oj.uz

Submission #706077

# Submission time Handle Problem Language Result Execution time Memory
706077 2023-03-05T20:14:02 Z pakhomovee Capital City (JOI20_capital_city) C++17
100 / 100
 2760 ms 383476 KB 
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <set>
#include <stdlib.h>
#include <map>
#include <random>
#include <cstring>
#include <functional>
#include <iomanip>
#include <cassert>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <array>
 
using namespace std;
 
const int inf = 1e9;
const int maxn = 200000;
 
int par[maxn];
int tin[maxn];
int tout[maxn];
int up[20][maxn];
int upp[20][maxn];
int d[maxn];
vector<int> gp[maxn * 21];
int timer = 0;
vector<int> c;
int id = maxn;
void dfs(int v, vector<vector<int>> &g, int p) {
    tin[v] = timer++;
    up[0][v] = p;
    gp[id].push_back(c[v]);
    upp[0][v] = id++;
    for (int i = 1; i < 20; ++i) {
        up[i][v] = up[i - 1][up[i - 1][v]];
        gp[id].push_back(upp[i - 1][up[i - 1][v]]);
        gp[id].push_back(upp[i - 1][v]);
        upp[i][v] = id++;
    }
    for (int u : g[v]) {
        if (u != p) {
            par[u] = v;
            d[u] = d[v] + 1;
            dfs(u, g, v);
        }
    }
    tout[v] = timer++;
}
 
void dfsrev(int v, vector<vector<int>> &g, int p) {
    gp[c[v]].push_back(id);
    upp[0][v] = id++;
    for (int i = 1; i < 20; ++i) {
        gp[upp[i - 1][up[i - 1][v]]].push_back(id);
        gp[upp[i - 1][v]].push_back(id);
        upp[i][v] = id++;
    }
    for (int u : g[v]) {
        if (u != p) {
            dfsrev(u, g, v);
        }
    }
}
 
bool isa(int u, int v) {
    return tin[u] <= tin[v] && tout[v] <= tout[u];
}
 
int lca(int u, int v) {
    if (isa(u, v)) return u;
    if (isa(v, u)) return v;
    for (int i = 19; i >= 0; --i) {
        if (!isa(u, v)) {
            u = up[i][u];
        }
    }
    return up[0][u];
}
 
vector<int> ord;
 
void dfs(int v, vector<int> *g, vector<bool> &used) {
    used[v] = true;
    for (int u : g[v]) {
        if (!used[u]) {
            dfs(u, g, used);
        }
    }
    ord.push_back(v);
}
 
void dfs(int v, vector<int> *g, vector<int> &color, int cur) {
    color[v] = cur;
    for (int u : g[v]) {
        if (!color[u]) {
            dfs(u, g, color, cur);
        }
    }
}
 
