Submission #1058283

#	Time	Username	Problem	Language	Result	Execution time	Memory
1058283		Forested	Thousands Islands (IOI22_islands)	C++17	55 / 100	176 ms	51904 KiB

islands

#include <bits/stdc++.h>
using namespace std;

using i32 = int;
using i64 = long long;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<VV<T>>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

#define OVERRIDE4(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, l, r) for (i32 i = (i32)(l); i < (i32)(r); ++i)
#define REP(...) OVERRIDE4(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, l, r) for (i32 i = (i32)(r)-1; i >= (i32)(l); --i)
#define PER(...) OVERRIDE4(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32) size(x)

void dbg(i32 x) { cerr << x; }
void dbg(i64 x) { cerr << x; }
template <typename T, typename U>
void dbg(pair<T, U> p) {
    cerr << '(';
    dbg(p.first);
    cerr << ", ";
    dbg(p.second);
    cerr << ')';
}
template <typename T>
void dbg(V<T> arr) {
    cerr << '[';
    REP(i, LEN(arr)) {
        if (i) {
            cerr << ", ";
        }
        dbg(arr[i]);
    }
    cerr << ']';
}
void debug() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug(Head head, Tail... tail) {
    dbg(head);
    cerr << ", ";
    debug(tail...);
}
#ifdef DEBUGF
#define DBG(...)                       \
    do {                               \
        cerr << #__VA_ARGS__ << " : "; \
        debug(__VA_ARGS__);            \
    } while (false)
#else
#define DBG(...) (void)0
#endif

#include <variant>
#include "islands.h"

VV<i32> scc(const VV<pair<i32, i32>> &g) {
    i32 n = LEN(g);
    VV<i32> ret;
    V<i32> alive(n, 1), in(n, -1), ord(n, -1), stc;
    auto dfs = [&](auto dfs, i32 v, i32 &t) -> void {
        in[v] = ord[v] = t++;
        stc.push_back(v);
        for (auto [u, e] : g[v]) {
            if (!alive[u]) {
                continue;
            }
            if (in[u] == -1) {
                dfs(dfs, u, t);
                chmin(ord[v], ord[u]);
            } else {
                chmin(ord[v], in[u]);
            }
        }
        if (in[v] == ord[v]) {
            V<i32> comp;
            while (true) {
                comp.push_back(stc.back());
                stc.pop_back();
                alive[comp.back()] = 0;
                if (comp.back() == v) {
                    break;
                }
            }
            ret.push_back(comp);
        }
    };
    i32 t = 0;
    REP(i, n) {
        if (in[i] == -1) {
            dfs(dfs, i, t);
        }
    }
    return ret;
}

variant<bool, V<i32>> find_journey(i32 n, i32 m, V<i32> u, V<i32> v) {
    VV<pair<i32, i32>> g(n);
    REP(i, m) { g[u[i]].emplace_back(v[i], i); }

    if (n == 2) {
        bool ok = (LEN(g[0]) >= 2 && LEN(g[1]) >= 1);
        if (!ok) {
            return false;
        }
        i32 e01a = g[0][0].second;
        i32 e01b = g[0][1].second;
        i32 e10 = g[1][0].second;
        V<i32> walk({e01a, e10, e01b, e01a, e10, e01b});
        return walk;
    }

    map<pair<i32, i32>, V<i32>> edgeid;
    REP(i, m) { edgeid[pair<i32, i32>(u[i], v[i])].push_back(i); }
    {
        V<i32> revc;
        REP(i, 1, n) {
            if (edgeid.count(pair<i32, i32>(0, i)) &&
                edgeid.count(pair<i32, i32>(i, 0))) {
                revc.push_back(i);
            }
        }
        if (LEN(revc) >= 2) {
            i32 u = revc[0];
            i32 v = revc[1];
            i32 e01 = edgeid[pair<i32, i32>(0, u)][0];
            i32 e10 = edgeid[pair<i32, i32>(u, 0)][0];
            i32 e02 = edgeid[pair<i32, i32>(0, v)][0];
            i32 e20 = edgeid[pair<i32, i32>(v, 0)][0];
            V<i32> walk({e01, e10, e02, e20, e10, e01, e20, e02});
            return walk;
        }
    }

    bool is_subtask3 = true, is_subtask4 = true;
    if (m % 2 == 0) {
        REP(i, m / 2) {
            if (u[2 * i] != v[2 * i + 1] || u[2 * i + 1] != v[2 * i]) {
                is_subtask3 = false;
            }
            if (u[2 * i] != u[2 * i + 1] || v[2 * i + 1] != v[2 * i]) {
                is_subtask4 = false;
            }
        }
    } else {
        is_subtask3 = is_subtask4 = false;
    }

    VV<i32> comps = scc(g);
    DBG(comps);

    V<i32> ccn(n);
    REP(i, LEN(comps)) {
        for (i32 v : comps[i]) {
            ccn[v] = i;
        }
    }

    V<i32> indeg(n, 0), outdeg(n, 0);
    REP(v, n) {
        for (auto [u, e] : g[v]) {
            if (ccn[v] == ccn[u]) {
                ++indeg[u];
                ++outdeg[v];
            }
        }
    }

