SPOJ ROUND 1A - Số gần nguyên tố

ROUD1APROA.cpp

#include <bits/stdc++.h>

#define _for(i,a,b) for(int i=(a),_b_=(b),_d_=(a<b?1:-1);i!=_b_;i+=_d_)
#define FOR(i,a,b) for(int i = a; i <= b; i++)
#define _it(i,v) for (typeof((v).begin()) i = (v).begin(); i != (v).end(); ++i)
#define _all(v) v.begin(), v.end()

#define DEBUG(x) { cout << #x << " = " << x << endl; }
#define sqr(x) ((x)*(x))
 
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
template<typename T> vector<T> &operator += (vector<T> &v, T x) {v.push_back(x);return v;}
 
const int base = 1000000000; const int base_digits = 9;
struct bigint {
    vector<int> a; int sign;
 
    bigint() :
        sign(1) {
    }
 
    bigint(long long v) {
        *this = v;
    }
 
    bigint(const string &s) {
        read(s);
    }
 
    void operator=(const bigint &v) {
        sign = v.sign;
        a = v.a;
    }
 
    void operator=(long long v) {
        sign = 1;
        if (v < 0)
            sign = -1, v = -v;
        for (; v > 0; v = v / base)
            a.push_back(v % base);
    }
 
    bigint operator+(const bigint &v) const {
        if (sign == v.sign) {
            bigint res = v;
 
            for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
                if (i == (int) res.a.size())
                    res.a.push_back(0);
                res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
                carry = res.a[i] >= base;
                if (carry)
                    res.a[i] -= base;
            }
            return res;
        }
        return *this - (-v);
    }
 
    bigint operator-(const bigint &v) const {
        if (sign == v.sign) {
            if (abs() >= v.abs()) {
                bigint res = *this;
                for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
                    res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
                    carry = res.a[i] < 0;
                    if (carry)
                        res.a[i] += base;
                }
                res.trim();
                return res;
            }
            return -(v - *this);
        }
        return *this + (-v);
    }
 
    void operator*=(int v) {
        if (v < 0)
            sign = -sign, v = -v;
        for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
            if (i == (int) a.size())
                a.push_back(0);
            long long cur = a[i] * (long long) v + carry;
            carry = (int) (cur / base);
            a[i] = (int) (cur % base);
            //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
        }
        trim();
    }
 
    bigint operator*(int v) const {
        bigint res = *this;
        res *= v;
        return res;
    }
 
    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
        int norm = base / (b1.a.back() + 1);
        bigint a = a1.abs() * norm;
        bigint b = b1.abs() * norm;
        bigint q, r;
        q.a.resize(a.a.size());
 
        for (int i = a.a.size() - 1; i >= 0; i--) {
            r *= base;
            r += a.a[i];
            int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
            int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
            int d = ((long long) base * s1 + s2) / b.a.back();
            r -= b * d;
            while (r < 0)
                r += b, --d;
            q.a[i] = d;
        }
 
        q.sign = a1.sign * b1.sign;
        r.sign = a1.sign;
        q.trim();
        r.trim();
        return make_pair(q, r / norm);
    }
 
    bigint operator/(const bigint &v) const {
        return divmod(*this, v).first;
    }
 
    bigint operator%(const bigint &v) const {
        return divmod(*this, v).second;
    }
 
    void operator/=(int v) {
        if (v < 0)
            sign = -sign, v = -v;
        for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
            long long cur = a[i] + rem * (long long) base;
            a[i] = (int) (cur / v);
            rem = (int) (cur % v);
        }
        trim();
    }
 
    bigint operator/(int v) const {
        bigint res = *this;
        res /= v;
        return res;
    }
 
    int operator%(int v) const {
        if (v < 0)
            v = -v;
        int m = 0;
        for (int i = a.size() - 1; i >= 0; --i)
            m = (a[i] + m * (long long) base) % v;
        return m * sign;
    }
 
    void operator+=(const bigint &v) {
        *this = *this + v;
    }
    void operator-=(const bigint &v) {
        *this = *this - v;
    }
    void operator*=(const bigint &v) {
        *this = *this * v;
    }
    void operator/=(const bigint &v) {
        *this = *this / v;
    }
 