void solve() {
    int n, k;
    cin >> n >> k;
    vector<vector<int>> g(n);
    for (int i = 1; i < n; ++i) {
        int u, v;
        cin >> u >> v;
        --u; --v;
        g[u].push_back(v);
        g[v].push_back(u);
    }
    fill(par, par + maxn, -1);
    c.resize(n);
    for (int& i : c) cin >> i;
    for (int& i : c) --i;
    dfs(0, g, 0);
    vector<vector<int>> groups(k);
    for (int i = 0; i < n; ++i) {
        groups[c[i]].push_back(i);
    }
    auto add_edges = [&] (int vertex, int v, int k) {
        ++k;
        for (int i = 19; i >= 0; --i) {
            if (k >= (1 << i)) {
                gp[vertex].push_back(upp[i][v]);
                v = up[i][v];
                k -= (1 << i);
            }
        }
    };
    for (vector<int> g : groups) {
        vector<pair<int, int>> x;
        for (int i : g) {
            x.push_back({ tin[i], i });
        }
        sort(x.begin(), x.end());
        vector<pair<int, int>> y = x;
        for (int i = 0; i + 1 < x.size(); ++i) {
            y.push_back({ tin[lca(x[i].second, x[i + 1].second)], lca(x[i].second, x[i + 1].second) });
        }
        sort(y.begin(), y.end());
        vector<int> st;
        for (auto [x, v] : y) {
            while (!st.empty() && !isa(st.back(), v)) st.pop_back();
            if (!st.empty()) {
                int k = d[v] - d[st.back()];
                add_edges(c[v], v, k);
            }
            st.push_back(v);
        }
    }
    vector<bool> used(id, false);
    for (int i = 0; i < id; ++i) {
        if (!used[i]) dfs(i, gp, used);
    }
    reverse(ord.begin(), ord.end());
    vector<int> color(id, 0);
    for (int i = 0; i < id; ++i) {
        gp[i].clear();
    }
    id = maxn;
    dfsrev(0, g, 0);
    auto add_rev_edges = [&] (int vertex, int v, int k) {
        ++k;
        for (int i = 19; i >= 0; --i) {
            if (k >= (1 << i)) {
                gp[upp[i][v]].push_back(vertex);
                v = up[i][v];
                k -= (1 << i);
            }
        }
    };
    for (vector<int> g : groups) {
        vector<pair<int, int>> x;
        for (int i : g) {
            x.push_back({ tin[i], i });
        }
        sort(x.begin(), x.end());
        vector<pair<int, int>> y = x;
        for (int i = 0; i + 1 < x.size(); ++i) {
            y.push_back({ tin[lca(x[i].second, x[i + 1].second)], lca(x[i].second, x[i + 1].second) });
        }
        sort(y.begin(), y.end());
        vector<int> st;
        for (auto [x, v] : y) {
            while (!st.empty() && !isa(st.back(), v)) st.pop_back();
            if (!st.empty()) {
                int k = d[v] - d[st.back()];
                add_rev_edges(c[v], v, k);
            }
            st.push_back(v);
        }
    }
    int cur = 1;
    for (int i : ord) {
        if (!color[i]) {
            dfs(i, gp, color, cur++);
        }
    }
    vector<int> sz(k, 1);
    sz.resize(id);
    vector<int> sum(id, 0);
    for (int i = 0; i < k; ++i) {
        sum[color[i] - 1] += sz[i];
    }
    int res = inf;
    --cur;
    vector<bool> ok(cur, true);
    for (int i = 0; i < id; ++i) {
        for (int j : gp[i]) {
            if (color[j] != color[i]) {
                ok[color[j] - 1] = false;
            }
        }
    }
    for (int i = 0; i < cur; ++i) {
        if (ok[i] && sum[i]) {
            res = min(res, sum[i]);
        }
    }
    cout << res - 1;
}
 
int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int t;
    t = 1;
    while (t--) {
        solve();
    }
}
/*
 12 4
 7 9
 1 3
 4 6
 2 4
 10 12
 1 2
 2 10
 11 1
 2 8
 5 3
 6 7
 3
 1 1 2 4 3 3 2 2 3 4 4
 
 6 3
 2 1
 3 5
 6 2
 3 4
 2 3
 1
 3 1 2 3 2
 */

Compilation message

capital_city.cpp: In function 'void solve()':
capital_city.cpp:142:31: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  142 |         for (int i = 0; i + 1 < x.size(); ++i) {
      |                         ~~~~~~^~~~~~~~~~
capital_city.cpp:184:31: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  184 |         for (int i = 0; i + 1 < x.size(); ++i) {
      |                         ~~~~~~^~~~~~~~~~

