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Submission #817715

# Submission time Handle Problem Language Result Execution time Memory
817715 2023-08-09T15:14:56 Z LucaIlie Mergers (JOI19_mergers) C++17
56 / 100
 3000 ms 105824 KB 
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 5e5;
const int MAX_LOG_N = 19;
int state[MAX_N + 1], parent[MAX_LOG_N + 1][MAX_N + 1], depth[MAX_N + 1], uplus[MAX_N + 1], uminus[MAX_N + 1];
vector<int> edges[MAX_N + 1], cities[MAX_N + 1];
set<int> stateEdges[MAX_N + 1];

struct DSU {
    int p[MAX_N + 1];

    void init( int k ) {
        for ( int u = 1; u <= k; u++ )
            p[u] = u;
    }

    int find( int u ) {
        if ( p[u] == u )
            return u;
        p[u] = find( p[u] );
        return p[u];
    }

    void merge( int u, int v ) {
        u = find( u );
        v = find( v );
        if ( u == v )
            return;

        p[u] = v;
    }
} dsu;

void dfs( int u, int p ) {
    depth[u] = depth[p] + 1;
    parent[0][u] = p;
    for ( int v: edges[u] ) {
        if ( v == p )
            continue;
        dfs( v, u );
    }
}

void init() {
    for ( int p = 1; p <= MAX_LOG_N; p++ ) {
        for ( int u = 0; u <= MAX_N; u++ )
            parent[p][u] = parent[p - 1][parent[p - 1][u]];
    }
}

int ancestor( int u, int d ) {
    for ( int p = MAX_LOG_N; p >= 0; p-- ) {
        if ( d >= (1 << p) ) {
            d -= (1 << p);
            u = parent[p][u];
        }
    }

    return u;
}

int lca( int u, int v ) {
    if ( depth[u] > depth[v] )
        swap( u, v );
    for ( int p = MAX_LOG_N; p >= 0; p-- ) {
        if ( depth[parent[p][v]] >= depth[u] )
            v = parent[p][v];
    }

    if ( u == v )
        return u;

    for ( int p = MAX_LOG_N; p >= 0; p-- ) {
        if ( parent[p][u] != parent[p][v] ) {
            u = parent[p][u];
            v = parent[p][v];
        }
    }

    return parent[0][u];
}

void dfsMerge( int u, int p, int upd ) {
    upd += uplus[u];

    if ( upd > 0 )
        dsu.merge( state[u], state[parent[0][u]] );

    for ( int v: edges[u] ) {
        if ( v == p )
            continue;
        dfsMerge( v, u, upd + uminus[u] );
    }
}

int main() {
    int n, k;

    cin >> n >> k;
    for ( int i = 0; i < n - 1; i++ ) {
        int u, v;
        cin >> u >> v;
        edges[u].push_back( v );
        edges[v].push_back( u );
    }
    for ( int u = 1; u <= n; u++ ) {
        cin >> state[u];
        cities[state[u]].push_back( u );
    }

    dfs( 1, 0 );

    init();
    for ( int s = 1; s <= k; s++ ) {
        for ( int i = 0; i < cities[s].size() - 1; i++ ) {
            int u = cities[s][i], v = cities[s][i + 1];
            int l = lca( u, v );
            int w = ancestor( u, depth[u] - depth[l] - 1 );
            int t = ancestor( v, depth[v] - depth[l] - 1 );
            if ( l == u ) {
                uplus[t]++;
                uminus[v]--;
            }
            else if ( l == v ) {
                uplus[w]++;
                uminus[u]--;
            }
            else {
                uplus[w]++;
                uminus[u]--;
                uplus[t]++;
                uminus[v]--;
            }
        }
    }

    dsu.init( k );
    for ( int s = 1; s <= k; s++ ) {
        for ( int i = 0; i < cities[s].size() - 1; i++ ) {
            int u = cities[s][i], v = cities[s][i + 1];
            while ( depth[u] > depth[v] ) {
                dsu.merge( state[u], state[parent[0][u]] );
                u = parent[0][u];
            }
            while ( depth[v] > depth[u] ) {
                dsu.merge( state[v], state[parent[0][v]] );
                v = parent[0][v];
            }
            while ( u != v ) {
                dsu.merge( state[u], state[parent[0][u]] );
                u = parent[0][u];
                dsu.merge( state[v], state[parent[0][v]] );
                v = parent[0][v];
            }
        }
    }

