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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 |
---|---|---|---|---|---|---|---|---|---|
#277471 | #6570. Who Watches the Watchmen? | ucup-team1198 | TL | 767ms | 3660kb | C++20 | 8.4kb | 2023-12-06 19:14:18 | 2023-12-06 19:14:18 |
Judging History
answer
#include <map>
#include <set>
#include <array>
#include <cmath>
#include <deque>
#include <bitset>
#include <random>
#include <string>
#include <vector>
#include <cassert>
#include <complex>
#include <iomanip>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#include <unordered_set>
#pragma GCC optimize("unroll-loops","Ofast")
using namespace std;
// #define int int64_t
struct Vector {
int x;
int y;
int z;
Vector(int x = 0, int y = 0, int z = 0): x(x), y(y), z(z) {}
Vector(const Vector& a, const Vector& b): x(b.x - a.x), y(b.y - a.y), z(b.z - a.z) {}
};
Vector operator-(const Vector& a, const Vector& b) {
return Vector(b, a);
}
Vector operator+(const Vector& a, const Vector& b) {
return {a.x + b.x, a.y + b.y, a.z + b.z};
}
int64_t operator*(const Vector& a, const Vector& b) {
return a.x * b.x + a.y * b.y + a.z * b.z;
}
__int128 dot(const Vector& a, const Vector& b) {
return (__int128)a.x * b.x + (__int128)a.y * b.y + (__int128)a.z * b.z;
}
Vector operator%(const Vector& a, const Vector& b) {
return Vector(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
}
int64_t vol(const Vector& a, const Vector& b, const Vector& c) {
return a * (b % c);
}
__int128 vol128(const Vector& a, const Vector& b, const Vector& c) {
return dot(a, (b % c));
}
istream& operator>>(istream& in, Vector& v) {
in >> v.x >> v.y >> v.z;
return in;
}
bool operator==(const Vector& a, const Vector& b) {
return a.x == b.x && a.y == b.y && a.z == b.z;
}
bool coplane(const Vector& a, const Vector& b, const Vector& c, const Vector& d) {
return vol(b - a, c - a, d - a) == 0;
}
const int MAXN = 600;
Vector p[MAXN], dir[MAXN];
struct CostEdge {
int from, to, cap, cost, nxt;
int flow = 0;
CostEdge() {}
CostEdge(int from, int to, int cap, int cost, int nxt): from(from), to(to), cap(cap), cost(cost), nxt(nxt) {}
};
struct CostFlow {
static constexpr int INF = 1e9;
int n;
int s, t;
vector<CostEdge> e;
vector<int> head;
CostFlow(int n, int s = -1, int t = -1): n(n), s(s), t(t), head(vector<int>(n, -1)) {}
void add_edge(int from, int to, int cap, int cost) {
/// cerr << from << " " << to << " " << cap << " " << cost << endl;
e.emplace_back(from, to, cap, cost, head[from]);
head[from] = e.size() - 1;
e.emplace_back(to, from, 0, -cost, head[to]);
head[to] = e.size() - 1;
}
vector<int> pot;
int cost = 0;
int flow = 0;
void calc_pot() {
pot = vector<int>(n, 0);
// pot[s] = 0;
// for (int i = 0; i < n; ++i) {
// for (auto e1 : e) {
// if (e1.flow < e1.cap) {
// pot[e1.to] = min(pot[e1.to], pot[e1.from] + e1.cost);
// }
// }
// }
}
bool step() {
vector<int> dist(n, INF);
vector<int> pred(n, -1);
vector<int> used(n, 0);
dist[s] = 0;
while (true) {
int v = -1;
for (int i = 0; i < n; ++i) {
if (used[i]) continue;
