P4325 [COCI2006-2007#1] Modulo

题面翻译

给出 $10$ 个整数，问这些整数除以 $42$ 后得到的余数有多少种。

• 第一个样例的十个结果是 $1,2,3,4,5,6,7,8,9,10$，有 $10$ 个不同的结果；
• 第二个样例结果都是 $0$，只有一个不同的结果；
• 第三个样例余数是 $39,40,41,0,1,2,40,41,0,1$，有 $0,1,2,39,40,41$ 这六个不同的结果。

题目描述

Given two integers A and B, A modulo B is the remainder when dividing A by B. For example, the numbers 7, 14, 27 and 38 become 1, 2, 0 and 2, modulo 3. Write a program that accepts 10 numbers as input and outputs the number of distinct numbers in the input, if the numbers are considered modulo 42.

输入格式

The input will contain 10 non-negative integers, each smaller than 1000, one per line.

输出格式

Output the number of distinct values when considered modulo 42 on a single line.

样例 #1

样例输入 #1

1
2
3
4
5
6
7
8
9
10

样例输出 #1

10

样例 #2

样例输入 #2

42
84
252
420
840
126
42
84
420
126

样例输出 #2

1

样例 #3

样例输入 #3

39
40
41
42
43
44
82
83
84
85

样例输出 #3

6

提示

In the first example, the numbers modulo 42 are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.
In the second example all numbers modulo 42 are 0.
In the third example, the numbers modulo 42 are 39, 40, 41, 0, 1, 2, 40, 41, 0 and 1. There are 6 distinct numbers.

代码实现

对于每个输入的整数直接取余，将余数收入集合，最终统计集合长度即可。

print(len(set(int(input()) % 42 for _ in range(10))))