UVa: 10015 (Joseph’s Cousin)



// http://uva.onlinejudge.org/external/100/10015.html
// Runtime: 1.300s
// Tag: Modular arithmetic, prime number

// @BEGIN_OF_SOURCE_CODE

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <cctype>
#include <stack>
#include <queue>
#include <list>
#include <vector>
#include <map>
#include <sstream>
#include <cmath>
#include <bitset>
#include <utility>
#include <set>
#include <numeric>
#include <ctime>

#define Inf 2147483647
#define Pi acos(-1.0)
#define N 50000
#define LL long long

inline LL Power(int b, int p) { LL ret = 1; for ( int i = 1; i <= p; i++ ) ret *= b; return ret; }
const int dr [] = {-1, -1, 0, 1, 1, 1, 0, -1};
const int dc [] = {0, 1, 1, 1, 0, -1, -1, -1};

#define F(i, a, b) for( int i = (a); i < (b); i++ )
#define Fs(i, sz) for( size_t i = 0; i < sz.size (); i++ )
#define Fe(i, x) for(typeof (x.begin()) i = x.begin(); i != x.end (); i++)
#define Set(a, s) memset(a, s, sizeof (a))
#define max(a, b)  (a < b ? b : a)
#define min(a, b)  (a > b ? b : a)

using namespace std;

bool mark [N];
vector <int> primeList;
int primeFactorCnt [N];

void sieve ()
{
	Set (mark, true);
	mark [0] = mark [1] = false;

	for ( int i = 4; i < N; i += 2 ) mark [i] = false;

	for ( int i = 3; i * i <= N; i += 2 )
		if ( mark [i] ) for ( int j = i * i; j < N; j += 2 * i ) mark [j] = false;

	primeList.push_back (2);

	for ( int i = 3; i < N; i += 2 ) if ( mark [i] ) primeList.push_back (i);

	// printf ("%d\n", primeList.size ());
}

int main () 
{
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);

	sieve();

	int n; 

	while ( scanf ("%d", &n) && n ) {

		vector <int> people;
		
		F(i, 0, n) people.push_back(i + 1);

		int ind = 0;
		int num_th = 0;

		while ( n > 1 ) {
			num_th = (num_th + (primeList [ind++] % n) - 1) % people.size();
			people.erase(people.begin() + num_th);
			n--;
		}
		
		printf ("%d\n", people [0]);

	}

	return 0;
}

// @END_OF_SOURCE_CODE

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