LA 3882 - And Then There Was One 【约瑟夫环变形】

题意：n个人围成一圈，编号从1-n，规定第一个被杀掉的人编号为m，然后开始每数k个数，杀掉一个人，问最后剩余的人。

思路：原本约瑟夫环f(n) = (f(n-1) + k) % n。现在我们把第m个人看做第一人就好了，最后结果(f(n)+m-k+1)%n。注意<=0时，加n。

AC代码：

#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <vector>
#define INF 0x3f3f3f
#define eps 1e-8
#define MAXN (2000+1)
#define MAXM (100000)
#define Ri(a) scanf("%d", &a)
#define Rl(a) scanf("%lld", &a)
#define Rf(a) scanf("%lf", &a)
#define Rs(a) scanf("%s", a)
#define Pi(a) printf("%d\n", (a))
#define Pf(a) printf("%.2lf\n", (a))
#define Pl(a) printf("%lld\n", (a))
#define Ps(a) printf("%s\n", (a))
#define W(a) while(a--)
#define CLR(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define LL long long
#define lson o<<1, l, mid
#define rson o<<1|1, mid+1, r
#define ll o<<1
#define rr o<<1|1
using namespace std;
int main()
{
    int n, k, m;
    while(~scanf("%d%d%d", &n, &k, &m))
    {
        if(n == 0 && k == 0 && m == 0)
            break;
        int last = 0;
        for(int i = 2; i <= n; i++)
            last = (k + last) % i;
        last = (m - k + 1 + last) % n;
        if(last <= 0)
            last += n;
        Pi(last);
    }
    return 0;
}