POJ 1808 平方剩余

Posted 2020-10-10 Flowersea

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：

31 ll mod_pow(ll x, ll n, ll mod) {
32     int res = 1;
33     while (n) {
34         if (n & 1) res = res * x % mod;
35         x = x * x % mod;
36         n >>= 1;
37     }
38     return res;
39 }
40 
41 ll mod_sqr(ll a, ll n) {
42     ll b, k, i, x;
43     //if (n == 2) return a%n;
44     if(mod_pow(a, (n - 1) / 2, n) == 1) {
45         return 1;
46         if (n % 4 == 3) x = mod_pow(a, (n + 1) / 4, n);
47         else {
48             for (b = 1; mod_pow(b, (n - 1) / 2, n) == 1; b++);
49             i = (n - 1) / 2;
50             k = 0;
51             do {
52                 i /= 2; 
53                 k /= 2;
54                 if ((mod_pow(a, i, n)*mod_pow(b, k, n) + 1) % n == 0)
55                     k += (n - 1) / 2;
56             } while (i % 2 == 0);
57             x = mod_pow(a, (i + 1) / 2, n)*mod_pow(b, k / 2, n) % n;
58         }
59         if (x * 2 > n) x = n - x;
60     }
61     return -1;
62 }
63 
64 int main() {
65     ios::sync_with_stdio(false), cin.tie(0);
66     int T;
67     cin >> T;
68     rep(cas, 1, T + 1) {
69         ll a, p;
70         cin >> a >> p;
71         a = (a%p + p) % p;
72         cout << "Scenario #" << cas << ":" << endl;
73         cout << mod_sqr(a, p) << endl << endl;
74     }
75     return 0;
76 }