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Submission #1054605

# Submission time Handle Problem Language Result Execution time Memory
1054605 2024-08-12T11:01:23 Z cot7302 Love Polygon (BOI18_polygon) C++17
100 / 100
 49 ms 15768 KB 
#include <bits/stdc++.h>
#define ALL(X) begin(X), end(X)
using namespace std;
using i64 = long long;

template <class T>
using vec = vector<T>;

vec<int> get_input(int n) {
    unordered_map<string, int> id;
    auto get_id = [&](const string& str) -> int {
        if (auto it = id.find(str); it != end(id))
            return it->second;
        int sz = size(id);
        return id[str] = sz;
    };
    vec<int> ret(n);
    for (int i = 0; i < n; i++) {
        string s, t; cin >> s >> t;
        ret[get_id(s)] = get_id(t);
    }
    return ret;
}

constexpr int inf = 1e9;

void solve1(int n) {
    if (n % 2 == 1)
        return void(cout << "-1\n");
    vec<int> to = get_input(n);
    vec<int> dp(1 << n, inf);
    dp[0] = 0;
    for (int mask = 1; mask < (1 << n); mask++) if (__builtin_popcount(mask) % 2 == 0) {
        for (int i = 0; i < n; i++) if ((mask >> i) & 1) {
            for (int j = 0; j < i; j++) if ((mask >> j) & 1) {
                dp[mask] = min(dp[mask], dp[mask ^ (1 << i) ^ (1 << j)] + (to[i] != j) + (to[j] != i));
            }
        }
    }
    cout << dp.back() << '\n';
}

void solve2(int n) {
    if (n % 2 == 1)
        return void(cout << "-1\n");
    vec<int> to = get_input(n);
    vec<bool> is_cir(n);
    vec<int> indeg(n), rt(n), sz(n);
    for (int i = 0; i < n; i++)
        ++indeg[to[i]];
    vec<vec<int>> G(n);
    {
        queue<int> q;
        for (int i = 0; i < n; i++)
            if (indeg[i] == 0)
                q.emplace(i);
        while (!empty(q)) {
            int x = q.front(); q.pop();
            G[to[x]].emplace_back(x);
            if (--indeg[to[x]] == 0)
                q.emplace(to[x]);
        }
    }
    vec<array<int, 2>> max_pair(n);
    for (int i = 0; i < n; i++) if (indeg[i]) {
        for (int x = i; indeg[x]; x = to[x]) {
            is_cir[x] = true;
            indeg[x] = 0;
            ++sz[i];
            auto dfs = [&](auto&& f, int y) -> void {
                rt[y] = x;
                for (auto nxt : G[y]) {
                    f(f, nxt);
                    max_pair[y][0] += max_pair[nxt][1];
                }
                for (auto nxt : G[y]) {
                    max_pair[y][1] = max(max_pair[y][1], max_pair[y][0] - max_pair[nxt][1] + max_pair[nxt][0] + 1);
                }
            };
            dfs(dfs, x);
            rt[x] = i;
        }
    }
    vec<array<int, 2>> dp0(n), dp1(n);
    vec<int> ans(n);
    for (int i = 0; i < n; i++) if (rt[i] == i) {
        if (sz[i] == 2) {
            ans[i] = 2 + max_pair[i][0] + max_pair[to[i]][0];
        }
        dp0[i][0] = max_pair[i][0];
        dp0[i][1] = -inf;
        dp1[i][0] = max_pair[i][0];
        dp1[i][1] = max_pair[i][1];
        int pre = i;
        for (int x = to[i], cnt = 1; cnt < sz[i]; x = to[x], ++cnt) {
            dp1[x][0] = max_pair[x][0] + dp1[pre][1];
            dp1[x][1] = max(max_pair[x][1] + dp1[pre][1], max_pair[x][0] + dp1[pre][0] + 1);
            if (pre != i) {
                dp0[x][0] = max_pair[x][0] + dp0[pre][1];
                dp0[x][1] = max(max_pair[x][1] + dp0[pre][1], max_pair[x][0] + dp0[pre][0] + 1);
            }
            else {
                dp0[x][0] = max_pair[x][0] + dp0[pre][0];
                dp0[x][1] = max(max_pair[x][1] + dp0[pre][0], max_pair[x][0] + dp0[pre][0]);
            }
            if (cnt == sz[i] - 1) {
                ans[i] = max({ans[i], dp0[x][1], dp1[x][0], dp1[x][1]});
                ans[i] = max(ans[i], dp0[x][0] + 1);
            }
            pre = x;
        }
        if (sz[i] == 1)
            ans[i] = max(max_pair[i][0], max_pair[i][1]);
    }
    int tot{};
    for (int i = 0; i < n; i++)
        if (rt[i] == i)
            tot += ans[i];
    cout << n - tot << '\n';
}

