i].coef > 0)
					cout << "+";
				cout << poly[i].coef;
			}
			else {
				if (fabs(poly[i].coef - 1) < P)
				{
					if (poly[i].coef < 0)
						cout << "-";
					else
						cout << "+";
				}
				else {
					if (poly[i].coef>0)
						cout << "+";
					cout << poly[i].coef;
				}
				if (poly[i].exp == 1)
					cout << "x";
				else
					cout << "x^" << poly[i].exp;
			}

		}
		else {
			if (fabs(poly[i].coef - 1) < P)
			{
				if (poly[i].coef < 0)
					cout << "-";
				else
					cout << "+";
			}
			else {
				if (poly[i].coef>0)
					cout << "+";
				cout << poly[i].coef;
			}
			cout << "x^" << poly[i].exp;
		}
	}
}
int main() {
	ios::sync_with_stdio(false); 
	cin.tie(false);
	freopen("D:/a.txt", "r",stdin);
	freopen("D:/b.txt", "w", stdout);
	polynomial poly1[100], poly2[100], poly3[100], poly4[100], poly5[100];
	int n1, n2, i, j, k;
	cin >> n1;
	Zero(100, poly5);
	for (i = 0; i < n1; i++) {
		cin >> poly1[i].coef >> poly1[i].exp;
		poly3[i] = poly1[i];
	}
	cin >> n2;
	for (i = 0; i < n2; i++) {
		cin >> poly2[i].coef >> poly2[i].exp;
		poly4[i] = poly2[i];
	}
	int n3 = Add(poly1, n1, poly2, n2);
	sort(poly1, poly1 + n3, comp);
	Print(poly1, n3);
	cout << endl;
	int n4 = Mult(poly3, n1, poly4, n2, poly5);
	sort(poly5, poly5 + n4, comp);
	Print(poly5, n4);
	return 0;
}

具体可以看这个

http://blog.sina.com.cn/s/blog_827ed2e00100tsff.html