QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#193508 | #7521. Find the Gap | ucup-team112# | WA | 0ms | 3844kb | C++17 | 16.1kb | 2023-09-30 17:17:54 | 2023-09-30 17:17:55 |
Judging History
answer
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
namespace templates {
// type
using ll = long long;
using ull = unsigned long long;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)
// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on
// const value
const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;
const double PI = acos(-1);
// other macro
#ifndef RIN__LOCAL
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)
// function
vector<char> stoc(string &S) {
int n = S.size();
vector<char> ret(n);
for (int i = 0; i < n; i++) ret[i] = S[i];
return ret;
}
string ctos(vector<char> &S) {
int n = S.size();
string ret = "";
for (int i = 0; i < n; i++) ret += S[i];
return ret;
}
template <class T>
auto min(const T &a) {
return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
return (a > r ? r : a < l ? l : a);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
auto b = clamp(a, l, r);
return (a != b ? a = b, 1 : 0);
}
template <typename T>
T sum(vector<T> &A) {
T tot = 0;
for (auto a : A) tot += a;
return tot;
}
template <typename T>
vector<T> compression(vector<T> X) {
sort(all(X));
X.erase(unique(all(X)), X.end());
return X;
}
// input and output
namespace io {
// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << ' ';
}
return os;
}
// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
is >> A.first >> A.second;
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
os << A.first << ' ' << A.second;
return os;
}
// vector<pair<S, T>>
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// set<T>
template <typename T>
ostream &operator<<(ostream &os, set<T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << ' ';
}
return os;
}
// unordered_set<T>
template <typename T>
ostream &operator<<(ostream &os, unordered_set<T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << ' ';
}
return os;
}
// multiset<T>
template <typename T>
ostream &operator<<(ostream &os, multiset<T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << ' ';
}
return os;
}
// unordered_multiset<T>
template <typename T>
ostream &operator<<(ostream &os, unordered_multiset<T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << endl;
}
return os;
}
// map<S, T>
template <typename S, typename T>
ostream &operator<<(ostream &os, map<S, T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << endl;
}
return os;
}
// unordered_map<S, T>
template <typename S, typename T>
ostream &operator<<(ostream &os, unordered_map<S, T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << endl;
}
return os;
}
// tuple
template <typename T, size_t N>
struct TuplePrint {
static ostream &print(ostream &os, const T &t) {
TuplePrint<T, N - 1>::print(os, t);
os << ' ' << get<N - 1>(t);
return os;
}
};
template <typename T>
struct TuplePrint<T, 1> {
static ostream &print(ostream &os, const T &t) {
os << get<0>(t);
return os;
}
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
return os;
}
// queue<T>
template <typename T>
ostream &operator<<(ostream &os, queue<T> &A) {
auto B = A;
while (!B.empty()) {
os << B.front();
B.pop();
if (!B.empty()) os << ' ';
}
return os;
}
// deque<T>
template <typename T>
ostream &operator<<(ostream &os, deque<T> &A) {
auto B = A;
while (!B.empty()) {
os << B.front();
B.pop_front();
if (!B.empty()) os << ' ';
}
return os;
}
// stack<T>
template <typename T>
ostream &operator<<(ostream &os, stack<T> &A) {
auto B = A;
stack<T> C;
while (!B.empty()) {
C.push(B.top());
B.pop();
}
while (!C.empty()) {
os << C.top();
C.pop();
if (!C.empty()) os << ' ';
}
return os;
}
