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답안 #762543

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
762543 2023-06-21T13:30:03 Z LucaIlie Min-max tree (BOI18_minmaxtree) C++17
100 / 100
 334 ms 46400 KB 
#include <bits/stdc++.h>

using namespace std;

struct query {
    int u, v, w;

    bool operator < ( const query &q ) const {
        return w < q.w;
    }
};

const int INF = (1 << 30);
const int MAX_N = 7e4 + 1;
const int MAX_LOG_N = 16;
const int undef = -1;
bool used[MAX_N];
int depth[MAX_N], parent[MAX_LOG_N + 1][MAX_N], asc[MAX_N], queryMin[MAX_N], queryMax[MAX_N], value[MAX_N];
vector<int> edges[MAX_N];
vector<query> mins, maxs;

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 );
    }
}

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][v];
}

int findParent( int u, int d ) {
    if ( d < 0 )
        return undef;

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

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

struct MATCH {
    const int NIL = 0;

    int n, m;
    int pairU[MAX_N + 1], pairV[MAX_N + 1], dist[MAX_N + 1];
    vector <int> edges[MAX_N + 1];

    void init( int _n, int _m ) {
        n = _n;
        m = _m;
    }

    void add_edge( int u, int v ) {
        edges[u].push_back( v );
    }

    bool bfs() {
        int u;
        queue <int> q;

        dist[NIL] = INF;
        for ( u = 1; u <= n; u++ ) {
            if ( pairU[u] == NIL ) {
                dist[u] = 0;
                q.push( u );
            } else
                dist[u] = INF;
        }

        while ( !q.empty() ) {
            u = q.front();
            q.pop();

            if ( dist[u] < dist[NIL] ) {
                for ( int v: edges[u] ) {
                    if ( dist[pairV[v]] == INF ) {
                        dist[pairV[v]] = dist[u] + 1;
                        q.push( pairV[v] );
                    }
                }
            }
        }

        return dist[NIL] != INF;
    }

    bool dfs( int u ) {
        if ( u == NIL )
            return true;

        for ( int v: edges[u] ) {
            if ( dist[pairV[v]] == dist[u] + 1 && dfs( pairV[v] ) ) {
                pairU[u] = v;
                pairV[v] = u;
                return true;
            }
        }

        dist[u] = INF;

        return false;
    }

    void maxMatch() {
        int maxMatch, u, v;

        for ( u = 0; u <= n; u++ )
            pairU[u] = NIL;
        for ( v = 0; v <= m; v++ )
            pairV[v] = NIL;


        while ( bfs() ) {
            for ( u = 1; u <= n; u++ ) {
                if ( pairU[u] == NIL )
                    dfs( u );
            }
        }
    }
};

MATCH match;


struct info {
    int minn, maxx;

    info operator + ( const info &x ) const {
        return { min( minn, x.minn ), max( maxx, x.maxx ) };
    }
};

struct SegTree {
    info segTree[4 * MAX_N];
    info lazy[4 * MAX_N];

    void init() {
        for ( int v = 0; v < 4 * MAX_N; v++ ) {
            lazy[v] = segTree[v] = { INF, -INF };
        }
    }

    void propag( int v, int l, int r ) {
        segTree[v] = segTree[v] + lazy[v];
        if ( l != r ) {
            lazy[v * 2 + 1] = lazy[v * 2 + 1] + lazy[v];
            lazy[v * 2 + 2] = lazy[v * 2 + 2] + lazy[v];
        }
    }

    void update( int v, int l, int r, int lu, int ru, info x ) {
        propag( v, l, r );

        if ( l > ru || r < lu )
            return;

        if ( lu <= l && r <= ru ) {
            lazy[v] = x;
            propag( v, l, r );
            return;
        }

        int mid = (l + r) / 2;
        update( v * 2 + 1, l, mid, lu, ru, x );
        update( v * 2 + 2, mid + 1, r, lu, ru, x );
        segTree[v] = segTree[v * 2 + 1] + segTree[v * 2 + 2];
    }

    info query( int v, int l, int r, int lq, int rq ) {
        propag( v, l, r );

        if ( l > rq || r < lq )
            return { INF, -INF };

        if ( lq <= l && r <= rq )
            return segTree[v];

        int mid = (l + r) / 2;
        return query( v * 2 + 1, l, mid, lq, rq ) + query( v * 2 + 2, mid + 1, r, lq, rq );
    }
};

