洛谷P2571 [SCOI2010]传送带

题目链接：

kma

题目分析：

裸的三分套三分啊，三分为什么是单峰的可以去看这篇博客的证明，感觉是目前写得最清楚的一篇

→人赢FSYolanda吊打集训队

不过其实最开始没有很搞懂三分求单峰函数最值是个啥东西，所以这里还是记录一下
手画图，不要吐槽有多丑

代码：

#include <bits/stdc++.h>
#define N (2000 + 10)
using namespace std;
inline int read() {
	int cnt = 0, f = 1; char c = getchar();
	while (!isdigit(c)) {if (c == '-') f = -f; c = getchar();}
	while (isdigit(c)) {cnt = (cnt << 3) + (cnt << 1) + c - '0'; c = getchar();}
	return cnt * f;
}
int x, y;
int P, Q, R;
const double eps = 1e-8;
int dcmp(double x) {
	if (fabs(x) < eps) return 0;
	else return x < 0 ? -1 : 1;
}
struct Vector{
	double x; double y;
	Vector (){};
	Vector (double x_, double y_) : x (x_), y (y_) { };
}A, B, C, D;
typedef Vector Point;
struct Line{
	Point u; Point v;
	Line (Point u_, Point v_) : u (u_), v(v_) { };
};
typedef Line Segment;

Vector operator + (Vector A, Vector B) {
	return Vector (A.x + B.x, A.y + B.y);
}

Vector operator - (Vector A, Vector B) { 
    return Vector (A.x - B.x, A.y - B.y);
}

Vector operator / (Vector A, double p) {
	return Vector (A.x / p, A.y / p);
}

double Dot (Vector a, Vector b) {
	return a.x * b.x + a.y * b.y;
}
double Length(Vector A){
    return sqrt(Dot(A, A));
}

double calc(Point X) {
	Point l = C, r = D;
	while (Length(l - r) > eps) {
		Point x = (r - l) / 3;
		Point lmid = l + x, rmid = r - x;
		double ans1 = Length(lmid - D) / Q + Length(X - lmid) / R;
		double ans2 = Length(rmid - D) / Q + Length(X - rmid) / R;
		if (ans2 - ans1 > eps) r = rmid;
		else l = lmid;
	}
	return Length(l - D) / Q + Length(X - l) / R;
}
double solve() {
	Point l = A, r = B;
	while (Length(l - r) > eps) {
		Point x = (r - l) / 3;
		Point lmid = l + x, rmid = r - x;
		double ans1 = calc(lmid) + Length(lmid - A) / P;
		double ans2 = calc(rmid) + Length(rmid - A) / P;
		if (ans2 - ans1 > eps) r = rmid;
		else l = lmid;
	} return calc(l) + Length(l - A) / P;
}
int main() {
	x = read(), y = read();
	A = Point(x, y);
	x = read(), y = read();
	B = Point(x, y);
	x = read(), y = read();
	C = Point(x, y);
	x = read(), y = read();
	D = Point(x, y);
	P = read(), Q = read(), R = read();
	return printf("%0.2lf", solve()), 0;
}