oj.uz

답안 #978206

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
978206 2024-05-09T03:18:21 Z model_code Spy 3 (JOI24_spy3) C++17
100 / 100
 81 ms 7144 KB 
#include "Aoi.h"
#include <bits/stdc++.h>

using namespace std;

using ll = long long;

namespace {
    const ll linf = 1LL << 60;

    string encode(ll num, int len) {
        string s;
        for (int i = len - 1; i >= 0; i--) s.push_back('0' + (num >> i & 1));
        return s;
    }

    // {dist, pre}
    pair<vector<ll>, vector<int>> dijkstra(int n, const vector<int> &a, const vector<int> &b, const vector<ll> &c) {
        vector<vector<tuple<int, ll, int>>> G(n);
        for (int i = 0; i < a.size(); i++) {
            if (c[i] == -1) continue;
            G[a[i]].emplace_back(b[i], c[i], i);
            G[b[i]].emplace_back(a[i], c[i], i);
        }
        vector<ll> dist(n, linf);
        vector<int> pre(n, -1);
        priority_queue<pair<ll, int>, vector<pair<ll, int >>, greater<>> pq;
        dist[0] = 0;
        pq.emplace(0, 0);
        while (!pq.empty()) {
            auto [d, u] = pq.top();
            pq.pop();
            if (d > dist[u]) continue;
            for (auto [v, len, id]: G[u]) {
                if (dist[v] > d + len) {
                    dist[v] = d + len;
                    pre[v] = id;
                    pq.emplace(dist[v], v);
                }
            }
        }
        return {dist, pre};
    }
}

std::string aoi(int n, int m, int q, int k, std::vector<int> a,
                std::vector<int> b, std::vector<long long> c,
                std::vector<int> t, std::vector<int> x) {
    vector<int> x_id(m, -1);
    for (int i = 0; i < k; i++) x_id[x[i]] = i;
    auto [dist, pre] = dijkstra(n, a, b, c);
    vector<vector<int>> G(n + q);   // 最短路木
    for (int i = 1; i < n; i++) {
        G[a[pre[i]] ^ b[pre[i]] ^ i].push_back(i);
    }
    vector<int> bit(n);  // bit[i] : é ‚ç‚¹ i の subtree に含まれる t[j] たちの集合を 0 ~ (1<<q)-1 で
    for (int i = 0; i < q; i++) bit[t[i]] = 1 << i;
    auto dfs = [&](auto &dfs, int u) -> void {
        for (int v: G[u]) {
            dfs(dfs, v);
            bit[u] |= bit[v];
        }
    };
    dfs(dfs, 0);
    vector<int> s(k);
    for (int i = 0; i < k; i++) {
        int e = x[i];
        if (dist[a[e]] > dist[b[e]]) swap(a[e], b[e]);
        if (pre[b[e]] == e) {
            s[i] = bit[b[e]];
        }
    }
    sort(bit.begin(), bit.end());
    bit.erase(unique(bit.begin(), bit.end()), bit.end());
    // è¦ç´ æ•°ã®æ˜‡é †ã«ã‚½ãƒ¼ãƒˆ
    sort(bit.begin(), bit.end(), [](int a, int b) { return __builtin_popcount(a) < __builtin_popcount(b); });
    vector<pair<int, int>> div(1 << q);   // div[i] : 集合 i は何と何に分割されるか
    {
        set<int> st;
        for (int i = 0; i < q; i++) {
            st.insert(1 << i);
        }
        for (int i: bit) {
            if (!i) continue;
            vector<int> mg;
            for (int j: st) if ((j & i) == j) mg.push_back(j);
            for (int j = 1; j < mg.size(); j++) {
                int now = mg[j - 1] | mg[j];
                div[now] = {mg[j - 1], mg[j]};
                st.erase(mg[j - 1]);
                st.erase(mg[j]);
                st.insert(now);
                mg[j] = now;
            }
        }
    }
    vector binom(q, vector<ll>(q));
    for (int i = 0; i < q; i++) {
        binom[i][0] = 1;
        for (int j = 1; j <= i; j++) {
            binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];
        }
    }
    vector<ll> dp(q + 1);   // dp[i] : {1, 2, ..., i} をいくつかの集合に分割する方法の数
    dp[1] = 1;
    for (int i = 2; i <= q; i++) {
        for (int j = 1; j < i; j++) {
            dp[i] += binom[i - 1][j - 1] * dp[j] * dp[i - j];
        }
    }
    vector<int> ls = {0};
    auto f = [&](auto &f, int now) -> ll {
        ls.push_back(now);
        int cnt = __builtin_popcount(now);
        if (cnt == 1) return 0;
        vector<int> fac;
        for (int i = 0; i < q; i++) if (now >> i & 1) fac.push_back(i);
        auto [l, r] = div[now];
        if (~l >> fac[0] & 1) swap(l, r);
        int lc = __builtin_popcount(l);
        int rc = __builtin_popcount(r);
        ll res = 0;
        for (int i = 1; i < lc; i++) {
            res += binom[cnt - 1][i - 1] * dp[i] * dp[cnt - i];
        }
        vector<int> nv;
        for (int i = 0; i < cnt; i++) {
            if (l >> fac[i] & 1) nv.push_back(0);
            else nv.push_back(1);
        }
        vector<int> v;
        for (int i = 0; i < lc; i++) v.push_back(0);
        for (int i = 0; i < rc; i++) v.push_back(1);
        do {
            if (v == nv) break;
            res += dp[lc] * dp[rc];
        } while (next_permutation(v.begin(), v.end()));
        ll lid = f(f, l);
        ll rid = f(f, r);
        res += lid * dp[rc] + rid;
        return res;
    };
    string res = encode(f(f, (1 << q) - 1), 53);
    for (int i = 0; i < k; i++) {
        res += encode(find(ls.begin(), ls.end(), s[i]) - ls.begin(), 5);
    }
    return res;
}
#include "Bitaro.h"
#include <bits/stdc++.h>

