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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#132507 | #6570. Who Watches the Watchmen? | Sorting# | WA | 1ms | 3612kb | C++23 | 7.5kb | 2023-07-30 03:08:30 | 2023-07-30 03:08:32 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T> void check_min(T &a, const T &b){ a = (a < b) ? a : b; }
template<class T> void check_max(T &a, const T &b){ a = (a > b) ? a : b; }
#define all(x) (x).begin(), (x).end()
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
const int N = 1000 + 3;
bool dfs(int a, int L, vector<vi>& g, vi& btoa, vi& A, vi& B) {
if (A[a] != L) return 0;
A[a] = -1;
for (int b : g[a]) if (B[b] == L + 1) {
B[b] = 0;
if (btoa[b] == -1 || dfs(btoa[b], L + 1, g, btoa, A, B))
return btoa[b] = a, 1;
}
return 0;
}
int hopcroftKarp(vector<vi>& g, vi& btoa) {
int res = 0;
vi A(g.size()), B(btoa.size()), cur, next;
for (;;) {
fill(all(A), 0);
fill(all(B), 0);
/// Find the starting nodes for BFS (i.e. layer 0).
cur.clear();
for (int a : btoa) if(a != -1) A[a] = -1;
rep(a,0,sz(g)) if(A[a] == 0) cur.push_back(a);
/// Find all layers using bfs.
for (int lay = 1;; lay++) {
bool islast = 0;
next.clear();
for (int a : cur) for (int b : g[a]) {
if (btoa[b] == -1) {
B[b] = lay;
islast = 1;
}
else if (btoa[b] != a && !B[b]) {
B[b] = lay;
next.push_back(btoa[b]);
}
}
if (islast) break;
if (next.empty()) return res;
for (int a : next) A[a] = lay;
cur.swap(next);
}
/// Use DFS to scan for augmenting paths.
rep(a,0,sz(g))
res += dfs(a, 0, g, btoa, A, B);
}
}
template<class T> struct Point3D {
typedef Point3D P;
typedef const P& R;
T x, y, z;
explicit Point3D(T x=0, T y=0, T z=0) : x(x), y(y), z(z) {}
bool operator<(R p) const {
return tie(x, y, z) < tie(p.x, p.y, p.z); }
bool operator==(R p) const {
return tie(x, y, z) == tie(p.x, p.y, p.z); }
P operator+(R p) const { return P(x+p.x, y+p.y, z+p.z); }
P operator-(R p) const { return P(x-p.x, y-p.y, z-p.z); }
P operator*(T d) const { return P(x*d, y*d, z*d); }
P operator/(T d) const { return P(x/d, y/d, z/d); }
T dot(R p) const { return x*p.x + y*p.y + z*p.z; }
P cross(R p) const {
return P(y*p.z - z*p.y, z*p.x - x*p.z, x*p.y - y*p.x);
}
T dist2() const { return x*x + y*y + z*z; }
double dist() const { return sqrt((double)dist2()); }
//Azimuthal angle (longitude) to x-axis in interval [-pi, pi]
double phi() const { return atan2(y, x); }
//Zenith angle (latitude) to the z-axis in interval [0, pi]
double theta() const { return atan2(sqrt(x*x+y*y),z); }
P unit() const { return *this/(T)dist(); } //makes dist()=1
//returns unit vector normal to *this and p
P normal(P p) const { return cross(p).unit(); }
//returns point rotated 'angle' radians ccw around axis
P rotate(double angle, P axis) const {
double s = sin(angle), c = cos(angle); P u = axis.unit();
return u*dot(u)*(1-c) + (*this)*c - cross(u)*s;
}
};
typedef Point3D<ll> P;
int n;
P p[N], v[N];
bool on_line(P a, P b, P c){
return (b - a).cross(c - a) == P();
}
bool same_direction(P a, P b){
return a.dot(b) > 0ll;
}
ll get_sign(P a, P dir_a, P b, P dir_b){
P n2 = dir_b.cross(dir_a.cross(dir_b));
ll sign_1 = (b - a).dot(n2);
sign_1 = (sign_1 > 0) - (sign_1 < 0);
sign_1 *= dir_a.dot(n2);
sign_1 = (sign_1 > 0) - (sign_1 < 0);
return sign_1;
}
bool intersect(P a, P dir_a, P b, P dir_b){
P n = dir_a.cross(dir_b);
if(n == P())
return false;
if((b - a).dot(n) != 0)
return false;
ll sign_1 = get_sign(a, dir_a, b, dir_b);
ll sign_2 = get_sign(b, dir_b, a, dir_a);
