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답안 #413272

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
413272 2021-05-28T12:19:52 Z blue 수도 (JOI20_capital_city) C++17
100 / 100
 1774 ms 98472 KB 
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

/*
Draw a directed edge between city A and city B, if there lies a town of city B on the path between two
towns of city A.

Answer = (minimum size of any SCC) - 1


*/
const int maxN = 200000;

int N, K;
vector<int> edge[1+maxN];
int col[1+maxN];
vector<int> col_count(1+maxN, 0);
int parent[1+maxN];



vector<int> order(1);
vector<int> order_index(1+maxN, 0);
vector<int> subtree(1+maxN, 1);


void dfs(int u)
{
    order_index[u] = order.size();
    order.push_back(u);

    for(int v: edge[u])
    {
        if(order_index[v]) continue;
        parent[v] = u;
        dfs(v);
        subtree[u] += subtree[v];
    }
}





struct segtree
{
    int l;
    int r;
    vector<int> v;

    segtree* left = NULL;
    segtree* right = NULL;

    segtree()
    {
        ;
    }

    segtree(int L, int R)
    {
        l = L;
        r = R;

        if(l == r)
        {
            v.push_back(col[ order[l] ]);
        }
        else
        {
            int m = (l+r)/2;
            left = new segtree(l, m);
            right = new segtree(m+1, r);

            for(int x: left->v) v.push_back(x);
            for(int x: right->v) v.push_back(x);
            sort(v.begin(), v.end());
        }
    }

    int count(int L, int R, int V)
    {
        if(R < l || r < L) return 0;
        else if(L <= l && r <= R)
        {
            int i1 = -1, i2 = -1;

            for(int bit = 18; bit >= 0; bit--)
            {
                if(i1 + (1 << bit) >= v.size()) continue;
                if(v[i1 + (1 << bit)] >= V) continue;
                i1 += (1 << bit);
            }
            i1++;

            if(v[i1] != V) return 0;

            for(int bit = 18; bit >= 0; bit--)
            {
                if(i2 + (1 << bit) >= v.size()) continue;
                if(v[i2 + (1 << bit)] > V) continue;
                i2 += (1 << bit);
            }

            return i2-i1+1;
        }
        else
        {
            return left->count(L, R, V) + right->count(L, R, V);
        }
    }
};




vector<int> newEdge[1+maxN];
vector<int> newEdgeRev[1+maxN];

vector<int> scc_dfs_order;
vector<int> visit(1+maxN, 0);

void scc_dfs_1(int u)
{
    for(int v: newEdge[u])
    {
        if(visit[v]) continue;
        visit[v] = 1;
        scc_dfs_1(v);
    }
    scc_dfs_order.push_back(u);
}

int curr_ct;

vector<int> scc_size(1, 0);
vector<int> scc(1+maxN, 0);
int scc_count = 0;

void scc_dfs_2(int u)
{
    scc_size[scc_count]++;
    scc[u] = scc_count;

    for(int v: newEdgeRev[u])
    {
        if(visit[v]) continue;
        visit[v] = 1;
        curr_ct++;
        scc_dfs_2(v);
    }
}


int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    cin >> N >> K;

    for(int i = 1; i <= N-1; i++)
    {
        int A, B;
        cin >> A >> B;

        edge[A].push_back(B);
        edge[B].push_back(A);
    }

    for(int i = 1; i <= N; i++)
    {
        cin >> col[i];
        col_count[ col[i] ]++;
    }

    parent[1] = 0;
    dfs(1);

    segtree S(1, N);

    // for(int i = 1; i <= N; i++) cerr << order[i] << ' ';
    // cerr << '\n';
    // for(int i = 1; i <= N; i++) cerr << order_index[i] << ' ';
    // cerr << '\n';

    for(int i = 2; i <= N; i++)
    {
        if(col[i] == col[ parent[i] ]) continue;

        int ct;

        ct = S.count(order_index[i], order_index[i] + subtree[i] - 1, col[parent[i]]);
        if(ct != col_count[ col[parent[i]] ] && ct != 0)
        {
            newEdge[ col[ parent[i] ] ].push_back(col[i]);
            newEdgeRev[ col[i] ].push_back(col[ parent[i] ]);
        }

        ct = S.count(order_index[i], order_index[i] + subtree[i] - 1, col[i]);
        if(ct != col_count[ col[i] ] && ct != 0)
        {
            newEdge[ col[i] ].push_back(col[ parent[i] ]);
            newEdgeRev[ col[parent[i]] ].push_back(col[i]);
        }
    }

    for(int j = 1; j <= K; j++)
    {
        if(visit[j]) continue;
        visit[j] = 1;
        scc_dfs_1(j);
    }

    reverse(scc_dfs_order.begin(), scc_dfs_order.end());

    // for(int j: scc_dfs_order) cerr << j << ' ';
    // cerr << '\n';

    visit = vector<int>(K+1, 0);
    for(int j: scc_dfs_order)
    {
        if(visit[j]) continue;

        scc_count++;
        scc_size.push_back(0);


        visit[j] = 1;
        curr_ct = 1;
        scc_dfs_2(j);