struct HPD {
    int n, curPos;
    int sz[MAX_N], parent[MAX_N], depth[MAX_N], heavy[MAX_N], head[MAX_N], leftPos[MAX_N];
    SegTree aint;

    void dfs( int u, int p ) {
        int maxSz = -1;

        parent[u] = p;
        depth[u] = depth[p] + 1;
        sz[u] = 1;
        heavy[u] = undef;
        for ( int v: edges[u] ) {
            if ( v == p )
                continue;
            dfs( v, u );
            sz[u] += sz[v];
            if ( sz[v] > maxSz ) {
                maxSz = sz[v];
                heavy[u] = v;
            }
        }
    }

    void decomp( int u, int p, int h ) {
        head[u] = h;
        leftPos[u] = ++curPos;
        if ( heavy[u] != undef )
            decomp( heavy[u], u, h );
        for ( int v: edges[u] ) {
            if ( v == p || v == heavy[u] )
                continue;
            decomp( v, u, v );
        }
    }

    void init( int _n ) {
        n = _n;
        aint.init();
        dfs( 1, 0 );
        decomp( 1, 0, 1 );
    }

    void updatePath( int u, int v, info x ) {
        while ( head[u] != head[v] ) {
            if ( depth[head[u]] < depth[head[v]] )
                swap( u, v );
            aint.update( 0, 1, n, leftPos[head[u]], leftPos[u], x );
            u = parent[head[u]];
        }
        if ( depth[u] > depth[v] )
            swap( u, v );
        aint.update( 0, 1, n, leftPos[u], leftPos[v], x );
    }

    info queryVertex( int u ) {
        return aint.query( 0, 1, n, leftPos[u], leftPos[u] );
    }
};

HPD arb;
unordered_map<int, int> indx;

int main() {
    int n, k;

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

    dfs( 1, 0 );
    init( n );

    cin >> k;
    for ( int i = 0; i < k; i++ ) {
        char ch;
        int u, v, w;
        cin >> ch >> u >> v >> w;
        if ( ch == 'm' )
            mins.push_back( { u, v, w } );
        else
            maxs.push_back( { u, v, w } );
    }

    arb.init( n );
    for ( int i = 0; i < mins.size(); i++ ) {
        indx[mins[i].w] = i;
        int u = mins[i].u, v = mins[i].v;
        int l = lca( u, v );
        int a = findParent( u, depth[u] - depth[l] - 1 );
        int b = findParent( v, depth[v] - depth[l] - 1 );
        if ( a != undef )
            arb.updatePath( u, a, { INF, mins[i].w, } );
        if ( b != undef )
            arb.updatePath( v, b, { INF, mins[i].w } );
    }
    for ( int i = 0; i < maxs.size(); i++ ) {
        indx[maxs[i].w] = i;
        int u = maxs[i].u, v = maxs[i].v;
        int l = lca( u, v );
        int a = findParent( u, depth[u] - depth[l] - 1 );
        int b = findParent( v, depth[v] - depth[l] - 1 );
        if ( a != undef )
            arb.updatePath( u, a, { maxs[i].w, -INF } );
        if ( b != undef )
            arb.updatePath( v, b, { maxs[i].w, -INF } );
    }
    indx[INF] = indx[-INF] = -1;

    for ( int u = 2; u <= n; u++ ) {
        queryMin[u] = indx[arb.queryVertex( u ).maxx];
        queryMax[u] = indx[arb.queryVertex( u ).minn];
        //printf( "%d %d\n", arb.queryVertex( u ).maxx, arb.queryVertex( u ).minn );
    }

    match.init( k, n - 1 );
    for ( int u = 2; u <= n; u++ ) {
        if ( queryMin[u] != -1 )
            match.add_edge( queryMin[u] + 1, u - 1 );
        if ( queryMax[u] != -1 )
            match.add_edge( mins.size() + queryMax[u] + 1, u - 1 );
    }
    match.maxMatch();

    for ( int u = 2; u <= n; u++ )
        value[u] = undef;
    for ( int i = 0; i < mins.size(); i++ )
        value[match.pairU[i + 1] + 1] = mins[i].w;
    for ( int i = 0; i < maxs.size(); i++ )
        value[match.pairU[mins.size() + i + 1] + 1] = maxs[i].w;

