bzoj1857: [Scoi2010]传送带

一看就是三分

然后打个表看了一下 确实有三分性

由于轨迹是线性的所以目标函数应该是单峰的，虽然会比二次函数偏差一点

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<string>

using namespace std;

void setIO(const string& a) {
    freopen((a+".in").c_str(), "r", stdin);
    freopen((a+".out").c_str(), "w", stdout);
}

double ax, ay, bx, by, cx, cy, dx, dy, P, Q, R;

#include<cmath>
double dis(double x1, double y1, double x2, double y2) {
    return hypot(x1 - x2, y1 - y2);
}

double calc(double x, double y) {
    double x1 = cx, y1 = cy, x2 = dx, y2 = dy;
    for(int i = 1; i <= 30; i++) {
        double mx1 = x1 + (x2 - x1) / 3, my1 = y1 + (y2 - y1) / 3;
        double mx2 = x1 + (x2 - x1) / 3 * 2, my2 = y1 + (y2 - y1) / 3 * 2;
        double cost1 = dis(x, y, mx1, my1) / R + dis(mx1, my1, dx, dy) / Q;
        double cost2 = dis(x, y, mx2, my2) / R + dis(mx2, my2, dx, dy) / Q;
        if(cost1 > cost2) x1 = mx1, y1 = my1;
        else x2 = mx2, y2 = my2;
    }
    return dis(x, y, x1, y1) / R + dis(x1, y1, dx, dy) / Q;
}

int main() {
    
    cin >> ax >> ay >> bx >> by;
//    if(ax > bx) swap(ax, bx), swap(ay, by);
    cin >> cx >> cy >> dx >> dy;
//    if(cx > dx) swap(cx, dx), swap(cy, dy);
    cin >> P >> Q >> R;
    
    double x1 = ax, y1 = ay, x2 = bx, y2 = by;
    
    for(int i = 1; i <= 30; i++) {
        double mx1 = x1 + (x2 - x1) / 3, my1 = y1 + (y2 - y1) / 3;
        double mx2 = x1 + (x2 - x1) / 3 * 2, my2 = y1 + (y2 - y1) / 3 * 2;
        double cost1 = dis(ax, ay, mx1, my1) / P + calc(mx1, my1);
        double cost2 = dis(ax, ay, mx2, my2) / P + calc(mx2, my2);
        if(cost1 > cost2) x1 = mx1, y1 = my1;
        else x2 = mx2, y2 = my2;
    }
    
    printf("%.2f
", dis(ax, ay, x1, y1) / P + calc(x1, y1));
    
    return 0;
}