    V<i32> is_ok(n, 0), reach_cycle(n, 0);
    for (const V<i32> &comp : comps) {
        i32 reach_edge = 0;
        for (i32 v : comp) {
            for (auto [u, e] : g[v]) {
                if (reach_cycle[u]) {
                    ++reach_edge;
                }
            }
        }
        if (LEN(comp) >= 2 || reach_edge) {
            for (i32 v : comp) {
                reach_cycle[v] = 1;
            }
        }

        if (reach_edge >= 2) {
            for (i32 v : comp) {
                is_ok[v] = 1;
            }
            continue;
        }

        bool outer = false;
        for (i32 v : comp) {
            for (auto [u, e] : g[v]) {
                if (is_ok[u]) {
                    outer = true;
                }
            }
        }
        if (outer) {
            for (i32 v : comp) {
                is_ok[v] = 1;
            }
            continue;
        }

        bool deg3 = false;
        for (i32 v : comp) {
            if (outdeg[v] >= 2 && indeg[v] >= 3) {
                deg3 = true;
            }
            if (outdeg[v] >= 2) {
                is_ok[v] = 1;
            }
        }
        if (deg3) {
            for (i32 v : comp) {
                is_ok[v] = 1;
            }
        }

        /*if (LEN(comp) >= 2) {
            for (i32 v : comp) {
                for (auto [u, e] : g[v]) {
                    if (reach_cycle[u]) {
                        is_ok[v] = 1;
                    }
                }
            }
        }*/
    }

    bool exists = is_ok[0];
    /*if (!exists) {
        return false;
    }*/

    auto get_path = [&](i32 from, i32 to) -> V<i32> {
        V<i32> dist(n, -1), pare(n, -1);
        queue<i32> que;
        dist[from] = 0;
        que.push(from);
        while (!que.empty()) {
            i32 v = que.front();
            que.pop();
            for (auto [u, e] : g[v]) {
                if (dist[u] == -1) {
                    dist[u] = dist[v] + 1;
                    pare[u] = e;
                    que.push(u);
                }
            }
        }
        V<i32> path;
        while (to != from) {
            i32 e = pare[to];
            path.push_back(e);
            to ^= u[e] ^ v[e];
        }
        reverse(ALL(path));
        return path;
    };

    if (is_subtask3) {
        if (!exists) {
            return false;
        }
        i32 c = -1;
        REP(i, n) {
            if (LEN(g[i]) >= 3 && ccn[i] == ccn[0]) {
                c = i;
            }
        }
        assert(c != -1);
        V<i32> path = get_path(0, c);
        i32 last = path.back();
        g[c].erase(
            find(ALL(g[c]), pair<i32, i32>(u[last] ^ v[last] ^ c, last ^ 1)));
        i32 e0 = g[c][0].second;
        i32 e0b = e0 ^ 1;
        i32 e1 = g[c][1].second;
        i32 e1b = e1 ^ 1;
        V<i32> ret = path;
        ret.push_back(e0);
        ret.push_back(e0b);
        ret.push_back(e1);
        ret.push_back(e1b);
        ret.push_back(e0b);
        ret.push_back(e0);
        ret.push_back(e1b);
        ret.push_back(e1);
        PER(i, LEN(path)) { ret.push_back(path[i]); }
        return ret;
    }

    auto get_simple_cycle = [&](i32 c) -> V<i32> {
        V<i32> vis(n, 0), par(n, -1), pare(n, -1);
        i32 back = -1, backe = -1;
        auto dfs = [&](auto dfs, i32 v) -> void {
            vis[v] = 1;
            for (auto [u, e] : g[v]) {
                if (ccn[u] != ccn[v]) {
                    continue;
                }
                if (u == c) {
                    back = v;
                    backe = e;
                }
                if (!vis[u]) {
                    par[u] = v;
                    pare[u] = e;
                    dfs(dfs, u);
                }
            }
        };
        dfs(dfs, c);
        assert(back != -1);
        DBG(back, backe, par, pare);
        V<i32> cycle;
        cycle.push_back(backe);
        while (back != c) {
            cycle.push_back(pare[back]);
            back = par[back];
        }
        reverse(ALL(cycle));
        return cycle;
    };

    if (is_subtask4) {
        if (!exists) {
            return false;
        }
        V<i32> dest(n, -1);
        for (const V<i32> &comp : comps) {
            if (LEN(comp) >= 2) {
                for (i32 v : comp) {
                    dest[v] = v;
                }
                continue;
            }
            i32 pct = -1;
            for (i32 v : comp) {
                for (auto [u, e] : g[v]) {
                    if (dest[u] != -1) {
                        pct = dest[u];
                    }
                }
            }
            for (i32 v : comp) {
                dest[v] = pct;
            }
        }
        i32 d0 = dest[0];
        assert(d0 != -1);
        DBG(d0);
        V<i32> path = get_path(0, d0);
        V<i32> cycle = get_simple_cycle(d0);
        DBG(path, cycle);
        V<i32> ret = path;
        REP(i, 2) {
            for (i32 e : cycle) {
                ret.push_back(e ^ i);
            }
        }
        REP(i, 2) {
            PER(j, LEN(cycle)) { ret.push_back(cycle[j] ^ i); }
        }
        PER(i, LEN(path)) { ret.push_back(path[i]); }
        return ret;
    }

    return exists;
}

• Subtask 1: 5 / 5
• Subtask 2: 5 / 5
• Subtask 3: 21 / 21
• Subtask 4: 24 / 24
• Subtask 5: 0 / 45