結果

問題 No.2677 Minmax Independent Set
ユーザー 👑 Nachia
提出日時 2024-03-16 15:57:40
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 90 ms / 2,000 ms
コード長 9,489 bytes
コンパイル時間 1,249 ms
コンパイル使用メモリ 113,156 KB
最終ジャッジ日時 2025-02-20 06:51:26
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 61
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#ifdef NACHIA
// #define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<(i64)(n); i++)
#define repr(i,n) for(i64 i=(i64)(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
const char* yn(bool x){ return x ? "Yes" : "No"; }
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;
#include <cassert>
namespace nachia{
template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = std::move(items[i].second);
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};
} // namespace nachia
namespace nachia{
struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
        int xorval() const { return from ^ to; }
    };
    Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    template<class Cin>
    static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){
        Graph res(n, undirected, m);
        for(int i=0; i<m; i++){
            int u, v; cin >> u >> v;
            res[i].from = u - offset;
            res[i].to = v - offset;
        }
        return res;
    }
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addNode() noexcept { return m_n++; }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
        m_n = newV;
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = newV[mapping[i]]++;
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};
} // namespace nachia
#include <type_traits>
namespace nachia{
template<
    class S,
    class RakeFunc,
    class CompressFunc,
    typename std::enable_if_t<std::is_invocable_r_v<S, RakeFunc, S, S>, void*> = nullptr,
    typename std::enable_if_t<std::is_invocable_r_v<S, CompressFunc, S, int, int>, void*> = nullptr
>
class TreeDP{
private:
    std::vector<S> low;
    std::vector<S> high;
    std::vector<int> XorEdge;
    std::vector<int> P;
    RakeFunc rake;
    CompressFunc compress;
public:
    // S rake(S a, S b)
    // S compress(S a, int edgeIndex, int newRoot)
    TreeDP(const Graph& tree, std::vector<S> node, RakeFunc _rake, CompressFunc _compress)
        : rake(std::move(_rake))
        , compress(std::move(_compress))
    {
        int n = tree.numVertices();
        auto adj = tree.getEdgeIndexArray(true);
        XorEdge.resize(n-1);
        for(int i=0; i<n-1; i++) XorEdge[i] = tree[i].from ^ tree[i].to;
        std::vector<int> bfs(n, 0);
        int bfsi = 1;
        P.assign(n, -1);
        for(int v : bfs){
            for(int e : adj[v]){
                int w = v ^ XorEdge[e];
                if(P[v] != e){ P[w] = e; bfs[bfsi++] = w; }
            }
        }
        low = node;
        for(int i=n-1; i>=1; i--){
            int w = bfs[i];
            int v = w ^ XorEdge[P[w]];
            low[v] = rake(low[v], compress(low[w], P[w], v));
        }
        
        high = node;
        for(int i=0; i<n; i++){
            int v = bfs[i];
            int C = adj[v].size();
            S fold = node[0];
            if(v != 0) fold = compress(high[v], P[v], v);
            for(int ci=C-1; ci>=0; ci--){
                int e = adj[v][ci];
                if(P[v] == e) continue;
                int w = v ^ XorEdge[e];
                high[w] = fold;
                fold = rake(compress(low[w], e, v), fold);
            }
            fold = node[v];
            for(int ci=0; ci<C; ci++){
                int e = adj[v][ci];
                if(P[v] == e) continue;
                int w = v ^ XorEdge[e];
                high[w] = rake(high[w], fold);
                fold = rake(fold, compress(low[w], e, v));
            }
        }
    }
    int edgeBetween(int u, int v){
        if(P[u] >= 0 && XorEdge[P[u]] == (u^v)) return P[u];
        return P[v];
    }
    S getAtVtx(int i){
        if(i == 0) return low[i];
        return rake(compress(high[i], P[i], i), low[i]);
    }
    S getAtEdge(int root, int edge){
        if(P[root] == edge) return low[root];
        return high[root ^ XorEdge[edge]];
    }
};
} // namespace nachia
void testcase(){
    int N; cin >> N;
    auto tree = nachia::Graph::Input(cin, N, true, N-1, 1);
    struct Node { int c0; int c1; };
    auto dp = nachia::TreeDP(tree, vector<Node>(N, {0,0}),
        [](Node a, Node b) -> Node { return { a.c0 + b.c0, a.c1 + b.c1 }; },
        [](Node x, int, int) -> Node { return { max(x.c0, x.c1+1), x.c0 }; }
    );
    int ans = N;
    rep(i,N) chmin(ans, dp.getAtVtx(i).c1 + 1);
    cout << ans << '\n';
}
int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    #ifdef NACHIA
    int T; cin >> T; for(int t=0; t<T; T!=++t?(cout<<'\n'),0:0)
    #endif
    testcase();
    return 0;
}
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