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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#132509 | #6570. Who Watches the Watchmen? | Sorting# | TL | 1ms | 3588kb | C++23 | 9.0kb | 2023-07-30 03:35:03 | 2023-07-30 03:35:07 |
Judging History
answer
#include <bits/stdc++.h>
#include <bits/extc++.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;
const ll INF = numeric_limits<ll>::max() / 4;
typedef vector<ll> VL;
struct MCMF {
int N;
vector<vi> ed, red;
vector<VL> cap, flow, cost;
vi seen;
VL dist, pi;
vector<pii> par;
MCMF(int N) :
N(N), ed(N), red(N), cap(N, VL(N)), flow(cap), cost(cap),
seen(N), dist(N), pi(N), par(N) {}
void addEdge(int from, int to, ll cap, ll cost) {
this->cap[from][to] = cap;
this->cost[from][to] = cost;
ed[from].push_back(to);
red[to].push_back(from);
}
void path(int s) {
fill(all(seen), 0);
fill(all(dist), INF);
dist[s] = 0; ll di;
__gnu_pbds::priority_queue<pair<ll, int>> q;
vector<decltype(q)::point_iterator> its(N);
q.push({0, s});
auto relax = [&](int i, ll cap, ll cost, int dir) {
ll val = di - pi[i] + cost;
if (cap && val < dist[i]) {
dist[i] = val;
par[i] = {s, dir};
if (its[i] == q.end()) its[i] = q.push({-dist[i], i});
else q.modify(its[i], {-dist[i], i});
}
};
while (!q.empty()) {
s = q.top().second; q.pop();
seen[s] = 1; di = dist[s] + pi[s];
for (int i : ed[s]) if (!seen[i])
relax(i, cap[s][i] - flow[s][i], cost[s][i], 1);
for (int i : red[s]) if (!seen[i])
relax(i, flow[i][s], -cost[i][s], 0);
}
rep(i,0,N) pi[i] = min(pi[i] + dist[i], INF);
}
pair<ll, ll> maxflow(int s, int t) {
ll totflow = 0, totcost = 0;
while (path(s), seen[t]) {
ll fl = INF;
for (int p,r,x = t; tie(p,r) = par[x], x != s; x = p)
fl = min(fl, r ? cap[p][x] - flow[p][x] : flow[x][p]);
totflow += fl;
for (int p,r,x = t; tie(p,r) = par[x], x != s; x = p)
if (r) flow[p][x] += fl;
else flow[x][p] -= fl;
}
rep(i,0,N) rep(j,0,N) totcost += cost[i][j] * flow[i][j];
return {totflow, totcost};
}
// If some costs can be negative, call this before maxflow:
void setpi(int s) { // (otherwise, leave this out)
fill(all(pi), INF); pi[s] = 0;
int it = N, ch = 1; ll v;
while (ch-- && it--)
rep(i,0,N) if (pi[i] != INF)
for (int to : ed[i]) if (cap[i][to])
if ((v = pi[i] + cost[i][to]) < pi[to])
pi[to] = v, ch = 1;
assert(it >= 0); // negative cost cycle
}
};
MCMF *mcmf = nullptr;
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){
while(true);
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;
}
}
}
mcmf = new MCMF(2 * n + 2);
adj.resize(n);
btoa.resize(n, -1);
for(int i = 0; i < n; ++i){
if(points_to[i] != -1){
mcmf->addEdge(i, n + points_to[i], 1, 0);
}
for(int j = 0; j < n; ++j){
if(j != i && j != points_to[i])
mcmf->addEdge(i, n + j, 1, 1);
}
mcmf->addEdge(2 * n, i, 1, 0);
mcmf->addEdge(i + n, 2 * n + 1, 1, 0);
}
cout << mcmf->maxflow(2 * n, 2 * n + 1).second << "\n";
}
ll solve_line(const vector<P> &p, const vector<P> &v, 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] + v.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, 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
*/
详细
Test #1:
score: 100
Accepted
time: 1ms
memory: 3548kb
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: 1ms
memory: 3588kb
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: -100
Time Limit Exceeded
input:
3 0 0 0 1 0 0 1 1 1 1 0 0 2 2 2 1 0 0