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OJ-Problems-Source/.ACM-Templates/TXTs/数论模板.txt

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2016-11-22 09:38:35 +08:00
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\begin{itemize}
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\item line2/3 <20>ߣ<EFBFBD><DFA3><EFBFBD>ʾΪ<CABE><CEAA><EFBFBD><EFBFBD>+<2B><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>߾<EFBFBD><DFBE>ʹ<EFBFBD><CDB4>㣬<EFBFBD><E3A3AC><EFBFBD>߽<EFBFBD><DFBD><EFBFBD><EFBFBD>߶<EFBFBD><DFB6>߶ν<DFB6><CEBD><EFBFBD><EFBFBD>߶ν<DFB6><CEBD><EFBFBD><EFBFBD>˻<EFBFBD><CBBB><EFBFBD>2ά<32><CEAC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>߾<EFBFBD><DFBE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ԣ<EFBFBD>3ά<33><CEAC><EFBFBD><EFBFBD>ƽ<EFBFBD>з<EFBFBD><D0B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>ԣ<EFBFBD><D4A3><EFBFBD><EFBFBD>ߵ<EFBFBD>ͶӰ<CDB6><D3B0>ͬ<EFBFBD>㣩
\item face3 <20>棬<EFBFBD><E6A3AC>ʾΪ<CABE><CEAA><EFBFBD><EFBFBD>+<2B><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʹ<EFBFBD><CDB4>㣬<EFBFBD><E3A3AC><EFBFBD>潻<EFBFBD><E6BDBB><EFBFBD><EFBFBD><EFBFBD>潻
\item circle2 Բ<><D4B2><EFBFBD><EFBFBD>ʾΪԲ<CEAA><D4B2>+<2B>뾶<EFBFBD><EBBEB6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Բ<EFBFBD><D4B2><EFBFBD><EFBFBD>ԲԲ<D4B2><D4B2><EFBFBD><EFBFBD><EFBFBD>㵽Բ<E3B5BD><D4B2><EFBFBD>е㣬Բ<E3A3AC><D4B2>Բ<EFBFBD>Ĺ<EFBFBD><C4B9><EFBFBD><EFBFBD>ߣ<EFBFBD><DFA3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>е㣬<D0B5><E3A3AC><EFBFBD><EFBFBD>ֱ<EFBFBD><D6B1><EFBFBD><EFBFBD><EFBFBD>˵<EFBFBD>Ϊ<EFBFBD><CEAA><EFBFBD>е㣬<D0B5><E3A3AC><EFBFBD>򷵻<EFBFBD>ֱ<EFBFBD>߶˵<DFB6>Ϊ<EFBFBD>е㣩
\item convex2 ͹<><CDB9><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>㲻<EFBFBD>ϸ<EFBFBD><CFB8><EFBFBD>͹<EFBFBD><CDB9><EFBFBD>ڣ<EFBFBD><DAA3><EFBFBD><EFBFBD><EFBFBD>͹<EFBFBD><CDB9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ˮƽ<CBAE><C6BD>Graham<61><6D>͹<EFBFBD><CDB9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ƽ<EFBFBD>潻<EFBFBD><E6BDBB><EFBFBD><EFBFBD>ƽ<EFBFBD><C6BD>Ϊ<EFBFBD><CEAA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ƽ<EFBFBD>棩
\end{itemize}
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#include <cstdio>
#include <cmath>
#include <vector>
#include <deque>
#include <algorithm>
const double eps = 1e-13;
const double pi = 3.14159265358979324;
struct point2
{
double x, y;
point2& operator += (point2 a)
{
x+=a.x, y+=a.y;
return *this;
}
point2& operator -= (point2 a)
{
x-=a.x, y-=a.y;
return *this;
}
point2& operator *= (double a)
{
x*=a, y*=a;
return *this;
}
point2& operator /= (double a)
{
x/=a, y/=a;
return *this;
}
};
point2 operator + (point2 a, point2 b)
{
point2 c(a);
c += b;
return c;
}
point2 operator - (point2 a, point2 b)
{
point2 c(a);
c -= b;
return c;
}
point2 operator * (point2 a, double b)
{
point2 c(a);
c *= b;
return c;
}
point2 operator * (double a, point2 b)
{
point2 c(b);
c *= a;
return c;
}
point2 operator / (point2 a, double b)
{
point2 c(a);
