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Submission #769560

# Submission time Handle Problem Language Result Execution time Memory
769560 2023-06-29T19:11:50 Z PurpleCrayon Capital City (JOI20_capital_city) C++17
100 / 100
 219 ms 65036 KB 
#include <bits/stdc++.h>
using namespace std;

#define sz(v) int(v.size())
#define ar array
typedef long long ll;
const int N = 2e5+10, MOD = 998244353;

struct DSU {
    vector<int> par, sz;
    DSU(int n): par(n) {
        iota(par.begin(), par.end(), 0);
        sz.assign(n, 1);
    }

    int find_set(int v) {
        return v == par[v] ? v : par[v] = find_set(par[v]);
    }

    bool union_sets(int a, int b) {
        if ((a = find_set(a)) == (b = find_set(b))) return false;
        if (sz[a] < sz[b]) swap(a, b);
        par[b] = a, sz[a] += sz[b], sz[b] = 0;
        return true;
    }
};

int n, k, col[N], my_out[N], tree_par[N], tree_st[N], tree_en[N], et[N];
vector<int> adj[N];

int tt = 0;
void dfs(int c, int p) {
    tree_par[c] = p;
    et[tree_st[c] = tt++] = c;
    for (int nxt : adj[c]) if (nxt != p) {
        dfs(nxt, c);
    }
    tree_en[c] = tt-1;
}

int par[N], min_st[N], max_st[N], cnt[N];
set<int> st[N];
multiset<int> ms[N];

void merge(int a, int b) {
    a = par[a], b = par[b];
    if (a == b) return;
    if (sz(st[a]) < sz(st[b])) swap(a, b);

    for (int x : st[b]) {
        ms[a].erase(x);
        st[a].insert(x);
        par[x] = a;
    }
    st[b].clear();
    cnt[a] += cnt[b];

    for (int x : ms[b]) {
        if (!st[a].count(x)) {
            ms[a].insert(x);
        }
    }
    ms[b].clear();

    min_st[a] = min(min_st[a], min_st[b]);
    max_st[a] = max(max_st[a], max_st[b]);
}

int get_out(int c) {
    c = par[c];

    int maybe = et[min_st[c]];
    int undo = -1;
    if (tree_par[maybe] != -1 && tree_en[maybe] >= max_st[c]) {
        undo = col[tree_par[maybe]];
        auto it = ms[c].find(undo);
        if (it != ms[c].end()) {
            ms[c].erase(it);
        } else {
            undo = -1;
        }
    }

    int ans = -1;
    if (sz(ms[c])) ans = *ms[c].begin();

    if (undo != -1) {
        ms[c].insert(undo);
    }
    return ans;
}


void solve() {
    cin >> n >> k;
    for (int i = 0; i < n-1; i++) {
        int a, b; cin >> a >> b, --a, --b;
        adj[a].push_back(b), adj[b].push_back(a);
    }
    dfs(0, -1);

    for (int i = 0; i < n; i++) cin >> col[i], --col[i];

    for (int i = 0; i < k; i++) {
        par[i] = i;
        cnt[i] = 1;
        st[i].insert(i);
    }

    fill(min_st, min_st + n, MOD);
    fill(max_st, max_st + n, -1);
    for (int i = 0; i < n; i++) {
        min_st[col[i]] = min(min_st[col[i]], tree_st[i]);
        max_st[col[i]] = max(max_st[col[i]], tree_st[i]);
        if (tree_par[i] != -1 && col[tree_par[i]] != col[i]) {
            ms[col[i]].insert(col[tree_par[i]]);
        }
    }

    memset(my_out, -1, sizeof(my_out));
    DSU d(k);
    for (int root = 0; root < k; root++) {
        my_out[par[root]] = get_out(root);
        while (my_out[par[root]] != -1) {
            if (d.union_sets(root, my_out[par[root]])) {
                break;
            } else {
                vector<int> use{par[my_out[par[root]]]};
                while (use.back() != par[root]) {
                    use.push_back(par[my_out[use.back()]]);
                }

                use.pop_back();
                for (int x : use) {
                    merge(x, root);
                }
                my_out[par[root]] = get_out(root);
            }
        }
    }

    int best = MOD;
    for (int i = 0; i < k; i++) {
        int c = par[i];
        if (my_out[c] == -1) {
            best = min(best, cnt[c] - 1);
        }
    }

    cout << best << '\n';
}

int main() {
    ios::sync_with_stdio(false); cin.tie(0);
    int T = 1;
    // cin >> T;
    while (T--) solve();
}

