编程介的小学生
2017-09-04 15:29Joseph's Problem
Joseph likes taking part in programming contests. His favorite problem is, of course, Joseph's problem.
It is stated as follows.
There are n persons numbered from 0 to n - 1 standing in a circle. The person numberk, counting from the person number 0, is executed. After that the person number k of the remaining persons is executed, counting from the person after the last executed one. The process continues until only one person is left. This person is a survivor. The problem is, given n and k detect the survivor's number in the original circle.
Of course, all of you know the way to solve this problem. The solution is very short, all you need is one cycle:
r := 0;
for i from 1 to n do
r := (r + k) mod i;
return r;
Here "x mod y" is the remainder of the division of x by y, But Joseph is not very smart. He learned the algorithm, but did not learn the reasoning behind it. Thus he has forgotten the details of the algorithm and remembers the solution just approximately.
He told his friend Andrew about the problem, but claimed that the solution can be found using the following algorithm:
r := 0;
for i from 1 to n do
r := r + (k mod i);
return r;
Of course, Andrew pointed out that Joseph was wrong. But calculating the function Joseph described is also very interesting.
Given n and k, find .
Input
Each case of the input file contains n and k (1≤ n, k ≤ 109) in a single line. Proceed to the end of file.
Output
For each case, output the sum requested in a line.
Sample Input
5 3
1 1
Sample Output
7
0
- 点赞
- 回答
- 收藏
- 复制链接分享
1条回答
为你推荐
- Magento和可配置的产品属性
- magento
- php
- 1个回答
- 如何在循环外存储变量
- php
- 1个回答
- 使用codeigniter中的foreach()为传递给bootstrap模式的数据添加限制
- codeigniter
- php
- 3个回答
- 格式化电子邮件中的文本
- php
- 3个回答
- 触发单击单选按钮,并在页面刷新时记住选择
- html
- javascript
- radio-button
- jquery
- php
- 1个回答