almostperfect.cpp

/**
 *  @brief   Kattis - NAME 
 *  @author  Donald Dong (@donaldong)
 *  @date    MM/DD/YYYY
 *  
 *  + Prime Factorization
 */

#include <algorithm>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <iostream>
#include <map>
#include <queue>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;

typedef unsigned int uint;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
#define hmap unordered_map
#define hset unordered_set
#define pq priority_queue
#define pb push_back
#define mp make_pair
#define putchar putchar_unlocked
#define rep(i, s, e) for (size_t i = s, fe__ = e; i < fe__; ++i)

inline void scan(int&);
inline void scan(ll&);
inline void print(uint);
inline void print(ull);
inline void print(string&);

hmap<int, int> prime_factors(int n) {
    hmap<int, int> F;
    while (n % 2 == 0) {
        n /= 2;
        ++F[2];
    }
    for (int i = 3; i * i <= n; i += 2) {
        while (n % i == 0) {
            n /= i;
            ++F[i];
        }
    }
    if (n > 2) ++F[n];
    return F;
}

int solve(int n, hmap<int, int> &F) {
    ull res = 1;
    for (auto &f : F) {
        res *= pow(f.first, f.second + 1) - 1;
        res /= f.first - 1;
    }
    res -= n;
    if (res == n) return 0;
    int a = res;
    a = abs(a - n);
    if (a <= 2) return 1;
    return -1;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n;
    while (true) {
        scan(n);
        if (!n) break;
        auto F = prime_factors(n);
        int res = solve(n, F);
        if (res == 0) cout << n << " perfect" << endl;
        else if (res == 1) cout << n << " almost perfect" << endl;
        else cout << n << " not perfect" << endl;
    }
    return 0;
}

inline void scan(int &number) {
    bool negative = false;
    int c;
    number = 0;
    c = getchar();
    if (c=='-') {
        negative = true;
        c = getchar();
    }
    for (; (c>47 && c<58); c=getchar()) number = number *10 + c - 48;
    if (negative) number *= -1;
}

inline void scan(ll &number) {
    bool negative = false;
    int c;
    number = 0;
    c = getchar();
    if (c=='-') {
        negative = true;
        c = getchar();
    }
    for (; (c>47 && c<58); c=getchar()) number = number *10 + c - 48;
    if (negative) number *= -1;
}

inline void print(uint n) {
    if (n == 0) {
        putchar('0');
        return;
    }
    char buf[11];
    int i = 10;
    while (n) {
        buf[i--] = n % 10 + '0';
        n /= 10;
    }
    while (i < 10) putchar(buf[++i]);
}

inline void print(ull n) {
    if (n == 0) {
        putchar('0');
        return;
    }
    char buf[20];
    int i = 19;
    while (n) {
        buf[i--] = n % 10 + '0';
        n /= 10;
    }
    while (i < 19) putchar(buf[++i]);
}

inline void print(string &s) {
    rep(i, 0, s.length()) putchar(s[i]);
}