Poj 1808 + Ural 1132 square meters remaining

Link: http://poj.org/problem? Id = 1808

Http://acm.timus.ru/problem.aspx? Space = 1 & num = 1132

Question: both questions are template questions. The first is to determine whether there is square surplus, and the second is to calculate the square surplus.

Train of Thought: The square surplus is given a, n (n is the prime number) Ask x ^ 2 then a (mod n) whether there is a solution, you can use a ^ (n-1)/2) when mod n is 1, it is a quadratic residue, and-1 is a non-quadratic residue.

MATERIALS: http://blog.csdn.net/acdreamers/article/details/10182281

The references are basically correct. Note that the same and equal relationships are distinguished.

Code:

LL w;LL pow_mod(LL aa,LL ii,LL nn){    if(ii==0)        return 1%nn;    LL temp=pow_mod(aa,ii>>1,nn);    temp=temp*temp%nn;    if(ii&1)        temp=temp*aa%nn;    return temp;}struct comp{    LL r,i;};comp multi(comp a, comp b, LL m)    {        comp ans;        ans.r = (a.r * b.r % m + a.i * b.i % m * w % m) % m;        ans.i = (a.r * b.i % m + a.i * b.r% m) % m;        return ans;    }    comp pow_mod(comp a, LL b,LL m)    {        comp ans;        ans.r = 1;        ans.i = 0;        while(b)        {            if(b & 1)            {                ans = multi(ans, a, m);                b--;            }            b >>= 1;            a = multi(a, a, m);        }        return ans;    }LL Legendre(LL a, LL p){    return pow_mod(a, (p-1)>>1, p);}LL Quadratic_residue(LL n,LL p){    if(p==2)        return 1;    if (Legendre(n, p) + 1 == p)        return -1;    LL a = -1, t;    while(1)    {        a = rand() % p;        t = a * a - n;        w=(t%p+p)%p;        if(Legendre(w, p) + 1 == p) break;    }    comp temp;    temp.r=a;    temp.i=1;    comp ans;    ans=pow_mod(temp,(p+1)>>1,p);    return ans.r;}