Subtask #1
1.0 / 1.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 24532 KB Output is correct
2 Correct 12 ms 24532 KB Output is correct
3 Correct 11 ms 24532 KB Output is correct
4 Correct 11 ms 24532 KB Output is correct
5 Correct 11 ms 24532 KB Output is correct
6 Correct 12 ms 24592 KB Output is correct
7 Correct 12 ms 24588 KB Output is correct
8 Correct 12 ms 24532 KB Output is correct
9 Correct 12 ms 24592 KB Output is correct
10 Correct 11 ms 24532 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 24532 KB Output is correct
2 Correct 12 ms 24532 KB Output is correct
3 Correct 11 ms 24532 KB Output is correct
4 Correct 11 ms 24532 KB Output is correct
5 Correct 11 ms 24532 KB Output is correct
6 Correct 12 ms 24592 KB Output is correct
7 Correct 12 ms 24588 KB Output is correct
8 Correct 12 ms 24532 KB Output is correct
9 Correct 12 ms 24592 KB Output is correct
10 Correct 11 ms 24532 KB Output is correct
11 Correct 12 ms 24912 KB Output is correct
12 Correct 12 ms 24868 KB Output is correct
13 Correct 12 ms 24864 KB Output is correct
14 Correct 13 ms 24856 KB Output is correct
15 Correct 13 ms 24916 KB Output is correct
16 Correct 13 ms 24912 KB Output is correct
17 Correct 12 ms 24788 KB Output is correct
18 Correct 12 ms 24788 KB Output is correct
19 Correct 13 ms 24900 KB Output is correct
20 Correct 12 ms 24860 KB Output is correct
21 Correct 12 ms 24868 KB Output is correct
22 Correct 15 ms 25036 KB Output is correct
23 Correct 13 ms 24916 KB Output is correct
24 Correct 14 ms 24916 KB Output is correct
25 Correct 13 ms 24900 KB Output is correct
26 Correct 13 ms 24900 KB Output is correct
27 Correct 13 ms 24916 KB Output is correct
28 Correct 13 ms 24912 KB Output is correct
29 Correct 12 ms 24916 KB Output is correct
30 Correct 13 ms 24924 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 150 ms 61080 KB Output is correct
2 Correct 87 ms 64968 KB Output is correct
3 Correct 156 ms 64676 KB Output is correct
4 Correct 90 ms 64972 KB Output is correct
5 Correct 127 ms 61536 KB Output is correct
6 Correct 87 ms 64800 KB Output is correct
7 Correct 123 ms 60852 KB Output is correct
8 Correct 83 ms 62216 KB Output is correct
9 Correct 201 ms 59856 KB Output is correct
10 Correct 203 ms 58576 KB Output is correct
11 Correct 215 ms 60156 KB Output is correct
12 Correct 203 ms 61644 KB Output is correct
13 Correct 192 ms 58084 KB Output is correct
14 Correct 219 ms 61880 KB Output is correct
15 Correct 194 ms 61336 KB Output is correct
16 Correct 201 ms 58568 KB Output is correct
17 Correct 208 ms 59084 KB Output is correct
18 Correct 204 ms 58956 KB Output is correct
19 Correct 205 ms 60760 KB Output is correct
20 Correct 204 ms 62668 KB Output is correct
21 Correct 12 ms 24532 KB Output is correct

