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题目链接:uva 1426 - Discrete Square Roots
题目大意:给出X,N,R,求出所有满足的r,使得r2≡x%N,并且R是一个其中的解。
解题思路:
#include <cstdio>
#include <cstring>
#include <cmath>
#include <set>
#include <algorithm>
using namespace std;
typedef long long ll;
ll X, N, R;
set<ll> ans;
void exgcd (ll a, ll b, ll& d, ll& x, ll& y) {
if (b == 0) {
d = a;
x = 1;
y = 0;
} else {
exgcd (b, a%b, d, y, x);
y -= (a/b) * x;
}
}
void solve (ll A, ll B, ll C) {
ll d, x, y;
exgcd(A, B, d, x, y);
if (C % d)
return;
x = x * C / d;
x = (x % (B/d) + (B/d))%(B/d);
ll s = x * A - C / 2;
ll k = A * B / d;
for (ll i = s; i < N; i += k)
if (i >= 0)
ans.insert(i);
}
int main () {
int cas = 1;
while (scanf("%lld%lld%lld", &X, &N, &R) == 3 && X + N + R) {
ans.clear();
ll m = sqrt(N+0.5);
for (ll i = 1; i <= m; i++) {
if (N%i)
continue;
solve(i, N/i, 2*R);
solve(N/i, i, 2*R);
}
printf("Case %d:", cas++);
for (set<ll>::iterator i = ans.begin(); i != ans.end(); i++)
printf(" %lld", *i);
printf("\n");
}
return 0;
}
uva 1426 - Discrete Square Roots(拓展欧几里得),布布扣,bubuko.com
uva 1426 - Discrete Square Roots(拓展欧几里得)
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原文地址:http://blog.csdn.net/keshuai19940722/article/details/36931617