题目

计算多项式乘法，按照x的递减，y的递增序输出。

分析

模拟。这里分成三个部分：1.将字符串分解成不同的单元（axmyn为一个单元）构成的多项式；2.计算乘法，并且排序，合并同类项；3.按照特定格式输出。

说明

注意系数和指数为0的情况。。。

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

const int _max_item_size = 1000;

typedef struct _item
{
	int    number;
	int    x_power;
	int    y_power;
	_item *next;
}item;
item Item[_max_item_size];
int  item_size = 0;

item* get_item(char buf[], int &index)
{
	if (!buf[index]) return NULL;
	int sign = 1;
	if (buf[index] == '-') {
		sign = -1;
		index ++;
	} else if (buf[index] == '+')
		index ++;
	
	Item[item_size].number = 0;
	while (buf[index] >= '0' && buf[index] <= '9') 
		Item[item_size].number = Item[item_size].number*10 + buf[index ++] - '0';
	Item[item_size].number = Item[item_size].number * sign;
	
	Item[item_size].x_power = 0;
	Item[item_size].y_power = 0;
	for (int k = 0; k < 2; ++ k) {
		if (buf[index] == 'x' || buf[index] == 'y') {
			char ch = buf[index ++];
			int  number = 0;
			
			while (buf[index] >= '0' && buf[index] <= '9') 
				number = number*10 + buf[index ++] - '0';
			
			if (number == 0 && buf[index-1] != '0') 
				number = 1;
			
			if (ch == 'x') 
				Item[item_size].x_power = number;
			else if (ch == 'y') 
				Item[item_size].y_power = number;
			
		} else break;
		
		if (Item[item_size].number == 0)
			Item[item_size].number = 1 * sign;
	}
	
	Item[item_size].next = NULL;
	return &Item[item_size ++];
}

typedef struct _polynomial
{
	item *item_list;
	int   size;
}polynomial;
polynomial Polynomial[3];
int polynomial_size;

polynomial* get_polynomial(char buf[])
{
	int index = 0;
	polynomial* pol = &Polynomial[polynomial_size ++];
	pol->size = 0;
	pol->item_list = NULL;
	item *pi = NULL;
	while (pi = get_item(buf, index)) {
		pi->next = pol->item_list;
		pol->item_list = pi;
		pol->size ++;
	}
	
	return pol;
}

void swap(int &a, int &b)
{
	int c = a;
	a = b;
	b = c;
}

polynomial* mul_polynomial(polynomial* A, polynomial* B)
{
	polynomial* pol = &Polynomial[polynomial_size ++];
	pol->size = 0;
	pol->item_list = NULL;
	for (item* pi = A->item_list; pi; pi = pi->next) 
		for (item* qi = B->item_list; qi; qi = qi->next) {
			Item[item_size].number = pi->number * qi->number;
			Item[item_size].x_power = pi->x_power + qi->x_power;
			Item[item_size].y_power = pi->y_power + qi->y_power;
			Item[item_size].next = pol->item_list;
			pol->item_list = &Item[item_size ++];
			pol->size ++;
		}
	
	// sort
	for (item* pi = pol->item_list; pi; pi = pi->next) 
		for (item* qi = pi->next; qi; qi = qi->next)
			if (pi->next && (pi->x_power < qi->x_power
							|| (pi->x_power == qi->x_power 
								&& pi->y_power > qi->y_power))) {
				swap(pi->number, qi->number);
				swap(pi->x_power, qi->x_power);
				swap(pi->y_power, qi->y_power);
			}
	
	// combine
	for (item* pi = pol->item_list; pi; pi = pi->next)
		if (pi->next && pi->x_power == pi->next->x_power 
				&& pi->y_power == pi->next->y_power) {
			pi->number += pi->next->number;
			pi->next = pi->next->next;
		}
	return pol;
}

char save_number[81];
void insert_number(int number, char buf[], int &index)
{
	int count = 0;
	while (number) {
		save_number[count ++] = number%10 + '0';
		number /= 10;
	}
	while (count > 0) 
		buf[index ++] = save_number[-- count];
}

void output_polynomial(polynomial* A)
{
	char line1[81], line2[81];
	for (int i = 0; i < 80; ++ i) 
		line1[i] = line2[i] = ' ';
	
	int  index = 0, number = 0;
	for (item* pi = A->item_list; pi; pi = pi->next) {
		if (!pi->number)
			continue;
		number = pi->number;
		if (pi != A->item_list) 
			line2[index ++] = ' ';
		if (number < 0) {
			line2[index ++] = '-';
			number = number*-1;
		} else if (pi != A->item_list) 
			line2[index ++] = '+';
		
		if (pi != A->item_list)
			line2[index ++] = ' ';
		if (number == 1) {
			if (pi->x_power == 0 && pi->y_power == 0)
				line2[index ++] = '1';
		} else
			insert_number(number, line2, index);
		
		if (pi->x_power > 0) {
			line2[index ++] = 'x';
			if (pi->x_power != 1) 
				insert_number(pi->x_power, line1, index);
		}
		if (pi->y_power > 0) {
			line2[index ++] = 'y';
			if (pi->y_power != 1) 
				insert_number(pi->y_power, line1, index);
		}
	}
	if (index == 0) {
		line1[index] = 0;
		line2[index ++] = '0';
	}
	line1[index] = line2[index] = 0;
	puts(line1);
	puts(line2);
}

int main()
{
	char buf[256];
	while (~scanf("%s", buf) && strcmp(buf, "#")) {
		item_size = 0;
		polynomial_size = 0;
		polynomial* A = get_polynomial(buf);
		scanf("%s", buf);
		polynomial* B = get_polynomial(buf);
		
		polynomial* C = mul_polynomial(A, B);
		output_polynomial(C);
	}
    return 0;
}