// priority_queue<T>
template <typename T>
ostream &operator<<(ostream &os, priority_queue<T> &A) {
auto B = A;
while (!B.empty()) {
os << B.top();
B.pop();
if (!B.empty()) os << endl;
}
return os;
}
// bitset<N>
template <size_t N>
ostream &operator<<(ostream &os, bitset<N> &A) {
for (size_t i = 0; i < N; i++) {
os << A[i];
}
return os;
}
// io functions
void FLUSH() {
cout << flush;
}
void print() {
cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
cout << head;
if (sizeof...(Tail)) cout << spa;
print(forward<Tail>(tail)...);
}
template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
int n = A.size();
for (int i = 0; i < n; i++) {
cout << A[i];
if (i != n - 1) cout << sep;
}
cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
cout << A << end;
}
template <typename T>
void prispa(T A) {
priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
if (f)
print(A);
else
print(B);
return f;
}
template <class... T>
void inp(T &...a) {
(cin >> ... >> a);
}
} // namespace io
using namespace io;
// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<int>> edges(n, vector<int>());
for (int i = 0; i < m; i++) {
INT(u, v);
u -= indexed;
v -= indexed;
edges[u].push_back(v);
if (!direct) edges[v].push_back(u);
}
return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
return read_edges(n, n - 1, false, indexed);
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
for (int i = 0; i < m; i++) {
INT(u, v);
T w;
inp(w);
u -= indexed;
v -= indexed;
edges[u].push_back({v, w});
if (!direct) edges[v].push_back({u, w});
}
return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
return read_wedges<T>(n, n - 1, false, indexed);
}
// yes / no
namespace yesno {
// yes
inline bool yes(bool f = true) {
cout << (f ? "yes" : "no") << endl;
return f;
}
inline bool Yes(bool f = true) {
cout << (f ? "Yes" : "No") << endl;
return f;
}
inline bool YES(bool f = true) {
cout << (f ? "YES" : "NO") << endl;
return f;
}
// no
inline bool no(bool f = true) {
cout << (!f ? "yes" : "no") << endl;
return f;
}
inline bool No(bool f = true) {
cout << (!f ? "Yes" : "No") << endl;
return f;
}
inline bool NO(bool f = true) {
cout << (!f ? "YES" : "NO") << endl;
return f;
}
// possible
inline bool possible(bool f = true) {
cout << (f ? "possible" : "impossible") << endl;
return f;
}
inline bool Possible(bool f = true) {
cout << (f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool POSSIBLE(bool f = true) {
cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// impossible
inline bool impossible(bool f = true) {
cout << (!f ? "possible" : "impossible") << endl;
return f;
}
inline bool Impossible(bool f = true) {
cout << (!f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool IMPOSSIBLE(bool f = true) {
cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// Alice Bob
inline bool Alice(bool f = true) {
cout << (f ? "Alice" : "Bob") << endl;
return f;
}
inline bool Bob(bool f = true) {
cout << (f ? "Bob" : "Alice") << endl;
return f;
}
// Takahashi Aoki
inline bool Takahashi(bool f = true) {
cout << (f ? "Takahashi" : "Aoki") << endl;
return f;
}
inline bool Aoki(bool f = true) {
cout << (f ? "Aoki" : "Takahashi") << endl;
return f;
}
} // namespace yesno
using namespace yesno;
} // namespace templates
using namespace templates;
//// https://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=4449247
#define INF 1000000000
const double EPS = 1e-8;
struct point3d {
double x, y, z;
point3d() : x(0), y(0), z(0) {}
point3d(const point3d &p) : x(p.x), y(p.y), z(p.z) {}
point3d(double x_, double y_, double z_) : x(x_), y(y_), z(z_) {}
point3d &operator+=(point3d a) {
x += a.x;
y += a.y;
z += a.z;
return *this;
}
point3d &operator-=(point3d a) {
x -= a.x;
y -= a.y;
z -= a.z;
return *this;
}
point3d &operator*=(double a) {