using namespace std;

namespace {
    using ll = long long;

    const ll linf = 1LL << 60;

    ll decode(string::iterator l, string::iterator r) {
        ll res = 0;
        while (l < r) {
            res *= 2;
            res += *l - '0';
            ++l;
        }
        return res;
    }

    // {dist, pre}
    pair<vector<ll>, vector<int>> dijkstra(int n, const vector<int> &a, const vector<int> &b, const vector<ll> &c) {
        vector<vector<tuple<int, ll, int>>> G(n);
        for (int i = 0; i < a.size(); i++) {
            if (c[i] == -1) continue;
            G[a[i]].emplace_back(b[i], c[i], i);
            G[b[i]].emplace_back(a[i], c[i], i);
        }
        vector<ll> dist(n, linf);
        vector<int> pre(n, -1);
        priority_queue<pair<ll, int>, vector<pair<ll, int >>, greater<>> pq;
        dist[0] = 0;
        pq.emplace(0, 0);
        while (!pq.empty()) {
            auto [d, u] = pq.top();
            pq.pop();
            if (d > dist[u]) continue;
            for (auto [v, len, id]: G[u]) {
                if (dist[v] > d + len) {
                    dist[v] = d + len;
                    pre[v] = id;
                    pq.emplace(dist[v], v);
                }
            }
        }
        return {dist, pre};
    }
}