if (v == -1 || dist[i] < dist[v]) {
v = i;
}
}
if (v == -1) break;
used[v] = true;
for (int i = head[v]; i != -1; i = e[i].nxt) {
if (e[i].flow == e[i].cap) continue;
if (dist[e[i].to] > dist[v] + e[i].cost + pot[v] - pot[e[i].to]) {
dist[e[i].to] = dist[v] + e[i].cost + pot[v] - pot[e[i].to];
pred[e[i].to] = i;
}
}
}
/**for (int i = 0; i < n; ++i) {
cerr << dist[i] << " ";
}
cerr << endl;*/
if (dist[t] == INF) return false;
int mn = INF;
int at = t;
int pr = pred[at];
while (pr != -1) {
mn = min(mn, e[pr].cap - e[pr].flow);
at = e[pr].from;
pr = pred[at];
}
at = t;
pr = pred[at];
while (pr != -1) {
e[pr].flow += mn;
e[pr ^ 1].flow -= mn;
at = e[pr].from;
pr = pred[at];
}
flow += mn;
cost += mn * (dist[t] + pot[t]);
for (int i = 0; i < n; ++i) {
pot[i] += dist[i];
}
return true;
}
pair<int, int> get() {
calc_pot();
while (step()) {
/// cerr << "step" << endl;
}
return {flow, cost};
}
};
signed main() {
#ifdef DEBUG
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#else
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
#endif
int n;
cin >> n;
for (int i = 0; i < n; ++i) {
cin >> p[i] >> dir[i];
}
if (n == 1) {
cout << "-1\n";
return 0;
}
bool is_col = (n % 2 != 0);
for (int i = 2; i < n; ++i) {
is_col &= ((p[i] - p[0]) % (p[1] - p[0]) == Vector());
}
auto add_from_segm = [&](int ind, int start, int fin, Vector go) {
int cnt = 0;
if (dir[ind] % go == Vector() && dir[fin] % go == Vector()) {
cnt += 2;
} else if (dir[ind] % go == Vector() || dir[fin] % go == Vector()) {
++cnt;
} else {
if (!coplane(p[start], p[fin], p[fin] + dir[fin], p[start] - dir[ind])) {
++cnt;
} else if (dir[fin] % dir[ind] == Vector()) {
++cnt;
} else {
Vector norm = go % dir[ind];
__int128 a = vol128(norm, go, dir[fin]);
__int128 b = vol128(norm, go, dir[ind]);
if (a < 0 && b < 0) {
++cnt;
} else if (a > 0 && b > 0) {
++cnt;
}
}
}
return cnt;
};
if (is_col) {
int ans = 2000;
Vector start = p[0];
Vector go = p[1] - p[0];
vector<int> ord(n);
iota(ord.begin(), ord.end(), 0);
sort(ord.begin(), ord.end(), [&](int i, int j) {
return (p[i] - start) * go < (p[j] - start) * go;
});
for (int i = 0; i < n; ++i) {
vector<int> lft;
for (int j = 0; j < n; ++j) {
if (j != i) {
lft.push_back(j);
}
}
vector<int> pref_cnt_both_dirs(n);
for (int i = 0; i < n - 1; ++i) {
int delta = 0;
if (i % 2 == 0) {
if (dir[ord[lft[i]]] % go == Vector() && dir[ord[lft[i]]] * go > 0) {
} else {
++delta;
}
} else {
if (dir[ord[lft[i]]] % go == Vector() && dir[ord[lft[i]]] * go < 0) {
} else {
++delta;
}
}
pref_cnt_both_dirs[i + 1] = pref_cnt_both_dirs[i] + delta;
}
vector<int> pref_cnt_dir1(n);
for (int i = 0; i < n - 1; ++i) {
int delta = 0;
if (dir[ord[lft[i]]] % go == Vector() && dir[ord[lft[i]]] * go > 0) {
} else {
++delta;
}
pref_cnt_dir1[i + 1] = pref_cnt_dir1[i] + delta;
}
vector<int> pref_cnt_dir2(n);
for (int i = 0; i < n - 1; ++i) {
int delta = 0;
if (dir[ord[lft[i]]] % go == Vector() && dir[ord[lft[i]]] * go < 0) {
} else {
++delta;
}
pref_cnt_dir2[i + 1] = pref_cnt_dir2[i] + delta;
}
int ind = ord[i];
for (int l = 0; l < n - 1; l += 2) {
