Solved problem 65C from codeforces

Author: AliOsm

CodeForces/65C. Harry Potter and the Golden Snitch.cpp

@@ -0,0 +1,81 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int const N = 1e4 + 10;
+
+struct point {
+  double x, y, z;
+
+  point() {}
+
+  point(double x, double y, double z) : x(x), y(y), z(z) {}
+
+  bool operator==(const point &p) const {
+    return x == p.x && y == p.y && z == p.z;
+  }
+
+  point operator-(const point &p) const {
+    return point(x - p.x, y - p.y, z - p.z);
+  }
+
+  point operator+(const point &p) const {
+    return point(x + p.x, y + p.y, z + p.z);
+  }
+
+  point operator*(const double &o) const {
+    return point(x * o, y * o, z * o);
+  }
+
+  double dist(const point &p) const {
+    return sqrt(pow(x - p.x, 2) + pow(y - p.y, 2) + pow(z - p.z, 2));
+  }
+} points[N];
+point p;
+
+int n;
+double vp, vs, t[N];
+
+int main() {
+  scanf("%d", &n);
+  for(int i = 0; i <= n; ++i)
+    scanf("%lf %lf %lf", &points[i].x, &points[i].y, &points[i].z);
+  scanf("%lf %lf", &vp, &vs);
+  scanf("%lf %lf %lf", &p.x, &p.y, &p.z);
+
+  if(p == points[0]) {
+    puts("YES");
+    puts("0.0000000000");
+    printf("%0.10lf %0.10lf %0.10lf\n", p.x, p.y, p.z);
+    return 0;
+  }
+
+  for(int i = 1; i <= n; ++i)
+    t[i] = points[i].dist(points[i - 1]) / vs + t[i - 1];
+
+  for(int i = 1; i <= n; ++i) {
+    if(p.dist(points[i]) / vp - 1e-9 < t[i]) {
+      double l = 0, r = 1, mid;
+      point res;
+      for(int j = 0; j < 100; ++j) {
+        mid = (l + r) / 2;
+        point cur = points[i - 1] + (points[i] - points[i - 1]) * mid;
+
+        if(p.dist(cur) / vp - 1e-15 < points[i - 1].dist(cur) / vs + t[i - 1])
+          res = cur, r = mid;
+        else
+          l = mid;
+      }
+
+      puts("YES");
+      printf("%0.10lf\n", p.dist(res) / vp);
+      printf("%0.10lf %0.10lf %0.10lf\n", res.x, res.y, res.z);
+
+      return 0;
+    }
+  }
+
+  puts("NO");
+
+  return 0;
+}

CodeForces/README.md

@@ -33,6 +33,7 @@
 - [59A. Word](http://codeforces.com/problemset/problem/59/A)
 - [61A. Ultra-Fast Mathematician](http://codeforces.com/contest/61/problem/A)
 - [61E. Enemy is weak](http://codeforces.com/contest/61/problem/E)
+- [65C. Harry Potter and the Golden Snitch](http://codeforces.com/contest/65/problem/C)
 - [68A. Irrational problem](http://codeforces.com/problemset/problem/68/A)
 - [69A. Young Physicist](http://codeforces.com/problemset/problem/69/A)
 - [69C. Game](http://codeforces.com/contest/69/problem/C)