    bool operator<(const bigint &v) const {
        if (sign != v.sign)
            return sign < v.sign;
        if (a.size() != v.a.size())
            return a.size() * sign < v.a.size() * v.sign;
        for (int i = a.size() - 1; i >= 0; i--)
            if (a[i] != v.a[i])
                return a[i] * sign < v.a[i] * sign;
        return false;
    }
 
    bool operator>(const bigint &v) const {
        return v < *this;
    }
    bool operator<=(const bigint &v) const {
        return !(v < *this);
    }
    bool operator>=(const bigint &v) const {
        return !(*this < v);
    }
    bool operator==(const bigint &v) const {
        return !(*this < v) && !(v < *this);
    }
    bool operator!=(const bigint &v) const {
        return *this < v || v < *this;
    }
 
    void trim() {
        while (!a.empty() && !a.back())
            a.pop_back();
        if (a.empty())
            sign = 1;
    }
 
    bool isZero() const {
        return a.empty() || (a.size() == 1 && !a[0]);
    }
 
    bigint operator-() const {
        bigint res = *this;
        res.sign = -sign;
        return res;
    }
 
    bigint abs() const {
        bigint res = *this;
        res.sign *= res.sign;
        return res;
    }
 
    long long longValue() const {
        long long res = 0;
        for (int i = a.size() - 1; i >= 0; i--)
            res = res * base + a[i];
        return res * sign;
    }
 
    friend bigint gcd(const bigint &a, const bigint &b) {
        return b.isZero() ? a : gcd(b, a % b);
    }
    friend bigint lcm(const bigint &a, const bigint &b) {
        return a / gcd(a, b) * b;
    }
 
    void read(const string &s) {
        sign = 1;
        a.clear();
        int pos = 0;
        while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
            if (s[pos] == '-')
                sign = -sign;
            ++pos;
        }
        for (int i = s.size() - 1; i >= pos; i -= base_digits) {
            int x = 0;
            for (int j = max(pos, i - base_digits + 1); j <= i; j++)
                x = x * 10 + s[j] - '0';
            a.push_back(x);
        }
        trim();
    }
 
    friend istream& operator>>(istream &stream, bigint &v) {
        string s;
        stream >> s;
        v.read(s);
        return stream;
    }
 
    friend ostream& operator<<(ostream &stream, const bigint &v) {
        if (v.sign == -1)
            stream << '-';
        stream << (v.a.empty() ? 0 : v.a.back());
        for (int i = (int) v.a.size() - 2; i >= 0; --i)
            stream << setw(base_digits) << setfill('0') << v.a[i];
        return stream;
    }
 
    static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
        vector<long long> p(max(old_digits, new_digits) + 1);
        p[0] = 1;
        for (int i = 1; i < (int) p.size(); i++)
            p[i] = p[i - 1] * 10;
        vector<int> res;
        long long cur = 0;
        int cur_digits = 0;
        for (int i = 0; i < (int) a.size(); i++) {
            cur += a[i] * p[cur_digits];
            cur_digits += old_digits;
            while (cur_digits >= new_digits) {
                res.push_back(int(cur % p[new_digits]));
                cur /= p[new_digits];
                cur_digits -= new_digits;
            }
        }
        res.push_back((int) cur);
        while (!res.empty() && !res.back())
            res.pop_back();
        return res;
    }
 
    typedef vector<long long> vll;
 
    static vll karatsubaMultiply(const vll &a, const vll &b) {
        int n = a.size();
        vll res(n + n);
        if (n <= 32) {
            for (int i = 0; i < n; i++)
                for (int j = 0; j < n; j++)
                    res[i + j] += a[i] * b[j];
            return res;
        }
 
        int k = n >> 1;
        vll a1(a.begin(), a.begin() + k);
        vll a2(a.begin() + k, a.end());
        vll b1(b.begin(), b.begin() + k);
        vll b2(b.begin() + k, b.end());
 
        vll a1b1 = karatsubaMultiply(a1, b1);
        vll a2b2 = karatsubaMultiply(a2, b2);
 
        for (int i = 0; i < k; i++)
            a2[i] += a1[i];
        for (int i = 0; i < k; i++)
            b2[i] += b1[i];
 
        vll r = karatsubaMultiply(a2, b2);
        for (int i = 0; i < (int) a1b1.size(); i++)
            r[i] -= a1b1[i];
        for (int i = 0; i < (int) a2b2.size(); i++)
            r[i] -= a2b2[i];
 