        // cerr << j << ' ' << curr_ct << '\n';
    }

    vector<int> scc_outdegree(scc_count+1, 0);
    for(int u = 1; u <= K; u++)
        for(int v: newEdge[u])
            if(scc[u] != scc[v])
                scc_outdegree[ scc[u] ]++;

    int res = 1e9;
    for(int x = 1; x <= scc_count; x++)
        if(scc_outdegree[x] == 0)
            res = min(res, scc_size[x] - 1);

    // for(int i = 1; i <= K; i++) cerr << scc[i] << ' ' << scc_outdegree[scc[i]] << ' ' << scc_size[scc[i]] << '\n';
    // cerr << '\n';

    cout << res << '\n';
}

Compilation message

capital_city.cpp: In member function 'int segtree::count(int, int, int)':
capital_city.cpp:91:36: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   91 |                 if(i1 + (1 << bit) >= v.size()) continue;
      |                    ~~~~~~~~~~~~~~~~^~~~~~~~~~~
capital_city.cpp:101:36: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  101 |                 if(i2 + (1 << bit) >= v.size()) continue;
      |                    ~~~~~~~~~~~~~~~~^~~~~~~~~~~

Subtask #1
1.0 / 1.0

# 결과 실행 시간 메모리 Grader output
1 Correct 14 ms 18252 KB Output is correct
2 Correct 13 ms 18252 KB Output is correct
3 Correct 12 ms 18252 KB Output is correct
4 Correct 12 ms 18296 KB Output is correct
5 Correct 12 ms 18288 KB Output is correct
6 Correct 14 ms 18252 KB Output is correct
7 Correct 11 ms 18264 KB Output is correct
8 Correct 11 ms 18252 KB Output is correct
9 Correct 13 ms 18296 KB Output is correct
10 Correct 11 ms 18252 KB Output is correct

Subtask #2
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 14 ms 18252 KB Output is correct
2 Correct 13 ms 18252 KB Output is correct
3 Correct 12 ms 18252 KB Output is correct
4 Correct 12 ms 18296 KB Output is correct
5 Correct 12 ms 18288 KB Output is correct
6 Correct 14 ms 18252 KB Output is correct
7 Correct 11 ms 18264 KB Output is correct
8 Correct 11 ms 18252 KB Output is correct
9 Correct 13 ms 18296 KB Output is correct
10 Correct 11 ms 18252 KB Output is correct
11 Correct 15 ms 18864 KB Output is correct
12 Correct 15 ms 18828 KB Output is correct
13 Correct 15 ms 18892 KB Output is correct
14 Correct 16 ms 18892 KB Output is correct
15 Correct 16 ms 18896 KB Output is correct
16 Correct 15 ms 18936 KB Output is correct
17 Correct 14 ms 18892 KB Output is correct
18 Correct 26 ms 18892 KB Output is correct
19 Correct 14 ms 18892 KB Output is correct
20 Correct 14 ms 18892 KB Output is correct
21 Correct 14 ms 18892 KB Output is correct
22 Correct 16 ms 19036 KB Output is correct
23 Correct 17 ms 18960 KB Output is correct
24 Correct 21 ms 18864 KB Output is correct
25 Correct 17 ms 18952 KB Output is correct
26 Correct 17 ms 18960 KB Output is correct
27 Correct 17 ms 19020 KB Output is correct
28 Correct 16 ms 18972 KB Output is correct
29 Correct 16 ms 18888 KB Output is correct
30 Correct 16 ms 18892 KB Output is correct

Subtask #3
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1774 ms 97916 KB Output is correct
2 Correct 485 ms 98344 KB Output is correct
3 Correct 1731 ms 97696 KB Output is correct
4 Correct 497 ms 98472 KB Output is correct
5 Correct 1290 ms 94928 KB Output is correct
6 Correct 493 ms 98248 KB Output is correct
7 Correct 1262 ms 94900 KB Output is correct
8 Correct 440 ms 97104 KB Output is correct
9 Correct 1676 ms 93304 KB Output is correct
10 Correct 1563 ms 91140 KB Output is correct
11 Correct 1393 ms 93448 KB Output is correct
12 Correct 1411 ms 95616 KB Output is correct
13 Correct 1563 ms 90636 KB Output is correct
14 Correct 1324 ms 95860 KB Output is correct
15 Correct 1525 ms 95872 KB Output is correct
16 Correct 1500 ms 91760 KB Output is correct
17 Correct 1508 ms 92192 KB Output is correct
18 Correct 1537 ms 92372 KB Output is correct
19 Correct 1583 ms 94896 KB Output is correct
20 Correct 1468 ms 96464 KB Output is correct
21 Correct 12 ms 18264 KB Output is correct

