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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
#111867#6570. Who Watches the Watchmen?KhNURE_KIVIWA 0ms3380kbC++2015.4kb2023-06-09 03:48:532023-06-09 03:48:57

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-06-09 03:48:57]
  • 评测
  • 测评结果:WA
  • 用时:0ms
  • 内存:3380kb
  • [2023-06-09 03:48:53]
  • 提交

answer

//#pragma GCC optimize("Ofast", "unroll-loops")
//#pragma GCC target("sse", "sse2", "sse3", "ssse3", "sse4")
#include <bits/stdc++.h>

#define all(a) a.begin(),a.end()
#define len(a) (int)(a.size())
#define mp make_pair
#define pb push_back
#define fir first
#define sec second
#define fi first
#define se second

using namespace std;

typedef pair<int, int> pii;
typedef long long ll;
typedef long double ld;

template<typename T>
inline bool umin(T &a, T b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

template<typename T>
inline bool umax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

#ifdef LOCAL
#define D for (bool _FLAG = true; _FLAG; _FLAG = false)
#define LOG(...) print(#__VA_ARGS__" ::", __VA_ARGS__) << endl
template <class ...Ts> auto &print(Ts ...ts) { return ((cerr << ts << " "), ...); }
#else
#define D while (false)
#define LOG(...)
#endif // LOCAL

const int max_n = -1, inf = 1000111222;


struct node {
    ll x, y, z, a, b, c;
};


inline bool check_eq (ll a, ll b, ll d, ll div) {
    return a * div == d * b;
}



namespace MIN_COST_MAX_FLOW {

/// source: https://codeforces.com/contest/1572/submission/129205002

#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define EACH(i,c) for(__typeof((c).begin()) i=(c).begin(),i##_end=(c).end();i!=i##_end;++i)
typedef ll Flow;
typedef ll Cost;
const Flow FLOW_INF = 1LL<<60;
const Cost COST_INF = 1LL<<60;

const int SIZE = 65;
vector<pair<Cost, int> > B[SIZE];
Cost last;
int sz;

int bsr(Cost c) {
    if (c == 0) return 0;
    return __lg(c)+1;
}

void init() {
    last = sz = 0;
    REP (i, SIZE) B[i].clear();
}

void push(Cost cst, int v) {
    assert(cst >= last);
    sz++;
    B[bsr(cst^last)].emplace_back(cst, v);
}

pair<Cost, int> pop_min() {
    assert(sz);
    if (B[0].empty()) {
    int k = 1;
    while (k < SIZE && B[k].empty()) k++;
    assert(k < SIZE);
    last = B[k][0].first;
    EACH (e, B[k]) umin(last, e->first);
    EACH (e, B[k]) B[bsr(e->first^last)].push_back(*e);
    B[k].clear();
    }
    assert(B[0].size());
    pair<Cost, int> ret = B[0].back();
    B[0].pop_back();
    sz--;
    return ret;
}

struct MinCostMaxFlow {
    struct Edge {
    int dst;
    Cost cst;
    Flow cap;
    int rev;
    };
    typedef vector<vector<Edge> > Graph;
    Graph G;
    bool negative_edge;
    MinCostMaxFlow(int N) : G(N) {
    negative_edge = false;
    }

    void add_edge(int u, int v, Cost x, Flow f) {
    if (u == v) return;
    if (x < 0) negative_edge = true;
    G[u].push_back((Edge){ v, x, f, (int)G[v].size() });
    G[v].push_back((Edge){ u, -x, 0, (int)G[u].size()-1 });
    }

    void bellman_ford(int s, vector<Cost> &h) {
    fill(h.begin(), h.end(), COST_INF);
    vector<bool> in(G.size());
    h[s] = 0;
    in[s] = true;
    vector <int> front, back;
    front.push_back(s);
    while (1) {
        if (front.empty()) {
        if (back.empty()) return;
        swap(front, back);
        reverse(front.begin(), front.end());
        }
        int v = front.back(); front.pop_back();
        in[v] = false;
        EACH (e, G[v]) if (e->cap) {
        int w = e->dst;
        if (h[w] > h[v] + e->cst) {
            h[w] = h[v] + e->cst;
            if (!in[w]) {
            back.push_back(w);
            in[w] = true;
            }
        }
        }
    }
    }