for (int r = l + 1; r < n - 1; r += 2) {
int cur_ans = add_from_segm(ind, ord[lft[l]], ord[lft[r]], go) + pref_cnt_both_dirs[l] + pref_cnt_both_dirs[n - 1] - pref_cnt_both_dirs[r + 1];
cur_ans += pref_cnt_dir1[r] - pref_cnt_dir1[l];
ans = min(ans, 1000 + cur_ans);
}
}
for (int l = 0; l < n - 1; l += 2) {
for (int r = l + 1; r < n - 1; r += 2) {
int cur_ans = add_from_segm(ind, ord[lft[r]], ord[lft[l]], go) + pref_cnt_both_dirs[l] + pref_cnt_both_dirs[n - 1] - pref_cnt_both_dirs[r + 1];
cur_ans += pref_cnt_dir2[r + 1] - pref_cnt_dir2[l + 1];
ans = min(ans, 1000 + cur_ans);
}
}
}
cout << ans << "\n";
return 0;
}
CostFlow mincost(2 * n + 2, 2 * n, 2 * n + 1);
for (int i = 0; i < n; ++i) {
mincost.add_edge(mincost.s, 2 * i + 1, 1, 0);
mincost.add_edge(2 * i, mincost.t, 1, 0);
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if (i == j) continue;
bool has_veiw = true;
for (int k = 0; k < n; ++k) {
if (k == i || k == j) continue;
if ((p[k] - p[i]) % (p[j] - p[i]) == Vector()) {
if ((p[i] - p[k]) * (p[j] - p[k]) < 0) {
has_veiw = false;
break;
}
}
}
if (!has_veiw) continue;
int cost = 1;
if (dir[i] % (p[j] - p[i]) == Vector() && dir[i] * (p[j] - p[i]) > 0) {
cost = 0;
}
mincost.add_edge(2 * i + 1, 2 * j, 1, cost);
}
}
/// cerr << "start mincost" << endl;
auto res = mincost.get();
/// cerr << res.first << endl;
assert(res.first == n);
cout << res.second << "\n";
return 0;
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 3468kb
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: 3580kb
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: 0ms
memory: 3456kb
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: 0ms
memory: 3460kb
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: 3500kb
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: 0
Accepted
time: 0ms
memory: 3520kb
input:
3 0 0 0 1 0 0 1 1 1 1 2 2 2 2 2 -1 -1 -1
output:
1000
result:
ok single line: '1000'
Test #7:
score: 0
Accepted
time: 1ms
memory: 3512kb
input:
3 0 0 0 1 0 0 1 1 1 1 2 2 2 2 2 1 1 1
output:
1001
result:
ok single line: '1001'
Test #8:
score: 0
Accepted
time: 1ms
memory: 3516kb
input:
1 0 0 0 3 1 4
output:
-1
result:
ok single line: '-1'
Test #9:
score: 0
Accepted
time: 0ms
memory: 3460kb
input:
4 0 0 0 1 1 1 1 0 0 -1 0 0 1 1 1 0 -1 0 1 0 1 0 1 0
output:
1
result:
ok single line: '1'
Test #10:
score: 0
Accepted
time: 767ms
memory: 3612kb
input:
500 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 7 0 0 1 0 0 8 0 0 1 0 0 9 0 0 1 0 0 10 0 0 -1 0 0 11 0 0 -1 0 0 12 0 0 1 0 0 13 0 0 -1 0 0 14 0 0 1 0 0 15 0 0 1 0 0 16 0 0 1 0 0 17 0 0 -1 0 0 18 0 0 -1 0 0 19 0 0 -1 0 0 20 0 0 -1 0 0 21 0 0 1 0 0 22 0 0 1 0 0...
output:
250
result:
ok single line: '250'
Test #11:
score: 0
Accepted
time: 763ms
memory: 3660kb
input:
500 0 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 7 0 0 1 0 0 8 0 0 1 0 0 9 0 0 1 0 0 10 0 0 -1 0 0 11 0 0 -1 0 0 12 0 0 1 0 0 13 0 0 -1 0 0 14 0 0 1 0 0 15 0 0 1 0 0 16 0 0 1 0 0 17 0 0 -1 0 0 18 0 0 -1 0 0 19 0 0 -1 0 0 20 0 0 -1 0 0 21 0 0 1 0 0 22 0 0 1 0...
