Du disorderly pile Problem Solving report

Du disorderly Pile description

Because of the well-known reasons, the Gang department has been owed to the real reason a bunch of bananas.
In order to seal up the mouth of real Daniel, the gang promised to buy her a banana if the problem was answered by Daniel:
At first, a \ (n\) Individual in a circle, starting from \ (1\) clockwise count, reported \ (m\) people were executed by the institution. And then the next one
The individual began to count off from \ (1\) until there was only one person left.
Lisa Habitat: "This is not Joseph question ..."
Aaron: "Assistant, you shut up!"
Although the real reason is already disoriented, but heard a car of bananas, two eyes then released the light.
"Well, it's really a banana for a car," he asked. If you can help me, I can have some bananas for you yo, eh
Hey. Come on, you. "

Input Format

The first line is an integer \ (t\) that represents the number of data groups.
Next \ (t\) line, two integers per line \ (n\) ,\ (m\).

Output Format

For each set of data, the output is an integer that represents the survivor's number

Constraints

Test point number	N	m
\ (1\)	\ (\le 10^5\)	\ (\le 10^5\)
\ (2\)	\ (\le 10^6\)	\ (\le 10^5\)
\ (3\)	\ (\le 10^9\)	\ (\le 2\)
\ (4\)	\ (\le 10^9\)	\ (\le 2\)
\ (5\)	\ (\le 10^9\)	\ (\le 3\)
\ (6\)	\ (\le 10^9\)	\ (\le 3\)
\ (7\)	\ (\le 10^9\)	\ (\le 10^3\)
\ (8\)	\ (\le 10^9\)	\ (\le 10^4\)
\ (9\)	\ (\le 10^9\)	\ (\le 10^5\)
\ (10\)	\ (\le 10^9\)	\ (\le 10^5\)

For \ (100\%\) data,\ (1 \le T \le 20\),\ (1 \le n \le 10^9\),\ (1 \le m \le 10^5\)

Solution

In fact, is the Joseph question, there is a mathematical conclusion, when the test wjyyy immortal hit the table, I \ (20pts\) of the balance of the tree violence has been played.

Conclusion: the Order \ (f_i\) represents a \ (i\) individual to delete the last person's number from the beginning, then there is

\[f_i=\left\{\begin{aligned} 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \,i=1 T;m \ \frac{m \times (f_{i '}-i\%m) \% i '}{m-1} \ I\ge m\end{aligned}\right.\]

\[i ' =i-\lfloor\frac{i}{m} \rfloor\]

Explain, the first number is from \ (0\) , we delete a number after each, in order to ensure that the next time or start from scratch, we delete the back of the location of the second number of " (0\), and then solve the sub-problem." function returned as long as the mapping of the number is OK, according to their own understanding on it.

Code:

#include <cstdio>int n,m,T;int dfs(int i){    int nt=i-i/m;    if(i>=m) return 1ll*((dfs(nt)-i%m)%nt+nt)%nt*m/(m-1);    return i==1?0:(dfs(i-1)+m)%i;}int main(){    scanf("%d",&T);    while(T--)    {        scanf("%d%d",&n,&m);        printf("%d\n",dfs(n)+1);    }    return 0;}

2018.10.19

Du disorderly pile Problem Solving report