Subtask #4
59.0 / 59.0

# 결과 실행 시간 메모리 Grader output
1 Correct 14 ms 18252 KB Output is correct
2 Correct 13 ms 18252 KB Output is correct
3 Correct 12 ms 18252 KB Output is correct
4 Correct 12 ms 18296 KB Output is correct
5 Correct 12 ms 18288 KB Output is correct
6 Correct 14 ms 18252 KB Output is correct
7 Correct 11 ms 18264 KB Output is correct
8 Correct 11 ms 18252 KB Output is correct
9 Correct 13 ms 18296 KB Output is correct
10 Correct 11 ms 18252 KB Output is correct
11 Correct 15 ms 18864 KB Output is correct
12 Correct 15 ms 18828 KB Output is correct
13 Correct 15 ms 18892 KB Output is correct
14 Correct 16 ms 18892 KB Output is correct
15 Correct 16 ms 18896 KB Output is correct
16 Correct 15 ms 18936 KB Output is correct
17 Correct 14 ms 18892 KB Output is correct
18 Correct 26 ms 18892 KB Output is correct
19 Correct 14 ms 18892 KB Output is correct
20 Correct 14 ms 18892 KB Output is correct
21 Correct 14 ms 18892 KB Output is correct
22 Correct 16 ms 19036 KB Output is correct
23 Correct 17 ms 18960 KB Output is correct
24 Correct 21 ms 18864 KB Output is correct
25 Correct 17 ms 18952 KB Output is correct
26 Correct 17 ms 18960 KB Output is correct
27 Correct 17 ms 19020 KB Output is correct
28 Correct 16 ms 18972 KB Output is correct
29 Correct 16 ms 18888 KB Output is correct
30 Correct 16 ms 18892 KB Output is correct
31 Correct 1774 ms 97916 KB Output is correct
32 Correct 485 ms 98344 KB Output is correct
33 Correct 1731 ms 97696 KB Output is correct
34 Correct 497 ms 98472 KB Output is correct
35 Correct 1290 ms 94928 KB Output is correct
36 Correct 493 ms 98248 KB Output is correct
37 Correct 1262 ms 94900 KB Output is correct
38 Correct 440 ms 97104 KB Output is correct
39 Correct 1676 ms 93304 KB Output is correct
40 Correct 1563 ms 91140 KB Output is correct
41 Correct 1393 ms 93448 KB Output is correct
42 Correct 1411 ms 95616 KB Output is correct
43 Correct 1563 ms 90636 KB Output is correct
44 Correct 1324 ms 95860 KB Output is correct
45 Correct 1525 ms 95872 KB Output is correct
46 Correct 1500 ms 91760 KB Output is correct
47 Correct 1508 ms 92192 KB Output is correct
48 Correct 1537 ms 92372 KB Output is correct
49 Correct 1583 ms 94896 KB Output is correct
50 Correct 1468 ms 96464 KB Output is correct
51 Correct 12 ms 18264 KB Output is correct
52 Correct 773 ms 82788 KB Output is correct
53 Correct 726 ms 82884 KB Output is correct
54 Correct 776 ms 82904 KB Output is correct
55 Correct 755 ms 82812 KB Output is correct
56 Correct 721 ms 83004 KB Output is correct
57 Correct 720 ms 82844 KB Output is correct
58 Correct 1135 ms 86184 KB Output is correct
59 Correct 1234 ms 86704 KB Output is correct
60 Correct 1085 ms 85688 KB Output is correct
61 Correct 1063 ms 85516 KB Output is correct
62 Correct 505 ms 98336 KB Output is correct
63 Correct 497 ms 98340 KB Output is correct
64 Correct 472 ms 97376 KB Output is correct
65 Correct 492 ms 98240 KB Output is correct
66 Correct 433 ms 87940 KB Output is correct
67 Correct 441 ms 87932 KB Output is correct
68 Correct 440 ms 87900 KB Output is correct
69 Correct 436 ms 87868 KB Output is correct
70 Correct 434 ms 87864 KB Output is correct
71 Correct 449 ms 87992 KB Output is correct
72 Correct 440 ms 87880 KB Output is correct
73 Correct 437 ms 87296 KB Output is correct
74 Correct 432 ms 87860 KB Output is correct
75 Correct 440 ms 87992 KB Output is correct
76 Correct 1408 ms 90336 KB Output is correct
77 Correct 1342 ms 88924 KB Output is correct
78 Correct 1403 ms 92296 KB Output is correct
79 Correct 1386 ms 90380 KB Output is correct
80 Correct 1367 ms 96200 KB Output is correct
81 Correct 1567 ms 93460 KB Output is correct
82 Correct 1477 ms 93716 KB Output is correct
83 Correct 1425 ms 90812 KB Output is correct
84 Correct 1665 ms 95408 KB Output is correct
85 Correct 1396 ms 94268 KB Output is correct
86 Correct 1539 ms 90184 KB Output is correct
87 Correct 1518 ms 91844 KB Output is correct
88 Correct 1616 ms 92500 KB Output is correct
89 Correct 1498 ms 88868 KB Output is correct
90 Correct 1535 ms 88888 KB Output is correct
91 Correct 1547 ms 91116 KB Output is correct
92 Correct 1547 ms 90236 KB Output is correct
93 Correct 1596 ms 89372 KB Output is correct
94 Correct 1510 ms 88868 KB Output is correct
95 Correct 1501 ms 90164 KB Output is correct
96 Correct 1498 ms 89780 KB Output is correct
97 Correct 1515 ms 91108 KB Output is correct