    Flow flow;
    Cost cost;
    Flow solve(int s, int t, Flow limit = FLOW_INF) {
    flow = 0;
    cost = 0;
    vector<Cost>len1(G.size()), h(G.size());
    if (negative_edge) bellman_ford(s, h);

    vector<int> prev(G.size()), prev_num(G.size());
    while (limit > 0) {
        init(); push(0, s);
        fill(len1.begin(), len1.end(), COST_INF);
        fill(prev.begin(), prev.end(), -1);
        len1[s] = 0;
        while (sz) {
        pair<Cost, int> p = pop_min();
        Cost cst = p.first;
        int v = p.second;
        if (cst > len1[v]) continue;
        for (int i=0; i<(int)G[v].size(); i++) {
            const Edge &f = G[v][i];
            Cost tmp = len1[v] + f.cst + h[v] - h[f.dst];
            if (f.cap > 0 && len1[f.dst] > tmp) {
            len1[f.dst] = tmp;
            push(tmp, f.dst);
            prev[f.dst] = v; prev_num[f.dst] = i;
            }
        }
        }

        if (prev[t] == -1) return flow;
        for (int i=0; i<(int)G.size(); i++) h[i] += len1[i];

        Flow f = limit;
        for (int v=t; v!=s; v=prev[v])
        f = min(f, G[prev[v]][prev_num[v]].cap);
        for (int v=t; v!=s; v=prev[v]) {
        Edge &e = G[prev[v]][prev_num[v]];
        e.cap -= f;
        G[e.dst][e.rev].cap += f;
        }
        limit -= f;
        flow += f;
        cost += f * h[t];
    }
    return flow;
    }
};
}; // namespace MIN_COST_MAX_FLOW;
using MinCostMaxFlow = MIN_COST_MAX_FLOW::MinCostMaxFlow;

namespace math {

inline ll det (ll a, ll b, ll c, ll d) {
    return a * d - b * c;
}

inline pair<pair<ll, ll>, pair<ll, ll> > solve (ll xa1, ll ya1, ll c1, ll xa2, ll ya2, ll c2) {
    ll d = det(xa1, ya1, xa2, ya2);
//    debug(xa1, ya1, c1, xa2, ya2, c2);
    if (d == 0) {
        return {{-1, 0}, {-1, 0}};
    }
    ll x = det(c1, ya1, c2, ya2);
    ll y = det(xa1, c1, xa2, c2);
    return {{x, d}, {y, d}};
}

}



using big = __int128;

inline bool check_good (pair<pair<ll, ll>, pair<ll, ll> > gg, ll a, ll b, ll c) {
    return big(a) * big(gg.first.first) * big(gg.second.second) +
            big(b) * big(gg.first.second) * big(gg.second.first)
            + big(c) * big(gg.first.second) * big(gg.second.second) == 0;
};


inline bool check_pos (pair<ll, ll> a) {
    if (a.first < 0) {
        a.first *= -1;
        a.second *= -1;
    }
    if (a.first == 0) {
        a.second = abs(a.second);
    }
    return a.second >= 0;
}

int main() {
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);