c /= b;
return c;
}
double operator * (point2 a, point2 b)
{
return a.x*b.x+a.y*b.y;
}
double operator % (point2 a, point2 b)
{
return a.x*b.y-a.y*b.x;
}
double dis(point2 a)
{
return sqrt(a.x * a.x + a.y * a.y);
}
double arg(point2 a)
{
return atan2(a.y, a.x);
}
point2 rotate(point2 a, double th)
{
point2 b;
b.x = a.x * cos(th) - a.y * sin(th);
b.y = a.x * sin(th) + a.y * cos(th);
return b;
}
int parallel(point2 a, point2 b)
{
return a * a < eps * eps || b * b < eps * eps
|| (a % b) * (a % b) / ((a * a) * (b * b)) < eps * eps;
}
int perpend(point2 a, point2 b)
{
return a * a < eps * eps || b * b < eps * eps
|| (a * b) * (a * b) / ((a * a) * (b * b)) < eps * eps;
}
struct line2
{
point2 a, s;
};
struct circle2
{
point2 a;
double r;
};
double point_line_dis(point2 a, line2 b, point2 *res = NULL)
{
point2 p;
p = b.a + ((a - b.a) * b.s) / (b.s * b.s) * b.s;
if (res != NULL) *res = p;
return dis(a - p);
}
int line_line_cross(line2 a, line2 b, point2 *res = NULL)
{
if (parallel(a.s, b.s))
if (parallel(b.a - a.a, a.s))
return -1;
else
return 0;
double k1 = (b.a - a.a) % b.s / (a.s % b.s);
if (res != NULL) *res = a.a + k1 * a.s;
return 1;
}
int segment_segment_cross(line2 a, line2 b, point2 *res = NULL)
{
if (a.s * a.s < eps * eps && b.s * b.s < eps * eps)
if ((b.a - a.a) * (b.a - a.a) < eps * eps)
{
if (res != NULL) *res = a.a;
return 1;
}
else
return 0;
if (parallel(a.s, b.s) && parallel(b.a - a.a, a.s) && parallel(a.a - b.a, b.s))
{
double y1, y2, y3, y4;
point2 y1p = a.a, y2p = a.a + a.s, y3p = b.a, y4p = b.a + b.s;
if (std::abs(a.s.x) < std::abs(a.s.y) || std::abs(b.s.x) < std::abs(b.s.y))
y1 = y1p.y, y2 = y2p.y, y3 = y3p.y, y4 = y4p.y;
else
y1 = y1p.x, y2 = y2p.x, y3 = y3p.x, y4 = y4p.x;
if (y1 > y2) std::swap(y1, y2), std::swap(y1p, y2p);
if (y3 > y4) std::swap(y3, y4), std::swap(y3p, y4p);
if (y2 - y1 < y4 - y3) std::swap(y1, y3), std::swap(y1p, y3p), std::swap(y2, y4), std::swap(y2p, y4p);
if (y3 > y2 + (y2 - y1) * eps || y4 < y1 - (y2 - y1) * eps)
return 0;
else if (fabs(y3 - y2) < (y2 - y1) * eps || fabs(y3 - y4) < eps)
{
if (res != NULL) *res = y3p;
return 1;
}
else if (fabs(y4 - y1) < (y2 - y1) * eps || fabs(y1 - y2) < eps)
{
if (res != NULL) *res = y1p;
return 1;
}
else
return -1;
}
else
{
double k1 = (b.a - a.a) % a.s, k2 = (b.a + b.s - a.a) % a.s;
k1 /= a.s * a.s, k2 /= a.s * a.s;
double k3 = (a.a - b.a) % b.s, k4 = (a.a + a.s - b.a) % b.s;
k3 /= b.s * b.s, k4 /= b.s * b.s;
int ret = (k1 < eps && k2 > -eps || k1 > -eps && k2 < eps)
&& (k3 < eps && k4 > -eps || k3 > -eps && k4 < eps);
if (ret) line_line_cross(a, b, res);
return ret;
}
}
int line_circle_cross(line2 a, circle2 b, point2 *res1 = NULL, point2 *res2 = NULL)
{
point2 p;
double d = point_line_dis(b.a, a, &p);
if (d / b.r > 1 + eps)
return 0;
else if (d / b.r > 1 - eps)
{
if (res1 != NULL) *res1 = p;
return 1;
}
else
{
d = sqrt(b.r * b.r - d * d) / dis(a.s);
if (res1 != NULL) *res1 = p + d * a.s;
if (res2 != NULL) *res2 = p - d * a.s;
return 2;
}
