Josephus Problem

/*
Josephus Problem
N people have decided to elect a leader by arranging themselves in a
circle and eliminating every M th person around the circle, closing
ranks as each person drops out. The problem is to find out which person
will be the last one remaining ( a mathematically inclined potential
leader will figure out ahead of time which position in the circle to take).
From Algorithms in C++.
*/

#include
#include

using namespace std;

struct node
{
    int item;
    node *next;
    node( int n, node *t ) { item = n; next = t; }
};

// typedef node *link; 
// Using link instead of linkk has compile error
// I don't know the reason.

typedef node *linkk;

// int main( int argc, char *argv[] )
int main()
{
    // int i, N = atoi(argv[1]), M = atoi(argv[2]);
    int i;
    int N = 9; // number of people 
    int M = 5;
    linkk t = new node( 1, 0 );
    t->next =  t;
    linkk x = t;
    for ( i = 2; i <= N; ++i )
    {
        x =  ( x->next =  new node(i, t) );
    }
    while (x != x->next )
    {
        // move the pointer M-1 times
        for ( i = 1; i < M; ++i ) x = x->next;
        // delete the next item from the list    
        linkk temp = x->next;
        x->next = x->next->next;
        delete temp;

    }
    cout << x->item << endl;

    return 0;
}