    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n;
    cin >> n;
    vector <node> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i].x >> a[i].y >> a[i].z >> a[i].a >> a[i].b >> a[i].c;
    }
    if (n == 1) {
        cout << "-1\n";
        return 0;
    }
    auto check = [&] (int i, int j, ll akx, ll aky, ll akz, bool what = false) {
        ll A = a[j].x - a[i].x;
        ll B = a[j].y - a[i].y;
        ll C = a[j].z - a[i].z;
        ll d = 0;
        ll div = 0;
        if (!A) {
            if (a[i].x != akx) {
                return false;
            }
        }
        else {
            d = akx - a[i].x;
            div = A;
        }
        if (!B) {
            if (a[i].y != aky) {
                return false;
            }
        }
        else {
            d = aky - a[i].y;
            div = B;
        }
        if (!C) {
            if (a[i].z != akz) {
                return false;
            }
        }
        else {
            d = akz - a[i].z;
            div = C;
        }
        if (A) {
            if (!check_eq(akx - a[i].x, A, d, div)) {
                return false;
            }
        }
        if (B) {
            if (!check_eq(aky - a[i].y, B, d, div)) {
                return false;
            }
        }
        if (C) {
            if (!check_eq(akz - a[i].z, C, d, div)) {
                return false;
            }
        }
        if (d < 0) {
            d *= -1;
            div *= -1;
        }
        assert(d != 0);
        if (div < 0) {
            return false;
        }
        if (what) {
            return true;
        }
        if (d < div) {
            return true;
        }
        return false;
    };
    vector <vector <int> > c(n, vector <int> (n, -1));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (i == j) {
                continue;
            }

            bool ok = true;
            for (int k = 0; k < n; k++) {
                if (k == i || k == j) {
                    continue;
                }
                if (check(i, j, a[k].x, a[k].y, a[k].z)) {
                    ok = false;
                    break;
                }
            }
            if (ok) {
                c[i][j] = 1;
                ll tox = a[i].x + a[i].a;
                ll toy = a[i].y + a[i].b;
                ll toz = a[i].z + a[i].c;
                if (check(i, j, tox, toy, toz, true)) {
                    c[i][j] = 0;
                }
            }
        }
    }
    MinCostMaxFlow g(2 * n + 2);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (c[i][j] == -1) {
                continue;
            }
            //LOG(i, j, c[i][j]);
            g.add_edge(i + 1, n + 1 + j, c[i][j], 1);
        }
        g.add_edge(0, i + 1, 0, 1);
        g.add_edge(n + i + 1, 2 * n + 1, 0, 1);
    }
    int ans = g.solve(0, 2 * n + 1);
    LOG(ans);
    if (ans != n) {
        ans = inf;
        int pos = -1;
        for (int i = 0; i < n; i++) {
            int cnt = 0;
            for (int j = 0; j < n; j++) {
                if (c[i][j] == -1) {
                    continue;
                }
                ++cnt;
            }
            assert(cnt <= 2);
            if (cnt == 1) {
                pos = i;
            }
        }
        vector <int> used(n);
        vector <int> order;
        for (int i = 0; i < n; i++) {
            LOG(pos);
            order.pb(pos);
            used[pos] = 1;
            int to = -1;
            for (int j = 0; j < n; j++) {
                if (c[pos][j] == -1 || used[j]) {
                    continue;
                }
                to = j;
            }
            pos = to;
        }
        auto solve = [&] () {
            for (int i = 0; i < n; i++) {
                vector <int> new_order;
                for (int j = 0; j < n; j++) {
                    if (i == j) {
                        continue;
                    }
                    new_order.pb(order[j]);
                }
                int I = order[i];
                order.swap(new_order);
                vector<int> pref(n, inf), suff(n, inf);
                int val = 0;
                suff[n - 1] = 0;
                ll A, B, C;
                for (int j = 1; j < n - 1; j += 2) {
                    A = a[order[j - 1]].x + a[order[j - 1]].a;
                    B = a[order[j - 1]].y + a[order[j - 1]].b;
                    C = a[order[j - 1]].z + a[order[j - 1]].c;
                    if (!check(order[j - 1], order[j], A, B, C, true)) {
                        ++val;
                    }
                    A = a[order[j]].x + a[order[j]].a;
                    B = a[order[j]].y + a[order[j]].b;
                    C = a[order[j]].z + a[order[j]].c;
                    if (!check(order[j], order[j - 1], A, B, C, true)) {
                        ++val;
                    }
                    pref[j] = val;
                }
                val = 0;
                for (int j = n - 2; j >= 0; j -= 2) {
                    A = a[order[j - 1]].x + a[order[j - 1]].a;
                    B = a[order[j - 1]].y + a[order[j - 1]].b;
                    C = a[order[j - 1]].z + a[order[j - 1]].c;
                    if (!check(order[j - 1], order[j], A, B, C, true)) {
                        ++val;
                    }
                    A = a[order[j]].x + a[order[j]].a;
                    B = a[order[j]].y + a[order[j]].b;
                    C = a[order[j]].z + a[order[j]].c;
                    if (!check(order[j], order[j - 1], A, B, C, true)) {
                        ++val;
                    }
                    suff[j] = val;
                }
                int prf = 0;
                for (int fst = 0; fst < n - 1; fst += 2) {
                    int cur = 1000 + prf;
                    int last = -1, f = -1;
                    for (int j = fst; j < n - 1; j++) {
                        if (last != -1) {
                            if (!check(last, order[j], A, B, C, true)) {
                                ++cur;
                            }
                        }
                        if (f == -1) {
                            f = order[j];
                        }
                        last = order[j];
                        A = a[order[j]].x + a[order[j]].a;
                        B = a[order[j]].y + a[order[j]].b;
                        C = a[order[j]].z + a[order[j]].c;
                        int res = cur + suff[j + 1];
                        if (j == fst) {
                            ll AA = a[order[j]].x + a[order[j]].a;
                            ll BB = a[order[j]].y + a[order[j]].b;
                            ll CC = a[order[j]].z + a[order[j]].c;
                            if (!check(order[j], I, AA, BB, CC, true)) {
                                ++res;
                            }
                            AA = a[I].x + a[I].a;
                            BB = a[I].y + a[I].b;
                            CC = a[I].z + a[I].c;
                            if (!check(I, order[j], AA, BB, CC, true)) {
                                ++res;
                            }
                            umin(ans, res);
                            continue;
                        }
                        ll xx = A - a[last].x;
                        ll yy = B - a[last].y;
                        ll zz = C - a[last].z;
                        ll tx = a[I].a;
                        ll ty = a[I].b;
                        ll tz = a[I].c;
                        ll tx1 = -(a[f].x - a[last].x);
                        ll ty1 = -(a[f].y - a[last].y);
                        ll tz1 = -(a[f].z - a[last].z);