Subtask #1
1.0 / 1.0

# Verdict Execution time Memory Grader output
1 Correct 50 ms 103232 KB Output is correct
2 Correct 50 ms 103176 KB Output is correct
3 Correct 51 ms 103224 KB Output is correct
4 Correct 52 ms 103228 KB Output is correct
5 Correct 51 ms 103188 KB Output is correct
6 Correct 50 ms 103240 KB Output is correct
7 Correct 50 ms 103224 KB Output is correct
8 Correct 52 ms 103252 KB Output is correct
9 Correct 50 ms 103232 KB Output is correct
10 Correct 50 ms 103240 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 50 ms 103232 KB Output is correct
2 Correct 50 ms 103176 KB Output is correct
3 Correct 51 ms 103224 KB Output is correct
4 Correct 52 ms 103228 KB Output is correct
5 Correct 51 ms 103188 KB Output is correct
6 Correct 50 ms 103240 KB Output is correct
7 Correct 50 ms 103224 KB Output is correct
8 Correct 52 ms 103252 KB Output is correct
9 Correct 50 ms 103232 KB Output is correct
10 Correct 50 ms 103240 KB Output is correct
11 Correct 59 ms 105784 KB Output is correct
12 Correct 58 ms 105692 KB Output is correct
13 Correct 61 ms 105796 KB Output is correct
14 Correct 62 ms 105676 KB Output is correct
15 Correct 58 ms 105780 KB Output is correct
16 Correct 58 ms 105768 KB Output is correct
17 Correct 59 ms 105784 KB Output is correct
18 Correct 58 ms 105764 KB Output is correct
19 Correct 58 ms 105816 KB Output is correct
20 Correct 61 ms 105768 KB Output is correct
21 Correct 59 ms 105780 KB Output is correct
22 Correct 60 ms 105872 KB Output is correct
23 Correct 59 ms 105784 KB Output is correct
24 Correct 59 ms 105764 KB Output is correct
25 Correct 61 ms 105704 KB Output is correct
26 Correct 60 ms 105700 KB Output is correct
27 Correct 59 ms 105744 KB Output is correct
28 Correct 64 ms 105804 KB Output is correct
29 Correct 60 ms 105660 KB Output is correct
30 Correct 60 ms 105672 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2655 ms 371736 KB Output is correct
2 Correct 1408 ms 375492 KB Output is correct
3 Correct 2680 ms 375032 KB Output is correct
4 Correct 1415 ms 375468 KB Output is correct
5 Correct 2501 ms 372944 KB Output is correct
6 Correct 1393 ms 375604 KB Output is correct
7 Correct 2485 ms 371112 KB Output is correct
8 Correct 1343 ms 374264 KB Output is correct
9 Correct 1958 ms 364904 KB Output is correct
10 Correct 1937 ms 362260 KB Output is correct
11 Correct 1944 ms 364992 KB Output is correct
12 Correct 1981 ms 368612 KB Output is correct
13 Correct 1973 ms 362120 KB Output is correct
14 Correct 1958 ms 368792 KB Output is correct
15 Correct 2083 ms 368556 KB Output is correct
16 Correct 1978 ms 362956 KB Output is correct
17 Correct 1981 ms 363740 KB Output is correct
18 Correct 1954 ms 363808 KB Output is correct
19 Correct 2075 ms 366904 KB Output is correct
20 Correct 2000 ms 369200 KB Output is correct
21 Correct 53 ms 103236 KB Output is correct

