PAT (Advanced Level) Practice 1002 A+B for Polynomials—Python

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已于 2023-09-06 16:09:39 修改

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分类专栏： PAT (Advanced Level) Practice 文章标签：算法数据结构 python

于 2023-09-05 23:11:04 首次发布

本文链接：https://blog.youkuaiyun.com/qq_65232540/article/details/132702261

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文章介绍了一个Python编程问题，涉及多项式相加，利用字典的键值特性存储和合并两个多项式，最后整理输出。

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摘要

本题考察了考生对于python数据结构的理解能力，如果能想到字典型具有键值不可重复的特性就能很轻松完成

原题

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 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 Input:

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

题目意思

现在有两个多项式A，B，分别用两行数据表示，其中每一行有K个数据，每个数据由次数和系数组成，现在要把两个多项式相加，问最终输出的多项式的每个次幂及其系数是多少。

本题的例子中A:2.4x + 3.2 B:1.2x^2 + 0.5x 两个式子相加就是1.2x^2 + 2.9x + 3.2

思路

python中字典具有键值不可重复的特性，那么只要先将a中的键值和数据先保存进result字典中，然后遍历b，把b中的数据放入与a键值相同的地方，最后逆序排序输出即可。

Python代码

# 输入数据，并保留本来的数据格式
a = [eval(i) for i in input().split()[1:]]
b = [eval(i) for i in input().split()[1:]]
result = {}
# 分别把数据存放入字典
for i in range(0, len(a), 2):
    result[a[i]] = result.get(a[i], 0) + a[i + 1]

for i in range(0, len(b), 2):
    result[b[i]] = result.get(b[i], 0) + b[i + 1]

# 删除系数为0的项
for i in list(result.keys()):
    if result[i] == 0:
        del result[i]

result = sorted(result.items(), key=lambda d: int(d[0]), reverse=True)

# 输出元素
print(len(result), end="")
for tup in result:
    print(" {} {:.1f}".format(tup[0], tup[1]), end="")