                        if (math::det(tx, tx1, tz, tz1)) {
                            auto gg = math::solve(tx, tx1, -xx, tz, tz1, -zz);
                            if (!check_good(gg, ty, ty1, yy) || !check_pos(gg.first) || !check_pos(gg.second)) {
                                ++res;
                            }
                        } else if (math::det(tx, tx1, ty, ty1)) {
                            auto gg = math::solve(tx, tx1, -xx, ty, ty1, -yy);
                            if (!check_good(gg, tz, tz1, zz) || !check_pos(gg.first) || !check_pos(gg.second)) {
                                ++res;
                            }
                        } else if (math::det(ty, ty1, tz, tz1)) {
                            auto gg = math::solve(ty, ty1, -yy, tz, tz1, -zz);
                            if (!check_good(gg, tx, tx1, xx) || !check_pos(gg.first) || !check_pos(gg.second)) {
                                ++res;
                            }
                        } else {
                            ++res;
                            if (check(last, f, A, B, C, true) ||
                                check(f, last, A, B, C, true)) {
                                ++res;
                            }
                        }
                        umin(ans, res);
                    }

                    prf = pref[fst + 1];
                }
                order.swap(new_order);
            }
        };
        solve();
        reverse(all(order));
        solve();
        cout << ans << '\n';
        return 0;
    }
    cout << g.cost << '\n';
}

详细

Test #1:

score: 0
Wrong Answer
time: 0ms
memory: 3380kb

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:

1001

result:

wrong answer 1st lines differ - expected: '1002', found: '1001'