程序代码：

#include <stdio.h>
#include <malloc.h>
int JosephusProblem_Solution(int n, int m);
int main()
{
    int n,m,k;
    scanf("%d%d",&n,&m);
    k = JosephusProblem_Solution(n,m);
    printf("%d \n",k+1);
    return 0;
}

int JosephusProblem_Solution(int n, int m)
{
    unsigned i;
    if(n < 1 || m < 1)
        return -1;

    int *f = (int*)malloc(sizeof(int)*(n+1));
    f[0] = f[1] = 0; 

    for(i = 2; i <= n; i++)
        f[i] = (f[i-1] + m) % i; //按递推公式进行计算

    int result = f[n];
    free(f);

    return result;
}

程序代码：

#include <stdio.h>
#include <stdlib.h>

// 链表节点
typedef struct _RingNode
{
    int pos;  // 位置
    struct _RingNode *next;
}RingNode, *RingNodePtr;

// 创建约瑟夫环，pHead:链表头指针，count:链表元素个数
void CreateRing(RingNodePtr pHead, int count)
{
    RingNodePtr pCurr = NULL, pPrev = NULL;
    int i = 1;
    pPrev = pHead;
    while(--count > 0)
    {
        pCurr = (RingNodePtr)malloc(sizeof(RingNode));
        i++;
        pCurr->pos = i;
        pPrev->next = pCurr;
        pPrev = pCurr;
    }
    pCurr->next = pHead;  // 构成环状链表
}

void PrintRing(RingNodePtr pHead)
{
    RingNodePtr pCurr;
    printf("%d", pHead->pos);
    pCurr = pHead->next;
    while(pCurr != NULL)
    {
        if(pCurr->pos == 1)
            break;
        printf("\n%d", pCurr->pos);
        pCurr = pCurr->next;
    }
}

void KickFromRing(RingNodePtr pHead, int m)
{
    RingNodePtr pCurr, pPrev;
    int i = 1;    // 计数
    pCurr = pPrev = pHead;
    while(pCurr != NULL)
    {
        if (i == m)
        {
            // 踢出环
            printf("\n%d", pCurr->pos);    // 显示出圈循序
            pPrev->next = pCurr->next;
            free(pCurr);
            pCurr = pPrev->next;
            i = 1;
        }
        pPrev = pCurr;
        pCurr = pCurr->next;
        if (pPrev == pCurr)
        {
            // 最后一个
            printf("\n%d", pCurr->pos);    // 显示出圈循序
            free(pCurr);
            break;
        }
        i++;
    }
}

int main()
{
    int m = 0, n = 0;
    RingNodePtr pHead = NULL;
    printf("---------------Josephus Ring---------------\n");
    printf("N(person count) = ");
    scanf("%d", &n);
    printf("M(out number) = ");
    scanf("%d", &m);
    if(n <= 0 || m <= 0)
    {
        printf("Input Error\n");
        system("pause");
        return 0;
    }
    // 建立链表
    pHead = (RingNodePtr)malloc(sizeof(RingNode));
    pHead->pos = 1;
    pHead->next = NULL;
    CreateRing(pHead, n);
#ifdef _DEBUG
    PrintRing(pHead);
#endif

    // 开始出圈
    printf("\nKick Order: ");
    KickFromRing(pHead, m);    
    printf("\n");
    system("pause");
    return 0;
}

程序代码：

====================纯数学==============================
#include <stdio.h>
int main()
{
    int n, m, i, s = 0;
    printf ("N M = ");
    scanf("%d%d", &n, &m);
    for (i = 2; i <= n; i++)
    {
        s = (s + m) % i;
    }
    printf ("\nThe winner is %d\n", s+1);
}