POJ 1808 平方剩余

链接：

http://poj.org/problem?id=1808

题意：

判断x^2同余a(modn)是否存在

题解：

平方剩余

代码：

ll mod_pow(ll x, ll n, ll mod) {
    int res = 1;
    while (n) {
        if (n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}

ll mod_sqr(ll a, ll n) {
    ll b, k, i, x;
    //if (n == 2) return a%n;
    if(mod_pow(a, (n - 1) / 2, n) == 1) {
        return 1;
        if (n % 4 == 3) x = mod_pow(a, (n + 1) / 4, n);
        else {
            for (b = 1; mod_pow(b, (n - 1) / 2, n) == 1; b++);
            i = (n - 1) / 2;
            k = 0;
            do {
                i /= 2; 
                k /= 2;
                if ((mod_pow(a, i, n)*mod_pow(b, k, n) + 1) % n == 0)
                    k += (n - 1) / 2;
            } while (i % 2 == 0);
            x = mod_pow(a, (i + 1) / 2, n)*mod_pow(b, k / 2, n) % n;
        }
        if (x * 2 > n) x = n - x;
    }
    return -1;
}

int main() {
    ios::sync_with_stdio(false), cin.tie(0);
    int T;
    cin >> T;
    rep(cas, 1, T + 1) {
        ll a, p;
        cin >> a >> p;
        a = (a%p + p) % p;
        cout << "Scenario #" << cas << ":" << endl;
        cout << mod_sqr(a, p) << endl << endl;
    }
    return 0;
}