Hdu 4717 The Moving Points (three Points)

Connection: hdu 4717 The Moving Points

N points are given. Each point has an initial position (x, y) and the moving distance per unit of time. The vector form is given. The maximum and minimum values of the distance between n points are the minimum and minimum values.

Solution: similar to the trigger of the binary algorithm, because if we make the maximum value d between the time t and the required two into a function curve, the monotonicity should first decrease and then increase progressively, therefore, we use the three-way method to obtain the extreme value.

#include 
  
   #include 
   
    #include 
    
     #include using namespace std;const int N = 305;const double eps = 1e-6;struct point {    double x;    double y;}s[N], p[N];int n;void init () {    scanf("%d", &n);    for (int i = 0; i < n; i++)        scanf("%lf%lf%lf%lf", &s[i].x, &s[i].y, &p[i].x, &p[i].y);}inline double dis (double x, double y) {    return sqrt(x*x+y*y);}double cat (double k) {    double ans = 0;    for (int i = 0; i < n; i++) {        double xi = s[i].x + p[i].x * k;        double yi = s[i].y + p[i].y * k;        for (int j = i + 1; j < n; j++) {            double pi = s[j].x + p[j].x * k;            double qi = s[j].y + p[j].y * k;            ans = max(ans, dis(xi-pi, yi-qi));        }    }    return ans;}void solve () {    double l = 0;    double r = 0xffffff;    while (fabs(r-l) > eps) {        double tmp = (r-l)/3;        double midl = l + tmp;        double midr = r - tmp;        if (cat(midl) < cat(midr))            r = midr;        else            l = midl;    }    printf("%.2lf %.2lf\n", l, cat(l));}int main () {    int cas;    scanf("%d", &cas);    for (int i = 1; i <= cas; i++) {        init ();        printf("Case #%d: ", i);        solve();    }    return 0;}