Subtask #4
59.0 / 59.0

# Verdict Execution time Memory Grader output
1 Correct 50 ms 103232 KB Output is correct
2 Correct 50 ms 103176 KB Output is correct
3 Correct 51 ms 103224 KB Output is correct
4 Correct 52 ms 103228 KB Output is correct
5 Correct 51 ms 103188 KB Output is correct
6 Correct 50 ms 103240 KB Output is correct
7 Correct 50 ms 103224 KB Output is correct
8 Correct 52 ms 103252 KB Output is correct
9 Correct 50 ms 103232 KB Output is correct
10 Correct 50 ms 103240 KB Output is correct
11 Correct 59 ms 105784 KB Output is correct
12 Correct 58 ms 105692 KB Output is correct
13 Correct 61 ms 105796 KB Output is correct
14 Correct 62 ms 105676 KB Output is correct
15 Correct 58 ms 105780 KB Output is correct
16 Correct 58 ms 105768 KB Output is correct
17 Correct 59 ms 105784 KB Output is correct
18 Correct 58 ms 105764 KB Output is correct
19 Correct 58 ms 105816 KB Output is correct
20 Correct 61 ms 105768 KB Output is correct
21 Correct 59 ms 105780 KB Output is correct
22 Correct 60 ms 105872 KB Output is correct
23 Correct 59 ms 105784 KB Output is correct
24 Correct 59 ms 105764 KB Output is correct
25 Correct 61 ms 105704 KB Output is correct
26 Correct 60 ms 105700 KB Output is correct
27 Correct 59 ms 105744 KB Output is correct
28 Correct 64 ms 105804 KB Output is correct
29 Correct 60 ms 105660 KB Output is correct
30 Correct 60 ms 105672 KB Output is correct
31 Correct 2655 ms 371736 KB Output is correct
32 Correct 1408 ms 375492 KB Output is correct
33 Correct 2680 ms 375032 KB Output is correct
34 Correct 1415 ms 375468 KB Output is correct
35 Correct 2501 ms 372944 KB Output is correct
36 Correct 1393 ms 375604 KB Output is correct
37 Correct 2485 ms 371112 KB Output is correct
38 Correct 1343 ms 374264 KB Output is correct
39 Correct 1958 ms 364904 KB Output is correct
40 Correct 1937 ms 362260 KB Output is correct
41 Correct 1944 ms 364992 KB Output is correct
42 Correct 1981 ms 368612 KB Output is correct
43 Correct 1973 ms 362120 KB Output is correct
44 Correct 1958 ms 368792 KB Output is correct
45 Correct 2083 ms 368556 KB Output is correct
46 Correct 1978 ms 362956 KB Output is correct
47 Correct 1981 ms 363740 KB Output is correct
48 Correct 1954 ms 363808 KB Output is correct
49 Correct 2075 ms 366904 KB Output is correct
50 Correct 2000 ms 369200 KB Output is correct
51 Correct 53 ms 103236 KB Output is correct
52 Correct 1739 ms 371116 KB Output is correct
53 Correct 1671 ms 371688 KB Output is correct
54 Correct 1667 ms 371312 KB Output is correct
55 Correct 1713 ms 371532 KB Output is correct
56 Correct 1693 ms 371416 KB Output is correct
57 Correct 1704 ms 371352 KB Output is correct
58 Correct 2358 ms 378624 KB Output is correct
59 Correct 2428 ms 378036 KB Output is correct
60 Correct 2324 ms 380732 KB Output is correct
61 Correct 2296 ms 383476 KB Output is correct
62 Correct 1447 ms 375500 KB Output is correct
63 Correct 1402 ms 375632 KB Output is correct
64 Correct 1365 ms 374220 KB Output is correct
65 Correct 1417 ms 375284 KB Output is correct
66 Correct 1628 ms 374332 KB Output is correct
67 Correct 1642 ms 374328 KB Output is correct
68 Correct 1619 ms 372896 KB Output is correct
69 Correct 1649 ms 375472 KB Output is correct
70 Correct 1661 ms 375120 KB Output is correct
71 Correct 1625 ms 372772 KB Output is correct
72 Correct 1627 ms 373036 KB Output is correct
73 Correct 1667 ms 376972 KB Output is correct
74 Correct 1622 ms 372904 KB Output is correct
75 Correct 1685 ms 376292 KB Output is correct
76 Correct 2504 ms 372904 KB Output is correct
77 Correct 2496 ms 371508 KB Output is correct
78 Correct 1993 ms 363892 KB Output is correct
79 Correct 2044 ms 360808 KB Output is correct
80 Correct 1920 ms 368680 KB Output is correct
81 Correct 2027 ms 365196 KB Output is correct
82 Correct 2012 ms 365472 KB Output is correct
83 Correct 1945 ms 361572 KB Output is correct
84 Correct 2052 ms 368652 KB Output is correct
85 Correct 1978 ms 366504 KB Output is correct
86 Correct 2058 ms 361140 KB Output is correct
87 Correct 1964 ms 363068 KB Output is correct
88 Correct 2573 ms 370420 KB Output is correct
89 Correct 2472 ms 365848 KB Output is correct
90 Correct 2541 ms 365700 KB Output is correct
91 Correct 2637 ms 367868 KB Output is correct
92 Correct 2760 ms 366912 KB Output is correct
93 Correct 2476 ms 366764 KB Output is correct
94 Correct 2465 ms 365916 KB Output is correct
95 Correct 2471 ms 367608 KB Output is correct
96 Correct 2530 ms 366684 KB Output is correct
97 Correct 2498 ms 368168 KB Output is correct