Subtask #4
59.0 / 59.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 24532 KB Output is correct
2 Correct 12 ms 24532 KB Output is correct
3 Correct 11 ms 24532 KB Output is correct
4 Correct 11 ms 24532 KB Output is correct
5 Correct 11 ms 24532 KB Output is correct
6 Correct 12 ms 24592 KB Output is correct
7 Correct 12 ms 24588 KB Output is correct
8 Correct 12 ms 24532 KB Output is correct
9 Correct 12 ms 24592 KB Output is correct
10 Correct 11 ms 24532 KB Output is correct
11 Correct 12 ms 24912 KB Output is correct
12 Correct 12 ms 24868 KB Output is correct
13 Correct 12 ms 24864 KB Output is correct
14 Correct 13 ms 24856 KB Output is correct
15 Correct 13 ms 24916 KB Output is correct
16 Correct 13 ms 24912 KB Output is correct
17 Correct 12 ms 24788 KB Output is correct
18 Correct 12 ms 24788 KB Output is correct
19 Correct 13 ms 24900 KB Output is correct
20 Correct 12 ms 24860 KB Output is correct
21 Correct 12 ms 24868 KB Output is correct
22 Correct 15 ms 25036 KB Output is correct
23 Correct 13 ms 24916 KB Output is correct
24 Correct 14 ms 24916 KB Output is correct
25 Correct 13 ms 24900 KB Output is correct
26 Correct 13 ms 24900 KB Output is correct
27 Correct 13 ms 24916 KB Output is correct
28 Correct 13 ms 24912 KB Output is correct
29 Correct 12 ms 24916 KB Output is correct
30 Correct 13 ms 24924 KB Output is correct
31 Correct 150 ms 61080 KB Output is correct
32 Correct 87 ms 64968 KB Output is correct
33 Correct 156 ms 64676 KB Output is correct
34 Correct 90 ms 64972 KB Output is correct
35 Correct 127 ms 61536 KB Output is correct
36 Correct 87 ms 64800 KB Output is correct
37 Correct 123 ms 60852 KB Output is correct
38 Correct 83 ms 62216 KB Output is correct
39 Correct 201 ms 59856 KB Output is correct
40 Correct 203 ms 58576 KB Output is correct
41 Correct 215 ms 60156 KB Output is correct
42 Correct 203 ms 61644 KB Output is correct
43 Correct 192 ms 58084 KB Output is correct
44 Correct 219 ms 61880 KB Output is correct
45 Correct 194 ms 61336 KB Output is correct
46 Correct 201 ms 58568 KB Output is correct
47 Correct 208 ms 59084 KB Output is correct
48 Correct 204 ms 58956 KB Output is correct
49 Correct 205 ms 60760 KB Output is correct
50 Correct 204 ms 62668 KB Output is correct
51 Correct 12 ms 24532 KB Output is correct
52 Correct 187 ms 50428 KB Output is correct
53 Correct 193 ms 50536 KB Output is correct
54 Correct 144 ms 50464 KB Output is correct
55 Correct 176 ms 50488 KB Output is correct
56 Correct 192 ms 50548 KB Output is correct
57 Correct 179 ms 50552 KB Output is correct
58 Correct 137 ms 55552 KB Output is correct
59 Correct 136 ms 55956 KB Output is correct
60 Correct 151 ms 56140 KB Output is correct
61 Correct 142 ms 56036 KB Output is correct
62 Correct 85 ms 64972 KB Output is correct
63 Correct 86 ms 65036 KB Output is correct
64 Correct 85 ms 62928 KB Output is correct
65 Correct 87 ms 64776 KB Output is correct
66 Correct 138 ms 53064 KB Output is correct
67 Correct 108 ms 52804 KB Output is correct
68 Correct 104 ms 52852 KB Output is correct
69 Correct 102 ms 52968 KB Output is correct
70 Correct 105 ms 52820 KB Output is correct
71 Correct 116 ms 52872 KB Output is correct
72 Correct 104 ms 52824 KB Output is correct
73 Correct 104 ms 52312 KB Output is correct
74 Correct 100 ms 52972 KB Output is correct
75 Correct 108 ms 52880 KB Output is correct
76 Correct 135 ms 59028 KB Output is correct
77 Correct 126 ms 57880 KB Output is correct
78 Correct 213 ms 58700 KB Output is correct
79 Correct 210 ms 57848 KB Output is correct
80 Correct 197 ms 62412 KB Output is correct
81 Correct 201 ms 60088 KB Output is correct
82 Correct 216 ms 59824 KB Output is correct
83 Correct 210 ms 57996 KB Output is correct
84 Correct 202 ms 61324 KB Output is correct
85 Correct 216 ms 60584 KB Output is correct
86 Correct 200 ms 57676 KB Output is correct
87 Correct 199 ms 58956 KB Output is correct
88 Correct 184 ms 59340 KB Output is correct
89 Correct 174 ms 57348 KB Output is correct
90 Correct 157 ms 57984 KB Output is correct
91 Correct 162 ms 58760 KB Output is correct
92 Correct 167 ms 57292 KB Output is correct
93 Correct 164 ms 57672 KB Output is correct
94 Correct 167 ms 57164 KB Output is correct
95 Correct 187 ms 58288 KB Output is correct
96 Correct 179 ms 56888 KB Output is correct
97 Correct 169 ms 58384 KB Output is correct