}
int circle_circle_cross(circle2 a, circle2 b, point2 *res1 = NULL, point2 *res2 = NULL)
{
double d = dis(a.a - b.a);
point2 u = (b.a - a.a) / d;
if (d / (a.r + b.r) > 1 + eps)
return 0;
else if (d / (a.r + b.r) > 1 - eps)
{
if (res1 != NULL) *res1 = a.a + u * a.r;
return 1;
}
else if ((d - fabs(a.r - b.r)) / (a.r + b.r) > eps)
{
double th = acos((a.r * a.r + d * d - b.r * b.r) / (2 * a.r * d));
if (res1 != NULL) *res1 = a.a + rotate(u * a.r, th);
if (res2 != NULL) *res2 = a.a + rotate(u * a.r, -th);
return 2;
}
else if ((d - fabs(a.r - b.r)) / (a.r + b.r) > -eps)
{
if (a.r / b.r < 1 - eps)
{
if (res1 != NULL) *res1 = b.a - u * b.r;
return 1;
}
else if (a.r / b.r > 1 + eps)
{
if (res1 != NULL) *res1 = a.a + u * a.r;
return 1;
}
else return -1;
}
else
return 0;
}
int point_circle_tangent(point2 a, circle2 b, point2 *res1 = NULL, point2 *res2 = NULL)
{
double d = dis(a - b.a);
point2 u = (a - b.a) / d;
if (d / b.r > 1 + eps)
{
double th = acos(b.r / d);
if (res1 != NULL) *res1 = b.a + rotate(u * b.r, th);
if (res2 != NULL) *res2 = b.a + rotate(u * b.r, -th);
return 2;
}
else if (d / b.r > 1 - eps)
{
if (res1 != NULL) *res1 = a;
return 1;
}
else
return 0;
}
int circle_circle_tangent(circle2 a, circle2 b, line2 *reso1 = NULL, line2 *reso2 = NULL, line2 *resi1 = NULL, line2 *resi2 = NULL)
{
double d = dis(a.a - b.a);
point2 u = (b.a - a.a) / d;
int cnt = 0;
if ((d - fabs(a.r - b.r)) / (a.r + b.r) > eps)
{
double th = acos((a.r - b.r) / d);
if (reso1 != NULL)
{
reso1->a = a.a + rotate(u * a.r, th);
reso1->s = b.a + rotate(u * b.r, th) - reso1->a;
}
if (reso2 != NULL)
{
reso2->a = a.a + rotate(u * a.r, -th);
reso2->s = b.a + rotate(u * b.r, -th) - reso2->a;
}
cnt += 2;
}
else if ((d - fabs(a.r - b.r)) / (a.r + b.r) > -eps)
{
if (a.r / b.r < 1 - eps)
{
if (reso1 != NULL)
{
reso1->a = b.a - u * b.r;
reso1->s = rotate(u, pi / 2);
}
cnt++;
}
else if (a.r / b.r > 1 + eps)
{
if (reso1 != NULL)
{
reso1->a = a.a + u * a.r;
reso1->s = rotate(u, pi / 2);
}
cnt++;
}
else return -1;
}
if (d / (a.r + b.r) > 1 + eps)
{
double th = acos((a.r + b.r) / d);
if (resi1 != NULL)
{
resi1->a = a.a + rotate(u * a.r, th);
resi1->s = b.a - rotate(u * b.r, th) - resi1->a;
}
if (resi2 != NULL)
{
resi2->a = a.a + rotate(u * a.r, -th);
resi2->s = b.a - rotate(u * b.r, -th) - resi2->a;
}
cnt += 2;
}
else if (d / (a.r + b.r) > 1 - eps)
{
if (resi1 != NULL)
{
resi1->a = a.a + u * a.r;
resi1->s = rotate(u, pi / 2);
}
cnt++;
}
return cnt;
}
typedef std::vector<point2> convex2;
double area(const convex2 &a)
{
double s = 0;
for (int i = 0; i < a.size(); i++)
s += a[i] % a[(i+1)%a.size()];
return fabs(s)/2;
}
int point_convex_inside(point2 a, const convex2 &b)
{
double sum = 0;
for (int i = 0; i < b.size(); i++)
sum += fabs((b[i] - a) % (b[(i+1)%b.size()] - a));
return fabs(sum / (2*area(b)) - 1) < eps;
}
int line_convex_cross(line2 a, const convex2 &b, point2 *res1 = NULL, point2 *res2 = NULL)
{
int cnt = 0;
for (int i = 0; i < b.size(); i++)
{
line2 ltmp;