        for (int i = 0; i < (int) r.size(); i++)
            res[i + k] += r[i];
        for (int i = 0; i < (int) a1b1.size(); i++)
            res[i] += a1b1[i];
        for (int i = 0; i < (int) a2b2.size(); i++)
            res[i + n] += a2b2[i];
        return res;
    }
 
    bigint operator*(const bigint &v) const {
        vector<int> a6 = convert_base(this->a, base_digits, 6);
        vector<int> b6 = convert_base(v.a, base_digits, 6);
        vll a(a6.begin(), a6.end());
        vll b(b6.begin(), b6.end());
        while (a.size() < b.size())
            a.push_back(0);
        while (b.size() < a.size())
            b.push_back(0);
        while (a.size() & (a.size() - 1))
            a.push_back(0), b.push_back(0);
        vll c = karatsubaMultiply(a, b);
        bigint res;
        res.sign = sign * v.sign;
        for (int i = 0, carry = 0; i < (int) c.size(); i++) {
            long long cur = c[i] + carry;
            res.a.push_back((int) (cur % 1000000));
            carry = (int) (cur / 1000000);
        }
        res.a = convert_base(res.a, 6, base_digits);
        res.trim();
        return res;
    }
};
// end of big int algorithm

// __gcd algorithm
ll gcd(ll a, ll b) {
    return b ? gcd(b, a%b) : a; 
}
// end __gcd

// power modulo algorithm
ll power_modulo(ll a, ll base, ll mod) {
    if(!base) { return 1; }
    ll temp = power_modulo(a, base / 2, mod);
    if(base & 1) return a * sqr(temp) % mod;
    return sqr(temp) % mod;
}
// end power modulo

// quick sort algorithm
void quick_sort(int A[], int l, int r) {
    int i = l, j = r;
    int pivot = A[(l + r) / 2];
    if(l >= r) return;
    while(i <= j) {
        while(A[i] < pivot) i++;
    while(A[j] > pivot) j--;
    if(i <= j) swap(A[i++], A[j--]);
    }
    quick_sort(A, l, j); quick_sort(A, i, r);
}
// End quick sort algorithm

// int_To_String algorithm
string int_To_String(int i)
{
    stringstream ss;
    ss << i;
    return ss.str();
}

int string_To_int(string s) {
    return atoi(s.c_str());
}
// end int_To_String algorithm

// KMP algorithm
int KMP(string s, string t) {
    int n = s.length(), m = t.length();
    int* pit = new int[m+1];
    if(m >= 0) pit[0] = 0;
    if(m >= 1) pit[1] = 0;
    FOR(i, 2, m) { 
        for(int j = pit[i-1]; ;j = pit[j]) {
            if(t[j] == t[i-1]) { pit[i] = j + 1; break; }
            if(j == 0) { pit[i] = 0; break; }
        }
    }
        for(int i = 0, j = 0; i < n; ) {
        if(s[i] == t[j]) {
            i++; j++;
            if(j == m) return i - m;
        } else if(j > 0) {
            j = pit[j];
        } else i++;
    } delete[] pit; return -1;
}
// end KMP algorithm

string s;
bigint B[105];
 
void init() {
	B[0] = 1;
	B[1] = 45;
	bigint b(10);
	FOR(i,2,103){
		B[i] = B[1]*b*i;
		b*=10;
	}
}
void solve() {
	bigint b=1, res = 0, n = s;
	FOR(i,0, s.size()-1) b*=10;
	FOR(i,0,s.size()) {
		int k = s[i]-'0'; // chu so dau tien
		if (s.size()-i > 1){
			res += b*k*(k-1)/2+B[s.size()-i-1]*k;
			res += (n%b+1)*k;
		} else
			res += k*(k+1)/2;
		n = n%b;
		b /= 10;
	}
	cout << res << '\n';
}

bool is_prime(int n) {
    int cur = sqrt(n);
    FOR(i,2,cur) {
        if(n%i==0) return false;
    }
    return true;
}
 
int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    // init();
    // cin >> s;
    // solve();

    ll n, x;
    cin >> n;
    while(n--) {
        cin >> x;
        ll t = sqrt(x);
        if(x == 1 || sqr(t) != x || !is_prime(t)) {
            cout << "NO\n";
        } else {
            cout << "YES\n";
        }
    }   

    return 0;
}