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#include<bits/stdc++.h>
#include "testlib.h"
using namespace std;
const double EPS_SPHERE = 1e-9; // Very strict for sphere constraint
const double EPS_DISTANCE = 1e-6; // For distance comparison (as per problem statement)
int n;
double distance(double x1, double y1, double z1, double x2, double y2, double z2) {
double dx = x1 - x2;
double dy = y1 - y2;
double dz = z1 - z2;
return sqrt(dx * dx + dy * dy + dz * dz);
}
bool doubleEqual(double a, double b, double eps) {
// Handle both absolute and relative error
if (abs(a) < eps && abs(b) < eps) return true;
return abs(a - b) <= eps * max(1.0, max(abs(a), abs(b)));
}
int main(int argc, char* argv[]) {
registerTestlibCmd(argc, argv);
// Read input
n = inf.readInt();
// Read reference answer
double ref_answer = ans.readDouble();
// Read participant's output
if (ouf.seekEof()) {
quitf(_wa, "No output provided");
}
double claimed_min_dist = ouf.readDouble();
if (claimed_min_dist < 0) {
quitf(_wa, "Minimum distance cannot be negative: %.10f", claimed_min_dist);
}
vector<tuple<double, double, double>> points;
// Read all n points
for (int i = 0; i < n; i++) {
if (ouf.seekEof()) {
quitf(_wa, "Expected %d points, but only found %d", n, i);
}
double x = ouf.readDouble();
double y = ouf.readDouble();
double z = ouf.readDouble();
// Check if point is within unit sphere (strict tolerance)
double dist_from_origin = sqrt(x * x + y * y + z * z);
if (dist_from_origin > 1.0 + EPS_SPHERE) {
quitf(_wa, "Point %d at (%.10f, %.10f, %.10f) is outside the unit sphere (distance from origin: %.15f)",
i + 1, x, y, z, dist_from_origin);
}
points.push_back({x, y, z});
}
if (!ouf.seekEof()) {
quitf(_wa, "Extra output found after %d points", n);
}
// Calculate actual minimum pairwise distance
double actual_min_dist = 1e18;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
double d = distance(get<0>(points[i]), get<1>(points[i]), get<2>(points[i]),
get<0>(points[j]), get<1>(points[j]), get<2>(points[j]));
actual_min_dist = min(actual_min_dist, d);
}
}
// Verify claimed distance matches actual distance (looser tolerance)
if (!doubleEqual(actual_min_dist, claimed_min_dist, EPS_DISTANCE)) {
quitf(_wa, "Claimed minimum distance %.10f does not match actual minimum distance %.10f (difference: %.10f)",
claimed_min_dist, actual_min_dist, abs(claimed_min_dist - actual_min_dist));
}
// Calculate score
double score_ratio = claimed_min_dist / ref_answer;
if (score_ratio < 0) score_ratio = 0.0;
double unbounded_ratio = max(0.0, score_ratio);
score_ratio = min(1.0, score_ratio);
quitp(score_ratio, "Min distance: %.10f. Ratio: %.6f, RatioUnbounded: %.6f", claimed_min_dist, score_ratio, unbounded_ratio);
return 0;
} |