output:
250
result:
ok single line: '250'
Test #12:
score: 0
Accepted
time: 766ms
memory: 3632kb
input:
500 0 0 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 7 0 0 1 0 0 8 0 0 1 0 0 9 0 0 1 0 0 10 0 0 -1 0 0 11 0 0 -1 0 0 12 0 0 1 0 0 13 0 0 -1 0 0 14 0 0 1 0 0 15 0 0 1 0 0 16 0 0 1 0 0 17 0 0 -1 0 0 18 0 0 -1 0 0 19 0 0 -1 0 0 20 0 0 -1 0 0 21 0 0 1 0 0 22 0 0 1...
output:
250
result:
ok single line: '250'
Test #13:
score: 0
Accepted
time: 0ms
memory: 3512kb
input:
5 1 0 0 1 -1 0 2 0 0 0 1 0 3 0 0 -1 0 0 4 0 0 -1 0 0 5 0 0 -1 0 0
output:
1000
result:
ok single line: '1000'
Test #14:
score: 0
Accepted
time: 0ms
memory: 3468kb
input:
5 1 0 0 1 0 0 2 0 0 1 0 0 3 0 0 1 0 0 4 0 0 0 1 0 5 0 0 -1 -1 0
output:
1000
result:
ok single line: '1000'
Test #15:
score: 0
Accepted
time: 0ms
memory: 3468kb
input:
6 0 1 0 1 0 0 0 2 0 0 2 0 0 3 0 0 3 0 0 4 0 0 4 0 0 5 0 0 5 0 0 6 0 0 6 0
output:
4
result:
ok single line: '4'
Test #16:
score: 0
Accepted
time: 0ms
memory: 3512kb
input:
9 1 0 0 1 0 0 2 0 0 1 0 0 3 0 0 1 0 0 0 1 0 0 1 0 0 2 0 0 1 0 0 3 0 0 1 0 0 0 1 0 0 1 0 0 2 0 0 1 0 0 3 0 0 1
output:
3
result:
ok single line: '3'
Test #17:
score: 0
Accepted
time: 101ms
memory: 3540kb
input:
499 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 7 0 0 1 0 0 8 0 0 1 0 0 9 0 0 1 0 0 10 0 0 -1 0 0 11 0 0 -1 0 0 12 0 0 1 0 0 13 0 0 -1 0 0 14 0 0 1 0 0 15 0 0 1 0 0 16 0 0 1 0 0 17 0 0 -1 0 0 18 0 0 -1 0 0 19 0 0 -1 0 0 20 0 0 -1 0 0 21 0 0 1 0 0 22 0 0 1 0 0...
output:
1220
result:
ok single line: '1220'
Test #18:
score: 0
Accepted
time: 97ms
memory: 3528kb
input:
499 0 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 7 0 0 1 0 0 8 0 0 1 0 0 9 0 0 1 0 0 10 0 0 -1 0 0 11 0 0 -1 0 0 12 0 0 1 0 0 13 0 0 -1 0 0 14 0 0 1 0 0 15 0 0 1 0 0 16 0 0 1 0 0 17 0 0 -1 0 0 18 0 0 -1 0 0 19 0 0 -1 0 0 20 0 0 -1 0 0 21 0 0 1 0 0 22 0 0 1 0...
output:
1220
result:
ok single line: '1220'
Test #19:
score: 0
Accepted
time: 101ms
memory: 3476kb
input:
499 0 0 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 7 0 0 1 0 0 8 0 0 1 0 0 9 0 0 1 0 0 10 0 0 -1 0 0 11 0 0 -1 0 0 12 0 0 1 0 0 13 0 0 -1 0 0 14 0 0 1 0 0 15 0 0 1 0 0 16 0 0 1 0 0 17 0 0 -1 0 0 18 0 0 -1 0 0 19 0 0 -1 0 0 20 0 0 -1 0 0 21 0 0 1 0 0 22 0 0 1...
