PAT甲级-1009-多项式乘除_多项式除法pat甲级-优快云博客

本文链接：https://blog.youkuaiyun.com/qq_36631553/article/details/95678232

本文详细介绍了一种解决多项式乘法问题的高效算法。通过分析输入多项式的非零项，利用双层循环进行逐项相乘并累加，最终输出结果多项式。算法特别注意了系数可能为零的情况，避免无效输出。

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 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 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

/*
1.maxn需要乘2
2.多项式乘加之后可能出现系数为0的情况，此时不应该输出
*/
#include <stdio.h>
#include <algorithm>
#include <stdlib.h>
#include <malloc.h>
#include <string.h>
#include <iostream>
#include <queue>
#include <string>
#include <vector>
#include <map>
using namespace std;
const int maxn = 2010;
const int INF = 0x3f3f3f3f;

int k;
int t;
int cnt_a = 0, cnt_b = 0;
double flo;
bool fg[maxn];
double num_a[maxn], num_b[maxn], num[maxn];
int dex_a[maxn], dex_b[maxn], dex[maxn];

bool cmp(int a, int b) { return a > b; }

int main() {
	cin >> k;
	memset(fg, false, sizeof fg);
	memset(num, 0, sizeof num);
	for (int i = 0; i < k; i++) {
		scanf("%d%lf", &t, &flo);
		dex_a[cnt_a++] = t;
		num_a[t] = flo;
	}
	cin >> k;
	for (int i = 0; i < k; i++) {
		scanf("%d%lf", &t, &flo);
		dex_b[cnt_b++] = t;
		num_b[t] = flo;
	}

	int cnt = 0;
	int ab;
	for (int i = 0; i < cnt_a; i++) {
		for (int j = 0; j < cnt_b; j++) {
			ab = dex_a[i] + dex_b[j];
			if (!fg[ab]) {
				fg[ab] = true;
				dex[cnt++] = ab;
			}
			num[ab] += num_a[dex_a[i]] * num_b[dex_b[j]];
		}
	}
	sort(dex, dex + cnt, cmp);
	
	int cntt = 0;
	for (int i = 0; i < cnt; i++) {
		if (num[dex[i]]) dex[cntt++] = dex[i];
	}
	printf("%d", cntt);
	for (int i = 0; i < cntt; i++) {
		printf(" %d %.1lf", dex[i], num[dex[i]]);
	}
	printf("\n");
}