point2 ptmp;
ltmp.a = b[i], ltmp.s = b[(i+1)%b.size()] - b[i];
int flag = line_line_cross(a, ltmp, &ptmp);
if (flag == -1) return -1;
if (flag == 0) continue;
double k = (ptmp - ltmp.a) * ltmp.s / (ltmp.s * ltmp.s);
if (k < eps || k > 1+eps) continue;
if (cnt == 0 && res1 != NULL) *res1 = ptmp;
else if (cnt == 1 && res2 != NULL) *res2 = ptmp;
cnt++;
}
return cnt;
}
int convex_gen_cmp(point2 a, point2 b)
{
return a.y < b.y - eps || fabs(a.y - b.y) < eps && a.x < b.x - eps;
}
int convex_gen(const convex2 &a, convex2 &b)
{
std::deque<point2> q;
convex2 t(a);
std::sort(t.begin(), t.end(), convex_gen_cmp);
q.push_back(t[0]), q.push_back(t[1]);
for (int i = 2; i < t.size(); i++)
{
while (q.size() > 1)
{
point2 p1 = t[i]-q[q.size()-1], p2 = q[q.size()-1]-q[q.size()-2];
if (p1 % p2 > 0 || parallel(p1, p2)) q.pop_back();
else break;
}
q.push_back(t[i]);
}
int pretop = q.size();
for (int i = t.size()-1; i >= 0; i--)
{
while (q.size() > pretop)
{
point2 p1 = t[i]-q[q.size()-1], p2 = q[q.size()-1]-q[q.size()-2];
if (p1 % p2 > 0 || parallel(p1, p2)) q.pop_back();
else break;
}
q.push_back(t[i]);
}
q.pop_back();
if (q.size() < 3)
{
b.clear();
return 0;
}
b.clear();
for (int i = 0; i < q.size(); i++) b.push_back(q[i]);
return 1;
}
int halfplane_cross_cmp(line2 a, line2 b)
{
double c1 = arg(a.s), c2 = arg(b.s);
return c1 < c2-eps || fabs(c1-c2) < eps && b.s % (a.a - b.a) / dis(b.s) > eps;
}
int halfplane_cross(const std::vector<line2> &a, convex2 &b)
{
std::vector<line2> t(a);
std::sort(t.begin(), t.end(), halfplane_cross_cmp);
int j = 0;
for (int i = 0; i < t.size(); i++)
if (!i || arg(t[i].s) > arg(t[i-1].s) + eps) t[j++] = t[i];
if (j > 0 && arg(t[j].s) > arg(t[0].s) + 2*pi - eps) j--;
t.resize(j);
std::deque<line2> q;
q.push_back(t[0]), q.push_back(t[1]);
point2 p;
for (int i = 2, k = 0; i < t.size(); i++)
{
for (; k < q.size() && t[i].s % q[k].s > 0; k++);
point2 s1 = q[q.size()-1].s, s2 = q[0].s;
if (k > 0 && k < q.size() && s1 % s2 > 0 && !parallel(s1, s2))
{
line_line_cross(q[k], q[k-1], &p);
double r1 = t[i].s % (p - t[i].a) / dis(t[i].s);
line_line_cross(q[0], q[q.size()-1], &p);
double r2 = t[i].s % (p - t[i].a) / dis(t[i].s);
if (r1 < eps && r2 < eps)
{
b.clear();
return 0;
}
else if (r1 > -eps && r2 > -eps)
continue;
}
while (q.size() > 1)
{
line_line_cross(q[q.size()-1], q[q.size()-2], &p);
if (t[i].s % (p - t[i].a) / dis(t[i].s) < eps)
{
q.pop_back();
if (k == q.size()) k--;
}
else break;
}
while (q.size() > 1)
{
line_line_cross(q[0], q[1], &p);
if (t[i].s % (p - t[i].a) / dis(t[i].s) < eps)
{
q.pop_front();
k--;
if (k < 0) k = 0;
}
else break;
}
q.push_back(t[i]);
}
b.clear();
for (int i = 0; i < q.size(); i++)
{
line_line_cross(q[i], q[(i+1)%q.size()], &p);
b.push_back(p);
}
return 1;
}
struct point3
{
double x, y, z;
point3& operator += (point3 a)
{
x+=a.x,y+=a.y,z+=a.z;
return *this;
}
point3& operator -= (point3 a)
{
x-=a.x,y-=a.y,z-=a.z;
return *this;
}
point3& operator *= (double a)
{
x*=a, y*=a, z*=a;