    for ( int u = 2; u <= n; u++ ) {
        if ( value[u] == undef ) {
            if ( queryMin[u] != undef )
                value[u] = mins[queryMin[u]].w;
            else if ( queryMax[u] != undef )
                value[u] = maxs[queryMax[u]].w;
            else
                value[u] = 0;
        }
        cout << u << " " << parent[0][u] << " " << value[u] << "\n";
    }

    return 0;
}

Compilation message

minmaxtree.cpp: In member function 'void MATCH::maxMatch()':
minmaxtree.cpp:134:13: warning: unused variable 'maxMatch' [-Wunused-variable]
  134 |         int maxMatch, u, v;
      |             ^~~~~~~~
minmaxtree.cpp: In function 'int main()':
minmaxtree.cpp:301:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<query>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  301 |     for ( int i = 0; i < mins.size(); i++ ) {
      |                      ~~^~~~~~~~~~~~~
minmaxtree.cpp:312:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<query>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  312 |     for ( int i = 0; i < maxs.size(); i++ ) {
      |                      ~~^~~~~~~~~~~~~
minmaxtree.cpp:342:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<query>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  342 |     for ( int i = 0; i < mins.size(); i++ )
      |                      ~~^~~~~~~~~~~~~
minmaxtree.cpp:344:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<query>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  344 |     for ( int i = 0; i < maxs.size(); i++ )
      |                      ~~^~~~~~~~~~~~~

Subtask #1
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 5 ms 8020 KB Output is correct
2 Correct 6 ms 8096 KB Output is correct
3 Correct 5 ms 8020 KB Output is correct
4 Correct 6 ms 8148 KB Output is correct

Subtask #2
22.0 / 22.0

# 결과 실행 시간 메모리 Grader output
1 Correct 291 ms 37120 KB Output is correct
2 Correct 299 ms 27664 KB Output is correct
3 Correct 282 ms 34836 KB Output is correct
4 Correct 287 ms 42740 KB Output is correct
5 Correct 283 ms 33060 KB Output is correct
6 Correct 283 ms 30084 KB Output is correct
7 Correct 250 ms 28228 KB Output is correct

Subtask #3
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 160 ms 21648 KB Output is correct
2 Correct 162 ms 23056 KB Output is correct
3 Correct 157 ms 33968 KB Output is correct
4 Correct 160 ms 39152 KB Output is correct
5 Correct 167 ms 25724 KB Output is correct
6 Correct 184 ms 27196 KB Output is correct
7 Correct 179 ms 23440 KB Output is correct
8 Correct 166 ms 23244 KB Output is correct

Subtask #4
42.0 / 42.0

# 결과 실행 시간 메모리 Grader output
1 Correct 5 ms 8020 KB Output is correct
2 Correct 6 ms 8096 KB Output is correct
3 Correct 5 ms 8020 KB Output is correct
4 Correct 6 ms 8148 KB Output is correct
5 Correct 291 ms 37120 KB Output is correct
6 Correct 299 ms 27664 KB Output is correct
7 Correct 282 ms 34836 KB Output is correct
8 Correct 287 ms 42740 KB Output is correct
9 Correct 283 ms 33060 KB Output is correct
10 Correct 283 ms 30084 KB Output is correct
11 Correct 250 ms 28228 KB Output is correct
12 Correct 160 ms 21648 KB Output is correct
13 Correct 162 ms 23056 KB Output is correct
14 Correct 157 ms 33968 KB Output is correct
15 Correct 160 ms 39152 KB Output is correct
16 Correct 167 ms 25724 KB Output is correct
17 Correct 184 ms 27196 KB Output is correct
18 Correct 179 ms 23440 KB Output is correct
19 Correct 166 ms 23244 KB Output is correct
20 Correct 315 ms 28256 KB Output is correct
21 Correct 300 ms 26836 KB Output is correct
22 Correct 294 ms 26924 KB Output is correct
23 Correct 288 ms 26784 KB Output is correct
24 Correct 273 ms 40628 KB Output is correct
25 Correct 280 ms 46400 KB Output is correct
26 Correct 265 ms 44712 KB Output is correct
27 Correct 334 ms 39072 KB Output is correct
28 Correct 308 ms 29856 KB Output is correct
29 Correct 303 ms 30260 KB Output is correct
30 Correct 284 ms 28684 KB Output is correct
31 Correct 296 ms 28208 KB Output is correct
32 Correct 296 ms 28432 KB Output is correct
33 Correct 286 ms 27588 KB Output is correct
34 Correct 302 ms 27668 KB Output is correct
35 Correct 282 ms 27076 KB Output is correct