    for ( int u = 1; u <= n; u++ )
        state[u] = dsu.find( state[u] );

    for ( int u = 1; u <= n; u++ ) {
        for ( int v: edges[u] ) {
            if ( state[u] == state[v] )
                continue;
            stateEdges[state[u]].insert( state[v] );
            stateEdges[state[v]].insert( state[u] );
        }
    }

    int leafs = 0;
    for ( int s = 1; s <= k; s++ ) {
        if ( stateEdges[s].size() == 1 )
            leafs++;
    }

    cout << (leafs + 1) / 2;

    return 0;
}

Compilation message

mergers.cpp: In function 'int main()':
mergers.cpp:117:28: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  117 |         for ( int i = 0; i < cities[s].size() - 1; i++ ) {
      |                          ~~^~~~~~~~~~~~~~~~~~~~~~
mergers.cpp:141:28: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  141 |         for ( int i = 0; i < cities[s].size() - 1; i++ ) {
      |                          ~~^~~~~~~~~~~~~~~~~~~~~~

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 38 ms 84428 KB Output is correct
2 Correct 39 ms 84428 KB Output is correct
3 Correct 38 ms 84428 KB Output is correct
4 Correct 38 ms 84476 KB Output is correct
5 Correct 38 ms 84452 KB Output is correct
6 Correct 40 ms 84412 KB Output is correct
7 Correct 39 ms 84556 KB Output is correct
8 Correct 38 ms 84368 KB Output is correct
9 Correct 38 ms 84480 KB Output is correct
10 Correct 46 ms 84456 KB Output is correct
11 Correct 40 ms 84392 KB Output is correct
12 Correct 38 ms 84448 KB Output is correct
13 Correct 39 ms 84480 KB Output is correct
14 Correct 38 ms 84396 KB Output is correct
15 Correct 39 ms 84392 KB Output is correct
16 Correct 39 ms 84432 KB Output is correct
17 Correct 39 ms 84428 KB Output is correct
18 Correct 38 ms 84408 KB Output is correct
19 Correct 39 ms 84428 KB Output is correct
20 Correct 38 ms 84436 KB Output is correct
21 Correct 44 ms 84488 KB Output is correct
22 Correct 39 ms 84428 KB Output is correct
23 Correct 44 ms 84384 KB Output is correct
24 Correct 44 ms 84524 KB Output is correct

Subtask #2
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 38 ms 84428 KB Output is correct
2 Correct 39 ms 84428 KB Output is correct
3 Correct 38 ms 84428 KB Output is correct
4 Correct 38 ms 84476 KB Output is correct
5 Correct 38 ms 84452 KB Output is correct
6 Correct 40 ms 84412 KB Output is correct
7 Correct 39 ms 84556 KB Output is correct
8 Correct 38 ms 84368 KB Output is correct
9 Correct 38 ms 84480 KB Output is correct
10 Correct 46 ms 84456 KB Output is correct
11 Correct 40 ms 84392 KB Output is correct
12 Correct 38 ms 84448 KB Output is correct
13 Correct 39 ms 84480 KB Output is correct
14 Correct 38 ms 84396 KB Output is correct
15 Correct 39 ms 84392 KB Output is correct
16 Correct 39 ms 84432 KB Output is correct
17 Correct 39 ms 84428 KB Output is correct
18 Correct 38 ms 84408 KB Output is correct
19 Correct 39 ms 84428 KB Output is correct
20 Correct 38 ms 84436 KB Output is correct
21 Correct 44 ms 84488 KB Output is correct
22 Correct 39 ms 84428 KB Output is correct
23 Correct 44 ms 84384 KB Output is correct
24 Correct 44 ms 84524 KB Output is correct
25 Correct 41 ms 84472 KB Output is correct
26 Correct 43 ms 84812 KB Output is correct
27 Correct 47 ms 84684 KB Output is correct
28 Correct 44 ms 84976 KB Output is correct
29 Correct 45 ms 85000 KB Output is correct
30 Correct 41 ms 84680 KB Output is correct
31 Correct 39 ms 84428 KB Output is correct
32 Correct 41 ms 84932 KB Output is correct
33 Correct 39 ms 84408 KB Output is correct
34 Correct 41 ms 84692 KB Output is correct
35 Correct 46 ms 84920 KB Output is correct
36 Correct 42 ms 84596 KB Output is correct
37 Correct 42 ms 84712 KB Output is correct
38 Correct 39 ms 84496 KB Output is correct
39 Correct 43 ms 84680 KB Output is correct
40 Correct 41 ms 84680 KB Output is correct
41 Correct 44 ms 84728 KB Output is correct
42 Correct 42 ms 84684 KB Output is correct
43 Correct 49 ms 84792 KB Output is correct
44 Correct 39 ms 84452 KB Output is correct
45 Correct 42 ms 84756 KB Output is correct
46 Correct 42 ms 84636 KB Output is correct
47 Correct 44 ms 84428 KB Output is correct
48 Correct 42 ms 84736 KB Output is correct
49 Correct 42 ms 84952 KB Output is correct
50 Correct 41 ms 84996 KB Output is correct
51 Correct 41 ms 84684 KB Output is correct
52 Correct 41 ms 84612 KB Output is correct
53 Correct 41 ms 84708 KB Output is correct
54 Correct 47 ms 84660 KB Output is correct