return *this;
}
point3& operator /= (double a)
{
x/=a, y/=a, z/=a;
return *this;
}
};
point3 operator + (point3 a, point3 b)
{
point3 c(a);
c += b;
return c;
}
point3 operator - (point3 a, point3 b)
{
point3 c(a);
c -= b;
return c;
}
point3 operator * (point3 a, double b)
{
point3 c(a);
c *= b;
return c;
}
point3 operator * (double a, point3 b)
{
point3 c(b);
c *= a;
return c;
}
point3 operator / (point3 a, double b)
{
point3 c(a);
c /= b;
return c;
}
double operator * (point3 a, point3 b)
{
return a.x*b.x+a.y*b.y+a.z*b.z;
}
point3 operator % (point3 a, point3 b)
{
point3 c;
c.x = a.y * b.z - a.z * b.y;
c.y = a.z * b.x - a.x * b.z;
c.z = a.x * b.y - a.y * b.x;
return c;
}
double dis(point3 a)
{
return sqrt(a.x * a.x + a.y * a.y + a.z * a.z);
}
int parallel(point3 a, point3 b)
{
return a * a < eps * eps || b * b < eps * eps
|| (a % b) * (a % b) / ((a * a) * (b * b)) < eps * eps;
}
int perpend(point3 a, point3 b)
{
return a * a < eps * eps || b * b < eps * eps
|| (a * b) * (a * b) / ((a * a) * (b * b)) < eps * eps;
}
struct line3
{
point3 a, s;
};
struct face3
{
point3 a, n;
};
struct circle3
{
point3 a;
double r;
};
point2 project(point3 a, face3 b, point3 xs)
{
point3 ys;
ys = b.n % xs;
point2 c;
c.x = ((a - b.a) * xs) / dis(xs), c.y = ((a - b.a) * ys) / dis(ys);
return c;
}
line2 project(line3 a, face3 b, point3 xs)
{
line2 c;
c.a = project(a.a, b, xs), c.s = project(a.a + a.s, b, xs) - c.a;
return c;
}
point3 revproject(point2 a, face3 b, point3 xs)
{
point3 ys;
ys = b.n % xs;
return a.x * xs / dis(xs) + a.y * ys / dis(ys) + b.a;
}
line3 revproject(line2 a, face3 b, point3 xs)
{
line3 c;
c.a = revproject(a.a, b, xs), c.s = revproject(a.a + a.s, b, xs) - c.a;
return c;
}
double point_line_dis(point3 a, line3 b, point3 *res = NULL)
{
point3 p;
p = b.a + ((a - b.a) * b.s) / (b.s * b.s) * b.s;
if (res != NULL) *res = p;
return dis(a - p);
}
double point_face_dis(point3 a, face3 b, point3 *res = NULL)
{
point3 p;
p = ((a - b.a) * b.n) / (b.n * b.n) * b.n;
if (res != NULL) *res = a - p;
return dis(p);
}
double line_line_dis(line3 a, line3 b, point3 *resa = NULL, point3 *resb = NULL)
{
point3 p;
if (parallel(a.s, b.s))
{
double d = point_line_dis(a.a, b, &p);
if (resa != NULL) *resa = a.a;
if (resb != NULL) *resb = p;
return d;
}
point3 n = a.s % b.s;
face3 f;
f.a = b.a, f.n = n;
double d = point_face_dis(a.a, f, &p);
double k1 = ((b.a - p) % b.s) * n / (n * n);
if (resb != NULL) *resb = p + k1 * a.s;
if (resa != NULL) *resa = a.a + k1 * a.s;
return d;
}
int line_face_cross(line3 a, face3 b, point3 *res = NULL)
{
if (perpend(a.s, b.n))
if (perpend(b.a - a.a, b.n))
return -1;
else
return 0;
double k = (b.a - a.a) * b.n / (a.s * b.n);
if (res != NULL) *res = a.a + k * a.s;
return 1;
}
int face_face_cross(face3 a, face3 b, line3 *res = NULL)
{
if (parallel(a.n, b.n))
if (perpend(b.a - a.a, a.n))
return -1;
else
return 0;
point3 s = a.n % b.n;
point3 p;
line3 t;
t.a = a.a, t.s = a.n % s;
line_face_cross(t, b, &p);
if (res != NULL)