void bitaro(int n, int m, int q, int k, std::vector<int> a, std::vector<int> b,
            std::vector<long long> c, std::vector<int> t, std::vector<int> x,
            std::string s) {
    vector binom(q, vector<ll>(q));
    for (int i = 0; i < q; i++) {
        binom[i][0] = 1;
        for (int j = 1; j <= i; j++) {
            binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];
        }
    }
    vector<ll> dp(q + 1);   // dp[i] : {1, 2, ..., i} をいくつかの集合に分割する方法の数
    dp[1] = 1;
    for (int i = 2; i <= q; i++) {
        for (int j = 1; j < i; j++) {
            dp[i] += binom[i - 1][j - 1] * dp[j] * dp[i - j];
        }
    }
    vector<int> ls = {0};
    auto f = [&](auto &f, int now, ll val) -> void {
        ls.push_back(now);
        int cnt = __builtin_popcount(now);
        if (cnt == 1) return;
        vector<int> fac;
        for (int i = 0; i < q; i++) if (now >> i & 1) fac.push_back(i);
        int lc = 1;
        for (;; lc++) {
            ll cur = binom[cnt - 1][lc - 1] * dp[lc] * dp[cnt - lc];
            if (val < cur) break;
            val -= cur;
        }
        int rc = cnt - lc;
        vector<int> v;
        for (int i = 0; i < lc; i++) v.push_back(0);
        for (int i = 0; i < rc; i++) v.push_back(1);
        do {
            if (val < dp[lc] * dp[rc]) break;
            val -= dp[lc] * dp[rc];
        } while (next_permutation(v.begin(), v.end()));
        int l = 0, r = 0;
        for (int i = 0; i < cnt; i++) {
            if (!v[i]) l |= 1 << fac[i];
            else r |= 1 << fac[i];
        }
        f(f, l, val / dp[rc]);
        f(f, r, val % dp[rc]);
    };
    f(f, (1 << q) - 1, decode(s.begin(), s.begin() + 53));
    vector use(q, vector<bool>(k));
    int iter = 53;
    for (int i = 0; i < k; i++) {
        int bit = ls[decode(s.begin() + iter, s.begin() + iter + 5)];
        iter += 5;
        for (int j = 0; j < q; j++) if (bit >> j & 1) use[j][i] = true;
    }
    for (int i = 0; i < q; i++) {
        for (int j = 0; j < k; j++) {
            if (use[i][j]) c[x[j]] = 0;
        }
        auto [dist, pre] = dijkstra(n, a, b, c);
        int now = t[i];
        vector<int> es;
        while (now) {
            es.push_back(pre[now]);
            now = a[pre[now]] ^ b[pre[now]] ^ now;
        }
        reverse(es.begin(), es.end());
        answer(es);
        for (int j = 0; j < k; j++) c[x[j]] = -1;
    }
}

Compilation message

Aoi.cpp: In function 'std::pair<std::vector<long long int>, std::vector<int> > {anonymous}::dijkstra(int, const std::vector<int>&, const std::vector<int>&, const std::vector<long long int>&)':
Aoi.cpp:20:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   20 |         for (int i = 0; i < a.size(); i++) {
      |                         ~~^~~~~~~~~~
Aoi.cpp: In function 'std::string aoi(int, int, int, int, std::vector<int>, std::vector<int>, std::vector<long long int>, std::vector<int>, std::vector<int>)':
Aoi.cpp:87:31: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   87 |             for (int j = 1; j < mg.size(); j++) {
      |                             ~~^~~~~~~~~~~

Bitaro.cpp: In function 'std::pair<std::vector<long long int>, std::vector<int> > {anonymous}::dijkstra(int, const std::vector<int>&, const std::vector<int>&, const std::vector<long long int>&)':
Bitaro.cpp:24:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   24 |         for (int i = 0; i < a.size(); i++) {
      |                         ~~^~~~~~~~~~

