1002. A+B for Polynomials

A+B for Polynomials

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

Input

Each input file contains one test case. Each case occupies 2 lines, and each line contains the information of a polynomial: K N1 aN1 N2 aN2 … NK aNK, where K is the number of nonzero terms in the polynomial, Ni and aNi (i=1, 2, …, K) are the exponents and coefficients, respectively. It is given that 1 <= K <= 10，0 <= NK < … < N2 < N1 <=1000.

Output
For each test case you should output the sum 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 to 1 decimal place.

Sample Output

2 1 2.4 0 3.2
2 2 1.5 1 0.5

Sample Output

3 2 1.5 1 2.9 0 3.2

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题意

输出两个多项式相加后的多项式。

思路

常规思路是分别用double数组来记录每一个多项式：数组的下标为指数，对应的值为系数（当然这只适用于正整数指数的情况）。当数组的值为0（即系数为0）时，表示多项式中不存在指数为该下标的项（用于判读是否输出）。将读入的两个多项式数组按对应下标相加，存入第三个数组中，即为目标多项式数组。
　　
因第一次提交时有一个测试点未通过，一时想不到问题所在（后已修正），就对原有代码进行了改进：只创建一个目标多项式数组，每一次读入、相加都直接在该数组中进行。

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代码实现——三数组版

#include <stdio.h>
#define maxSize 1001

struct poly_arr 
{
	double poly[maxSize];
	int max_index;			// 系数非零项的最大指数
	int count;				// 非零项个数
};

void init_poly(poly_arr &X)
{
	int i;
	X.max_index = 0;
	X.count = 0;
	for (i=0; i < maxSize; ++i)
		X.poly[i] = 0;
}

void insert_poly(poly_arr &X)
{
	int expo;
	double coef;
	scanf("%d %lf", &expo, &coef);
	X.poly[expo] = coef;
	++X.count;
	if (X.max_index < expo)			// 更新多项式最大指数
		X.max_index = expo;
}

void add_poly(poly_arr A, poly_arr B, poly_arr &C)
{
	int i;
	int max;
	max = A.max_index > B.max_index ? A.max_index : B.max_index;
	for (i = 0; i <= max; ++i)
		if (A.poly[i] != 0.0 || B.poly[i] != 0.0)
		{
			C.poly[i] = A.poly[i] + B.poly[i];
			if (C.poly[i] != 0.0)	// 规范应该为fabs(x - 0.0) > 1e-8
			{
				++C.count;
				C.max_index = i;	// 系数非零时才更新最大指数
			}
		}
}

void print_poly(poly_arr X)
{
	int i;
	printf("%d", X.count);
	for (i = X.max_index; i >= 0; --i)
		if (X.poly[i] != 0.0)
			printf(" %d %.1lf", i, X.poly[i]);
}

int main(void)
{
	poly_arr A, B, C;
	int k;
	int i; 
	init_poly(A);
	init_poly(B);
	init_poly(C);
	scanf("%d", &k);
	for (i = 0; i < k; ++i)
		insert_poly(A);
	scanf("%d", &k);
	for (i = 0; i < k; ++i)
		insert_poly(B);
	add_poly(A, B, C);
	print_poly(C);
}

代码实现——单数组版

#include <stdio.h>
#define maxSize 1001

struct poly
{
	double arr[maxSize];
	int count;
	int max_index;
};

void init_poly(poly &X)
{
	X.count = 0;
	X.max_index = 0;
	for (int i = 0;i < maxSize; ++i)
		X.arr[i] = 0;
}

void add_poly(poly &X)
{
	double coef;
	int expo;
	scanf("%d %lf", &expo, &coef);
	if (X.arr[expo] == 0.0)		// 原系数为零时项数+1
		++X.count;
	X.arr[expo] = X.arr[expo] + coef;
	if (X.arr[expo] == 0.0)		// 相加后系数为零时项数-1
		--X.count;
	if (X.max_index < expo)		// 更新最大指数
		X.max_index = expo;
}

void print_poly(poly X)
{
	printf("%d", X. count);
	for (int i = X.max_index; i >= 0; --i)
		if (X.arr[i] != 0.0)
			printf(" %d %.1lf", i, X.arr[i]);
}

int main(void)
{
	int i, j, K;
	poly C;
	init_poly(C);
	for (i = 0; i < 2; ++i)
	{
		scanf("%d", &K);
		for (j=0; j<K; ++j)
			add_poly(C);
	}	
	print_poly(C);
}