Subtask #3
0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 38 ms 84428 KB Output is correct
2 Correct 39 ms 84428 KB Output is correct
3 Correct 38 ms 84428 KB Output is correct
4 Correct 38 ms 84476 KB Output is correct
5 Correct 38 ms 84452 KB Output is correct
6 Correct 40 ms 84412 KB Output is correct
7 Correct 39 ms 84556 KB Output is correct
8 Correct 38 ms 84368 KB Output is correct
9 Correct 38 ms 84480 KB Output is correct
10 Correct 46 ms 84456 KB Output is correct
11 Correct 40 ms 84392 KB Output is correct
12 Correct 38 ms 84448 KB Output is correct
13 Correct 39 ms 84480 KB Output is correct
14 Correct 38 ms 84396 KB Output is correct
15 Correct 39 ms 84392 KB Output is correct
16 Correct 39 ms 84432 KB Output is correct
17 Correct 39 ms 84428 KB Output is correct
18 Correct 38 ms 84408 KB Output is correct
19 Correct 39 ms 84428 KB Output is correct
20 Correct 38 ms 84436 KB Output is correct
21 Correct 44 ms 84488 KB Output is correct
22 Correct 39 ms 84428 KB Output is correct
23 Correct 44 ms 84384 KB Output is correct
24 Correct 44 ms 84524 KB Output is correct
25 Correct 38 ms 84400 KB Output is correct
26 Correct 130 ms 91932 KB Output is correct
27 Correct 156 ms 91572 KB Output is correct
28 Correct 43 ms 84632 KB Output is correct
29 Correct 39 ms 84368 KB Output is correct
30 Correct 41 ms 84444 KB Output is correct
31 Correct 153 ms 91536 KB Output is correct
32 Correct 49 ms 84704 KB Output is correct
33 Execution timed out 3069 ms 95820 KB Time limit exceeded
34 Halted 0 ms 0 KB -

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 149 ms 90448 KB Output is correct
2 Correct 177 ms 102032 KB Output is correct
3 Correct 41 ms 84812 KB Output is correct
4 Correct 45 ms 84632 KB Output is correct
5 Correct 38 ms 84436 KB Output is correct
6 Correct 39 ms 84452 KB Output is correct
7 Correct 42 ms 84596 KB Output is correct
8 Correct 170 ms 94056 KB Output is correct
9 Correct 41 ms 84688 KB Output is correct
10 Correct 158 ms 91784 KB Output is correct
11 Correct 39 ms 84496 KB Output is correct
12 Correct 189 ms 91804 KB Output is correct
13 Correct 170 ms 94860 KB Output is correct
14 Correct 201 ms 103484 KB Output is correct
15 Correct 128 ms 91844 KB Output is correct
16 Correct 41 ms 84740 KB Output is correct
17 Correct 38 ms 84432 KB Output is correct
18 Correct 181 ms 102428 KB Output is correct
19 Correct 167 ms 105824 KB Output is correct
20 Correct 43 ms 84796 KB Output is correct
21 Correct 38 ms 84408 KB Output is correct
22 Correct 176 ms 94984 KB Output is correct
23 Correct 41 ms 84672 KB Output is correct
24 Correct 164 ms 92904 KB Output is correct
25 Correct 179 ms 105028 KB Output is correct
26 Correct 44 ms 84940 KB Output is correct
27 Correct 41 ms 85052 KB Output is correct
28 Correct 41 ms 84724 KB Output is correct
29 Correct 42 ms 84704 KB Output is correct
30 Correct 42 ms 84788 KB Output is correct