x *= a;
y *= a;
z *= a;
return *this;
}
point3d &operator/=(double a) {
x /= a;
y /= a;
z /= a;
return *this;
}
point3d operator+(point3d a) const {
return point3d(x, y, z) += a;
}
point3d operator-(point3d a) const {
return point3d(x, y, z) -= a;
}
point3d operator*(double a) const {
return point3d(x, y, z) *= a;
}
point3d operator/(double a) const {
return point3d(x, y, z) /= a;
}
bool operator<(point3d a) const {
return (x != a.x ? x < a.x : (y != a.y ? y < a.y : z < a.z));
}
bool operator==(point3d a) const {
return (abs(x - a.x) < EPS && abs(y - a.y) < EPS && abs(z - a.z) < EPS);
}
bool operator!=(point3d a) const {
return !(*this == a);
}
};
struct segment3d : public array<point3d, 2> {
segment3d(const point3d &a, const point3d &b) {
at(0) = a;
at(1) = b;
}
};
double abs(point3d p) {
return sqrt(p.x * p.x + p.y * p.y + p.z * p.z);
}
double dot(point3d a, point3d b) {
return a.x * b.x + a.y * b.y + a.z * b.z;
}
point3d cross(point3d a, point3d b) {
return point3d(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
}
double angle(point3d a, point3d b) {
return acos(dot(a, b) / (abs(a) * abs(b)));
}
struct plane {
double a, b, c, d;
plane() : a(0), b(0), c(0), d(0) {}
plane(double a_, double b_, double c_, double d_) : a(a_), b(b_), c(c_), d(d_) {}
plane(point3d p1, point3d p2, point3d p3) {
point3d A = p2 - p1;
point3d B = p3 - p1;
point3d p = cross(A, B);
a = p.x;
b = p.y;
c = p.z;
d = -(a * p1.x + b * p1.y + c * p1.z);
}
double assignment(point3d p) {
return a * p.x + b * p.y + c * p.z + d;
}
};
double distance(point3d p, plane pl) {
double a = (p.x * pl.a + p.y * pl.b + p.z * pl.c + pl.d);
if (a == 0) return 0;
double b = sqrt(pl.a * pl.a + pl.b * pl.b + pl.c * pl.c);
return a / b;
}
double distance(plane p, point3d pl) {
return distance(pl, p);
}
point3d projection(point3d p, plane pl) {
double d = distance(p, pl);
point3d a = point3d(pl.a, pl.b, pl.c);
a /= abs(a);
point3d ret = p + a * d;
if (distance(ret, pl) < EPS) return ret;
return p - a * d;
}
point3d crossPoint3d(segment3d s, plane p) {
double bunsi = p.a * s[0].x + p.b * s[0].y + p.c * s[0].z + p.d;
double bunbo = p.a * (s[0].x - s[1].x) + p.b * (s[0].y - s[1].y) + p.c * (s[0].z - s[1].z);
if (abs(bunbo) < EPS) return point3d(INF, INF, INF);
double t = bunsi / bunbo;
return s[0] + (s[1] - s[0]) * t;
}
namespace std {
istream &operator>>(std::istream &is, point3d &p) {
is >> p.x >> p.y >> p.z;
return is;
}
ostream &operator<<(ostream &os, const point3d &p) {
os << p.x << " " << p.y << " " << p.z;
return os;
}
ostream &operator<<(ostream &os, const plane &p) {
os << p.a << "x + " << p.b << "y + " << p.c << "z + " << p.d;
return os;
}
} // namespace std
using ld = long double;
void solve() {
INT(n);
VEC(point3d, P, n);
if (n <= 3) {
print(0);
return;
}
ld ans = 1e50;
fori(i, n) fori(j, i + 1, n) fori(k, j + 1, n) {
plane pl(P[i], P[j], P[k]);
ld mi = 1e30;
ld ma = -1e30;
fori(t, n) {
ld d = distance(P[t], pl);
chmin(mi, d);
chmax(ma, d);
}
chmin(ans, ma - mi);
}
fori(i, n) fori(j, i + 1, n) {
fori(k, i, n) fori(l, k + 1, n) {
if (i == k or i == l or j == k or j == l) continue;
point3d a = P[i];
point3d b = P[j];
point3d c = P[l] + P[i] - P[k];
plane pl(a, b, c);
ld mi = 1e30;
ld ma = -1e30;
fori(t, n) {
ld d = distance(P[t], pl);
chmin(mi, d);
chmax(ma, d);
}
chmin(ans, ma - mi);
}
}
print(ans);
}
int main() {
cin.tie(0)->sync_with_stdio(0);
cout << fixed << setprecision(12);
int t;
t = 1;
// cin >> t;
while (t--) solve();
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 0
Wrong Answer
time: 0ms
memory: 3844kb
input:
8 1 1 1 1 1 2 1 2 1 1 2 2 2 1 1 2 1 2 2 2 1 2 2 2
output:
0.000000000000
result:
wrong answer 1st numbers differ - expected: '1.0000000', found: '0.0000000', error = '1.0000000'