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int n; cin >> n;
    /*if (n <= 20) solve1(n);
    else */solve2(n);
}

Subtask #1
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 34 ms 10472 KB Output is correct
5 Correct 36 ms 10448 KB Output is correct
6 Correct 33 ms 10436 KB Output is correct
7 Correct 0 ms 348 KB Output is correct

Subtask #3
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 40 ms 11836 KB Output is correct
2 Correct 49 ms 12668 KB Output is correct
3 Correct 27 ms 10448 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 45 ms 15768 KB Output is correct
6 Correct 37 ms 11136 KB Output is correct
7 Correct 37 ms 11132 KB Output is correct
8 Correct 36 ms 10624 KB Output is correct
9 Correct 33 ms 10448 KB Output is correct
10 Correct 28 ms 10792 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 344 KB Output is correct

Subtask #4
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 34 ms 10472 KB Output is correct
20 Correct 36 ms 10448 KB Output is correct
21 Correct 33 ms 10436 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 40 ms 11836 KB Output is correct
24 Correct 49 ms 12668 KB Output is correct
25 Correct 27 ms 10448 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 45 ms 15768 KB Output is correct
28 Correct 37 ms 11136 KB Output is correct
29 Correct 37 ms 11132 KB Output is correct
30 Correct 36 ms 10624 KB Output is correct
31 Correct 33 ms 10448 KB Output is correct
32 Correct 28 ms 10792 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 0 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 0 ms 344 KB Output is correct
37 Correct 39 ms 12000 KB Output is correct
38 Correct 39 ms 10696 KB Output is correct
39 Correct 38 ms 10812 KB Output is correct
40 Correct 39 ms 11144 KB Output is correct
41 Correct 38 ms 11132 KB Output is correct
42 Correct 40 ms 11388 KB Output is correct
43 Correct 45 ms 11644 KB Output is correct
44 Correct 39 ms 11388 KB Output is correct
45 Correct 43 ms 11608 KB Output is correct
46 Correct 38 ms 11392 KB Output is correct
47 Correct 33 ms 10620 KB Output is correct
48 Correct 39 ms 11900 KB Output is correct
49 Correct 43 ms 12608 KB Output is correct
50 Correct 26 ms 10448 KB Output is correct
51 Correct 0 ms 344 KB Output is correct
52 Correct 40 ms 15720 KB Output is correct
53 Correct 37 ms 11068 KB Output is correct
54 Correct 36 ms 11136 KB Output is correct
55 Correct 35 ms 10620 KB Output is correct
56 Correct 33 ms 10448 KB Output is correct
57 Correct 32 ms 11040 KB Output is correct
58 Correct 0 ms 348 KB Output is correct
59 Correct 0 ms 348 KB Output is correct
60 Correct 0 ms 348 KB Output is correct
61 Correct 0 ms 456 KB Output is correct
62 Correct 0 ms 348 KB Output is correct
63 Correct 0 ms 348 KB Output is correct
64 Correct 0 ms 348 KB Output is correct
65 Correct 35 ms 10396 KB Output is correct
66 Correct 32 ms 10436 KB Output is correct
67 Correct 34 ms 10600 KB Output is correct
68 Correct 0 ms 348 KB Output is correct
69 Correct 0 ms 348 KB Output is correct
70 Correct 0 ms 456 KB Output is correct
71 Correct 0 ms 348 KB Output is correct
72 Correct 0 ms 348 KB Output is correct
73 Correct 0 ms 348 KB Output is correct
74 Correct 0 ms 348 KB Output is correct
75 Correct 0 ms 456 KB Output is correct
76 Correct 0 ms 348 KB Output is correct
77 Correct 0 ms 348 KB Output is correct
78 Correct 0 ms 348 KB Output is correct
79 Correct 0 ms 456 KB Output is correct
80 Correct 0 ms 348 KB Output is correct
81 Correct 0 ms 348 KB Output is correct
82 Correct 0 ms 348 KB Output is correct
83 Correct 0 ms 348 KB Output is correct