poj2517And Then There Was One 约瑟夫问题

And Then There Was One

Time Limit: 5000MS Memory Limit: 65536KTotal Submissions: 4849 Accepted: 2578

Description

Let’s play a stone removing game.

Initially, n stones are arranged on a circle and numbered 1, …, n clockwise (Figure 1). You are also given two numbers k and m. From this state, remove stones one by one following the rules explained below, until only one remains. In step 1, remove stone m. In step 2, locate the k-th next stone clockwise from m and remove it. In subsequent steps, start from the slot of the stone removed in the last step, make k hops clockwise on the remaining stones and remove the one you reach. In other words, skip (k − 1) remaining stones clockwise and remove the next one. Repeat this until only one stone is left and answer its number. For example, the answer for the case n = 8, k = 5, m = 3 is 1, as shown in Figure 1.

Initial state
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Final state Figure 1: An example game

Initial state: Eight stones are arranged on a circle.

Step 1: Stone 3 is removed since m = 3.

Step 2: You start from the slot that was occupied by stone 3. You skip four stones 4, 5, 6 and 7 (since k = 5), and remove the next one, which is 8.

Step 3: You skip stones 1, 2, 4 and 5, and thus remove 6. Note that you only count stones that are still on the circle and ignore those already removed. Stone 3 is ignored in this case.

Steps 4–7: You continue until only one stone is left. Notice that in later steps when only a few stones remain, the same stone may be skipped multiple times. For example, stones 1 and 4 are skipped twice in step 7.

Final State: Finally, only one stone, 1, is on the circle. This is the final state, so the answer is 1.

Input

The input consists of multiple datasets each of which is formatted as follows.

n k m

The last dataset is followed by a line containing three zeros. Numbers in a line are separated by a single space. A dataset satisfies the following conditions.

2 ≤ n ≤ 10000, 1 ≤ k ≤ 10000, 1 ≤ m ≤ n

The number of datasets is less than 100.

Output

For each dataset, output a line containing the stone number left in the final state. No extra characters such as spaces should appear in the output.

Sample Input

8 5 3100 9999 9810000 10000 100000 0 0

Sample Output

1932019

Source

Japan 2007

如果有n个人，一定存在一个人不死的人【废话，设这个不死的人的坐标是x，经过n-1次变换，x这个人被筛选出来了，如果，从你n-1次开始倒推，可以得出这样一个公式x=(x‘+m)%i i为当前的人数 而本题由于初始人的位置不一定是0，则最后一步优化即可

code：

#include <iostream>
using namespace std;
int main()
{
long long  n,k,m;
while(cin>>n>>k>>m)
{
if(n==0&&k==0&&m==0) break;
int result=0;
for(int i=1;i<n;i++)
result=(result+k)%i;
result=(result+m)%n+1;
cout<<result<<endl;
}
return 0;
}