UVa : 11960 (Divisor Game)



// http://uva.onlinejudge.org/external/119/11960.html
// Runtime: 0.652s
// Tag: Prime, divisor, Sieve

// @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>

#define INF_MAX 2147483647
#define INF_MIN -2147483647
#define pi acos(-1.0)
#define N 1000005
#define LL long long

#define For(i, a, b) for( int i = (a); i < (b); i++ )
#define Fors(i, sz) for( size_t i = 0; i < sz.size (); i++ )
#define Fore(it, x) for(typeof (x.begin()) it = x.begin(); it != x.end (); it++)
#define Set(a, s) memset(a, s, sizeof (a))
#define Read(r) freopen(r, "r", stdin)
#define Write(w) freopen(w, "w", stdout)

int dr [] = {-1, -1, 0, 1, 1, 1, 0, -1};
int dc [] = {0, 1, 1, 1, 0, -1, -1, -1};

using namespace std;

bool mark [N];
int primeList [100000];
int divisors [N];
int maxDivisor [N];

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

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

    int len = sqrt (N);

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

    int ind = 0;
    primeList [ind++] = 2;

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

int findDivisors (int n)
{
    int len = sqrt (n);
    int ind = 0;
    int power;
    int ret = 1;

    while ( primeList [ind]  <= len ) {
        power = 0;
        while ( n % primeList [ind] == 0 ) {
            power++;
            n /= primeList [ind];
        }
        ret *= power + 1;
        ind++;
    }

    if ( n > 1 ) ret *= 2;

    return ret;
}

int main ()
{
    sieve ();

    for ( int i = 1; i < N; i++ ) divisors [i] = findDivisors (i);

    maxDivisor [1] = 1;

    for ( int i = 2; i < N; i++ )
        maxDivisor [i] = divisors [i] >= divisors [maxDivisor [i - 1]] ? i : maxDivisor [i - 1];

    int testCase; scanf ("%d", &testCase);

    while ( testCase-- ) {
        int n; scanf ("%d", &n);
        printf ("%d\n", maxDivisor [n]);
    }

	return 0;
}

// @END_OF_SOURCE_CODE

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