Subtask #5
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 38 ms 84428 KB Output is correct
2 Correct 39 ms 84428 KB Output is correct
3 Correct 38 ms 84428 KB Output is correct
4 Correct 38 ms 84476 KB Output is correct
5 Correct 38 ms 84452 KB Output is correct
6 Correct 40 ms 84412 KB Output is correct
7 Correct 39 ms 84556 KB Output is correct
8 Correct 38 ms 84368 KB Output is correct
9 Correct 38 ms 84480 KB Output is correct
10 Correct 46 ms 84456 KB Output is correct
11 Correct 40 ms 84392 KB Output is correct
12 Correct 38 ms 84448 KB Output is correct
13 Correct 39 ms 84480 KB Output is correct
14 Correct 38 ms 84396 KB Output is correct
15 Correct 39 ms 84392 KB Output is correct
16 Correct 39 ms 84432 KB Output is correct
17 Correct 39 ms 84428 KB Output is correct
18 Correct 38 ms 84408 KB Output is correct
19 Correct 39 ms 84428 KB Output is correct
20 Correct 38 ms 84436 KB Output is correct
21 Correct 44 ms 84488 KB Output is correct
22 Correct 39 ms 84428 KB Output is correct
23 Correct 44 ms 84384 KB Output is correct
24 Correct 44 ms 84524 KB Output is correct
25 Correct 41 ms 84472 KB Output is correct
26 Correct 43 ms 84812 KB Output is correct
27 Correct 47 ms 84684 KB Output is correct
28 Correct 44 ms 84976 KB Output is correct
29 Correct 45 ms 85000 KB Output is correct
30 Correct 41 ms 84680 KB Output is correct
31 Correct 39 ms 84428 KB Output is correct
32 Correct 41 ms 84932 KB Output is correct
33 Correct 39 ms 84408 KB Output is correct
34 Correct 41 ms 84692 KB Output is correct
35 Correct 46 ms 84920 KB Output is correct
36 Correct 42 ms 84596 KB Output is correct
37 Correct 42 ms 84712 KB Output is correct
38 Correct 39 ms 84496 KB Output is correct
39 Correct 43 ms 84680 KB Output is correct
40 Correct 41 ms 84680 KB Output is correct
41 Correct 44 ms 84728 KB Output is correct
42 Correct 42 ms 84684 KB Output is correct
43 Correct 49 ms 84792 KB Output is correct
44 Correct 39 ms 84452 KB Output is correct
45 Correct 42 ms 84756 KB Output is correct
46 Correct 42 ms 84636 KB Output is correct
47 Correct 44 ms 84428 KB Output is correct
48 Correct 42 ms 84736 KB Output is correct
49 Correct 42 ms 84952 KB Output is correct
50 Correct 41 ms 84996 KB Output is correct
51 Correct 41 ms 84684 KB Output is correct
52 Correct 41 ms 84612 KB Output is correct
53 Correct 41 ms 84708 KB Output is correct
54 Correct 47 ms 84660 KB Output is correct
55 Correct 38 ms 84400 KB Output is correct
56 Correct 130 ms 91932 KB Output is correct
57 Correct 156 ms 91572 KB Output is correct
58 Correct 43 ms 84632 KB Output is correct
59 Correct 39 ms 84368 KB Output is correct
60 Correct 41 ms 84444 KB Output is correct
61 Correct 153 ms 91536 KB Output is correct
62 Correct 49 ms 84704 KB Output is correct
63 Execution timed out 3069 ms 95820 KB Time limit exceeded
64 Halted 0 ms 0 KB -