Subtask #1
100.0 / 100.0

# 결과 실행 시간 메모리 Grader output
1 Correct 26 ms 4924 KB Output is correct
2 Correct 0 ms 776 KB Output is correct
3 Correct 58 ms 5968 KB Output is correct
4 Correct 52 ms 6048 KB Output is correct
5 Correct 65 ms 5788 KB Output is correct
6 Correct 61 ms 6152 KB Output is correct
7 Correct 63 ms 5760 KB Output is correct
8 Correct 58 ms 5904 KB Output is correct
9 Correct 52 ms 6036 KB Output is correct
10 Correct 23 ms 5668 KB Output is correct
11 Correct 61 ms 6176 KB Output is correct
12 Correct 77 ms 6304 KB Output is correct
13 Correct 65 ms 5884 KB Output is correct
14 Correct 61 ms 5736 KB Output is correct
15 Correct 64 ms 5880 KB Output is correct
16 Correct 19 ms 5300 KB Output is correct
17 Correct 64 ms 6340 KB Output is correct
18 Correct 64 ms 6028 KB Output is correct
19 Correct 66 ms 6344 KB Output is correct
20 Correct 48 ms 6140 KB Output is correct
21 Correct 61 ms 6188 KB Output is correct
22 Correct 72 ms 6160 KB Output is correct
23 Correct 51 ms 6176 KB Output is correct
24 Correct 72 ms 6244 KB Output is correct
25 Correct 76 ms 6240 KB Output is correct
26 Correct 69 ms 5964 KB Output is correct
27 Correct 1 ms 1300 KB Output is correct
28 Correct 57 ms 6316 KB Output is correct
29 Correct 34 ms 4832 KB Output is correct
30 Correct 62 ms 6308 KB Output is correct
31 Correct 35 ms 6064 KB Output is correct
32 Correct 77 ms 6256 KB Output is correct
33 Correct 67 ms 6424 KB Output is correct
34 Correct 74 ms 7144 KB Output is correct
35 Correct 59 ms 6884 KB Output is correct
36 Correct 60 ms 6580 KB Output is correct
37 Correct 16 ms 3424 KB Output is correct
38 Correct 37 ms 4772 KB Output is correct
39 Correct 34 ms 5028 KB Output is correct
40 Correct 10 ms 4112 KB Output is correct
41 Correct 77 ms 6644 KB Output is correct
42 Correct 45 ms 6488 KB Output is correct
43 Correct 81 ms 6952 KB Output is correct
44 Correct 24 ms 6324 KB Output is correct
45 Correct 19 ms 3456 KB Output is correct
46 Correct 32 ms 4408 KB Output is correct
47 Correct 32 ms 4668 KB Output is correct
48 Correct 0 ms 772 KB Output is correct
49 Correct 1 ms 776 KB Output is correct
50 Correct 17 ms 4960 KB Output is correct
51 Correct 2 ms 1816 KB Output is correct
52 Correct 1 ms 1304 KB Output is correct
53 Correct 28 ms 4884 KB Output is correct
54 Correct 17 ms 3496 KB Output is correct
55 Correct 46 ms 4880 KB Output is correct
56 Correct 44 ms 6188 KB Output is correct
57 Correct 59 ms 6048 KB Output is correct
58 Correct 58 ms 5172 KB Output is correct
59 Correct 72 ms 6812 KB Output is correct
60 Correct 65 ms 6452 KB Output is correct
61 Correct 74 ms 6536 KB Output is correct
62 Correct 67 ms 6316 KB Output is correct
63 Correct 77 ms 6716 KB Output is correct
64 Correct 19 ms 5400 KB Output is correct
65 Correct 37 ms 4436 KB Output is correct
66 Correct 32 ms 6332 KB Output is correct
67 Correct 37 ms 4224 KB Output is correct
68 Correct 32 ms 6436 KB Output is correct
69 Correct 0 ms 784 KB Output is correct
70 Correct 0 ms 784 KB Output is correct
71 Correct 0 ms 784 KB Output is correct
72 Correct 17 ms 3332 KB Output is correct
73 Correct 43 ms 4408 KB Output is correct
74 Correct 39 ms 4456 KB Output is correct
75 Correct 11 ms 3856 KB Output is correct
76 Correct 0 ms 776 KB Output is correct
77 Correct 57 ms 6564 KB Output is correct
78 Correct 52 ms 6580 KB Output is correct
79 Correct 59 ms 6624 KB Output is correct
80 Correct 1 ms 792 KB Output is correct
81 Correct 63 ms 5860 KB Output is correct
82 Correct 59 ms 5876 KB Output is correct
83 Correct 67 ms 6008 KB Output is correct