res->a = p, res->s = s;
return 1;
}
=============<3D><><EFBFBD><EFBFBD>ģ<EFBFBD><C4A3>==========
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ģ<EFBFBD>壬<EFBFBD><EFBFBD><EFBFBD>а<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
\begin{itemize}
\item ext\_gcd<63><64><EFBFBD><EFBFBD>չŷ<D5B9><C5B7><EFBFBD><EFBFBD><EFBFBD>÷<EFBFBD><C3B7><EFBFBD><EFBFBD><EFBFBD> $ax+by=\gcd(a,b)$<24><><EFBFBD>ú<EFBFBD><C3BA><EFBFBD><EFBFBD><EFBFBD>֤<EFBFBD><D6A4> $a,b>0$ ʱ $x>0$<24><>
\item flsum<75><6D>ŷ<EFBFBD><C5B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD>˼<EFBFBD><CBBC><EFBFBD><EFBFBD> $\sum_{x=st}^{ed}\lfloor\frac{ax+b}c\rfloor$<24><>
\item ind<6E><64>С<EFBFBD><D0A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>㷨<EFBFBD><E3B7A8> $a^x=m\pmod b$<24><>
\item prepare\_inv<6E><76>$O(p)$ <20><>ģ $p$ <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>з<EFBFBD><D0B7><EFBFBD>Ԫ<EFBFBD><D4AA><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA>$p$ <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
\end{itemize}
#include <cstdlib>
#include <cmath>
#include <map>
#include <vector>
#include <algorithm>
void ext_gcd(int a, int b, int &x, int &y)
{
if (!b) x = 1, y = 0;
else if (!a) x = 1, y = -1;
else if (a > b) ext_gcd(a % b, b, x, y), y += a / b * x;
else ext_gcd(a, b % a, x, y), x += b / a * y;
}
long long flsum_t (long long a, long long b, long long c, long long n)
{
if (n < 0) return 0;
if (c < 0) a = -a, b = -b, c = -c;
n++;
long long res = 0;
if (a < 0 || a >= c)
{
long long ra = (a % c + c) % c;
long long k = (a - ra) / c;
res += k * n * (n - 1) / 2;
a = ra;
}
if (b < 0 || b >= c)
{
long long rb = (b % c + c) % c;
long long k = (b - rb) / c;
res += k * n;
b = rb;
}
if (a * n + b < c) return res;
else return res + flsum_t(c, (a * n + b) % c, a, (a * n + b) / c - 1);
}
long long flsum (long long a, long long b, long long c, long long st, long long ed)
{
return flsum_t(a, b, c, ed) - flsum_t(a, b, c, st - 1);
}
int power(int n, int k, int r)
{
int t = n, s = 1;
for (; k; k >>= 1, t = 1LL * t * t % r)
if (k & 1) s = 1LL * s * t % r;
return s;
}
int millerrabin(int x, int tester)
{
int k = x-1;
for (; !(k & 1); k >>= 1);
int y = power(tester, k, x);
if (y == 1) return 1;
for (; k < x-1; k <<= 1, y = 1LL * y * y % x)
if (y == x-1) return 1;
return 0;
}
int isprime(int x)
{
if (x == 2 || x == 7 || x == 61) return 1;
return millerrabin(x, 2) && millerrabin(x, 7) && millerrabin(x, 61);
}
int rho_f(int x, int c, int p)
{
return (1LL * x * x + c) % p;
}
int rho(int n)
{
int c = rand() % (n-1) + 1, x = 2, y = x, d = 1;
while (d == 1)
{
x = rho_f(x, c, n);
y = rho_f(rho_f(y, c, n), c, n);
d = std::__gcd(y > x ? y-x : x-y, n);
}
return d;
}
void factor(int n, std::vector<int> &res)
{
if (n == 1) return;
else if (isprime(n)) res.push_back(n);
else if (n == 4) res.push_back(2), res.push_back(2);
else
{
int d;
while ((d = rho(n)) == n);
factor(d, res), factor(n / d, res);
}
}
int ind(int a, int b, int m)
{
a %= m, b %= m;