output:
1220
result:
ok single line: '1220'
Test #20:
score: 0
Accepted
time: 1ms
memory: 3512kb
input:
5 0 0 0 0 -1 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
output:
1001
result:
ok single line: '1001'
Test #21:
score: 0
Accepted
time: 0ms
memory: 3536kb
input:
5 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 0 1 0
output:
1001
result:
ok single line: '1001'
Test #22:
score: 0
Accepted
time: 0ms
memory: 3456kb
input:
5 0 0 0 1 0 0 1 0 0 1 0 0 2 0 0 0 -1 0 3 0 0 1 0 0 4 0 0 -1 0 0
output:
1001
result:
ok single line: '1001'
Test #23:
score: 0
Accepted
time: 0ms
memory: 3460kb
input:
5 0 0 0 1 0 0 1 0 0 -1 0 0 2 0 0 1 0 0 3 0 0 0 -1 0 4 0 0 1 0 0
output:
1001
result:
ok single line: '1001'
Test #24:
score: 0
Accepted
time: 0ms
memory: 3456kb
input:
5 0 0 0 1 1 0 1 0 0 1 0 0 2 0 0 1 0 0 3 0 0 1 0 0 4 0 0 -1 -1 0
output:
1001
result:
ok single line: '1001'
Test #25:
score: 0
Accepted
time: 0ms
memory: 3520kb
input:
5 0 0 0 1 1 0 1 0 0 1 0 0 2 0 0 1 0 0 3 0 0 1 0 0 4 0 0 1 1 0
output:
1001
result:
ok single line: '1001'
Test #26:
score: 0
Accepted
time: 0ms
memory: 3456kb
input:
5 0 0 0 5 -1 0 1 0 0 1 0 0 2 0 0 1 0 0 3 0 0 1 0 0 4 0 0 1 -1 0
output:
1001
result:
ok single line: '1001'
Test #27:
score: 0
Accepted
time: 1ms
memory: 3536kb
input:
17 0 0 0 0 0 1 0 1 0 0 0 1 0 2 0 0 0 1 0 3 0 0 0 1 0 4 0 0 0 1 0 -1 0 0 0 1 0 -2 0 0 0 1 0 -3 0 0 0 1 0 -4 0 0 0 1 1 3 0 0 0 1 2 3 0 0 0 1 -1 3 0 0 0 1 -2 3 0 0 0 1 1 -3 0 0 0 1 2 -3 0 0 0 1 -1 -3 0 0 0 1 -2 -3 0 0 0 1
output:
17
result:
ok single line: '17'
Test #28:
score: 0
Accepted
time: 1ms
memory: 3492kb
input:
17 0 0 0 0 4 0 0 1 0 0 -1 0 0 2 0 0 -2 0 0 3 0 0 -3 0 0 4 0 0 -4 0 0 -1 0 0 1 0 0 -2 0 0 2 0 0 -3 0 0 3 0 0 -4 0 0 4 0 1 3 0 -1 -3 0 2 3 0 -1 -2 0 -1 3 0 1 -3 0 -2 3 0 2 -3 0 1 -3 0 -1 3 0 2 -3 0 -2 3 0 -1 -3 0 1 3 0 -2 -3 0 2 3 0
output:
10
result:
ok single line: '10'
Test #29:
score: 0
Accepted
time: 1ms
memory: 3544kb
input:
17 0 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 2 -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 1 3 0 -1 0 0 2 3 0 -1 0 0 -1 3 0 -1 0 0 -2 3 0 4 -6 0 1 -3 0 -1 0 0 2 -3 0 -1 0 0 -1 -3 0 -1 0 0 -2 -3 0 2 -1 0
output:
3
result:
ok single line: '3'
Test #30:
score: 0
Accepted
time: 0ms
memory: 3452kb
input:
5 0 0 0 1 1 1 0 0 1 0 0 1 0 0 2 0 0 1 0 0 3 0 0 1 0 0 4 0 -1 1
output:
1001
result:
ok single line: '1001'
Test #31:
score: -100
Time Limit Exceeded
input:
500 -455212 958307 274912 -88656 390687 881409 -498879 -623821 322766 -916023 347922 541726 -594515 -554311 -413504 -881701 -506880 -144667 658945 -503396 791805 314816 -830920 -769486 -200847 845218 468338 -166468 -49854 -287877 -820402 914874 916800 258029 -210000 -296727 702016 -389491 -31529 -52...