return (sign_1 > 0) && (sign_2 > 0);
}
bool b[N][N];
int points_to[N];
vector<vi> adj;
vi btoa;
void solve(){
for(int i = 0; i < n; ++i){
for(int j = i + 1; j < n; ++j){
bool ok = true;
for(int j2 = 0; j2 < n; ++j2){
if(j2 == i || j2 == j) continue;
if(on_line(p[i], p[j], p[j2]) && same_direction(p[j2] - p[i], p[j] - p[j2])){
ok = false;
break;
}
}
b[i][j] = b[j][i] = ok;
}
}
for(int i = 0; i < n; ++i){
points_to[i] = -1;
for(int j = 0; j < n; ++j){
if(i == j) continue;
if(!b[i][j]) continue;
if(on_line(p[i], p[j], p[i] + v[i]) && same_direction(v[i], p[j] - p[i])){
points_to[i] = j;
break;
}
}
}
adj.resize(n);
btoa.resize(n, -1);
for(int i = 0; i < n; ++i){
if(points_to[i] != -1){
adj[i].push_back(points_to[i]);
}
}
cout << n - hopcroftKarp(adj, btoa) << "\n";
}
ll solve_line(const vector<P> &p, const vector<P> &v, P p_chosen, P v_chosen){
ll cnt_in_dir = 0, cnt_not = 0;
for(int j = 0; j < (int)v.size() - 1; ++j){
if(on_line(p[0], p[1], p[0] + v[j]) && same_direction(v[j], p[1] - p[0])){
++cnt_in_dir;
}
else{
++cnt_not;
}
}
bool d_chosen = !on_line(p[0], p[1], p[0] + v_chosen);
bool d_back = !on_line(p[0], p[1], p[0] + p.back());
ll ans = cnt_not;
if(d_chosen && d_back){
if(!intersect(p.back(), v.back(), p[0], P()-v_chosen))
++ans;
}
else{
if(d_chosen || d_back){
++ans;
}
else{
ans += 2;
}
}
return ans;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
cin >> n;
for(int i = 0; i < n; ++i){
cin >> p[i].x >> p[i].y >> p[i].z;
cin >> v[i].x >> v[i].y >> v[i].z;
}
if(n == 1){
cout << "-1\n";
return 0;
}
if(n == 2){
int ans = 2;
ans -= on_line(p[0], p[1], p[0] + v[0]) && same_direction(p[1] - p[0], v[0]);
ans -= on_line(p[1], p[0], p[1] + v[1]) && same_direction(p[0] - p[1], v[1]);
cout << ans << "\n";
return 0;
}
bool one_line = true;
for(int i = 2; i < n; ++i)
one_line &= on_line(p[0], p[1], p[i]);
if(one_line){
ll ans = 1000;
for(int chosen = 0; chosen < n; ++chosen){
vector<pair<P, P>> new_points;
for(int j = 0; j < n; ++j){
if(chosen == j) continue;
new_points.push_back({p[j], v[j]});
}
sort(all(new_points));
for(int dir = 0; dir <= 1; ++dir, reverse(all(new_points))){
vector<P> new_p, new_v;
for(int i = 0; i < new_points.size(); ++i){
new_p.push_back(new_points[i].first);
new_v.push_back(new_points[i].second);
}
ll curr = solve_line(new_p, new_v, p[chosen], v[chosen]);
check_min(ans, curr);
}
}
cout << 1000 + ans << "\n";
return 0;
}
solve();
}
/*
3
0 0 0 0 0 1
0 0 1 0 -1 -1
0 0 2 0 -1 1
*/
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3560kb
input:
7 0 0 0 1 0 0 1 0 0 -1 0 0 2 0 0 1 0 0 3 0 0 1 0 0 4 0 0 1 0 0 5 0 0 1 0 0 6 0 0 -1 0 0
output:
1002
result:
ok single line: '1002'
Test #2:
score: 0
Accepted
time: 0ms
memory: 3544kb
input:
4 66 45 10 73 39 36 95 14 26 47 84 59 14 66 89 89 36 78 16 27 94 79 24 24
output:
4
result:
ok single line: '4'
Test #3:
score: 0
Accepted
time: 1ms
memory: 3612kb
input:
3 0 0 0 1 0 0 1 1 1 1 0 0 2 2 2 1 0 0
output:
1002
result:
ok single line: '1002'
Test #4:
score: 0
Accepted
time: 1ms
memory: 3544kb
input:
3 0 0 0 1 1 1 1 1 1 1 0 0 2 2 2 1 0 0
output:
1001
result:
ok single line: '1001'
Test #5:
score: 0
Accepted
time: 0ms
memory: 3536kb
input:
3 0 0 0 1 0 0 1 1 1 1 0 0 2 2 2 -1 -1 -1
output:
1001
result:
ok single line: '1001'
Test #6:
score: -100
Wrong Answer
time: 1ms
memory: 3532kb
input:
3 0 0 0 1 0 0 1 1 1 1 2 2 2 2 2 -1 -1 -1
output:
1001
result:
wrong answer 1st lines differ - expected: '1000', found: '1001'