std::map<int, int> hash;
int r = (int)(sqrt(m)), k = 1;
if (r * r < m) r++;
for (int i = 0; i < r; i++, k = 1LL * k * a % m)
if (hash.find(k) == hash.end())
hash.insert(std::make_pair(k, i));
int s = 1;
std::map<int, int>::iterator it;
for (int i = 0; i < r; i++, s = 1LL * s * k % m)
{
int x, y, t;
ext_gcd(s, m, x, y);
t = 1LL * b * x % m;
if ((it = hash.find(t)) != hash.end())
return i * r + it->second;
}
}
void prepare_inv(int *inv, int p)
{
inv[1] = 1;
for (int i = 2; i < p; i++)
inv[i] = 1LL * inv[p%i] * (p - p/i) % p;
}
=================<3D><>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD>=============
<EFBFBD><EFBFBD>ֵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ģ<EFBFBD>壬<EFBFBD>ں<EFBFBD><EFBFBD><EFBFBD>
\begin{itemize}
\item area\_simpson<6F><6E>Simpson<6F><6E><EFBFBD>󶨻<EFBFBD><F3B6A8BB>֡<EFBFBD>
\item fft\_prepare<72><65><EFBFBD><EFBFBD> $maxn$ <20>ε<EFBFBD>λ<EFBFBD><CEBB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ָ<EFBFBD><D6B8><EFBFBD><EFBFBD>
\item dft<66><74><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ $N(N|maxn)$ <20><>DFT<46><54><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> $f=-1$ <20><><EFBFBD><EFBFBD>IDFT<46><54>
\end{itemize}
#include <cmath>
#include <algorithm>
#include <complex>
const double pi = 3.14159265358979324;
typedef double (*__F) (double);
double area(double x, double y, double fl, double fmid, double fr)
{
return (fl + 4 * fmid + fr) * (y - x) / 6;
}
double area_simpson_solve(__F f, double x, double mid, double y, double fl, double fmid, double fr, double pre, double zero)
{
double lmid = (x + mid) / 2, rmid = (mid + y) / 2;
double flmid = f(lmid), frmid = f(rmid);
double al = area(x, mid, fl, flmid, fmid), ar = area(mid, y, fmid, frmid, fr);
if (fabs(al + ar - pre) < zero) return al + ar;
else return area_simpson_solve(f, x, lmid, mid, fl, flmid, fmid, al, zero) + area_simpson_solve(f, mid, rmid, y, fmid, frmid, fr, ar, zero);
}
double area_simpson(__F f, double x, double y, double zero = 1e-10)
{
double mid = (x + y) / 2, fl = f(x), fmid = f(mid), fr = f(y);
return area_simpson_solve(f, x, mid, y, fl, fmid, fr, area(x, y, fl, fmid, fr), zero);
}
typedef std::complex<double> complex;
void fft_prepare(int maxn, complex *&e)
{
e = new complex[2 * maxn - 1];
e += maxn - 1;
e[0] = complex(1, 0);
for (int i = 1; i < maxn; i <<= 1)
e[i] = complex(cos(2 * pi * i / maxn), sin(2 * pi * i / maxn));
for (int i = 3; i < maxn; i++)
if ((i & -i) != i) e[i] = e[i - (i & -i)] * e[i & -i];
for (int i = 1; i < maxn; i++) e[-i] = e[maxn - i];
}
/* f = 1: dft; f = -1: idft */
void dft(complex *a, int N, int f, complex *e, int maxn)
{
int d = maxn / N * f;
complex x;
for (int n = N, m; m = n / 2, m >= 1; n = m, d *= 2)
for (int i = 0; i < m; i++)
for (int j = i; j < N; j += n)
x = a[j] - a[j+m], a[j] += a[j+m], a[j+m] = x * e[d * i];
for (int i = 0, j = 1; j < N - 1; j++)
{
for (int k = N / 2; k > (i ^= k); k /= 2);
if (j < i) std::swap(a[i], a[j]);
}
}