結果

問題 No.2893 Minahoshi (Hard)
コンテスト
ユーザー Nachia
提出日時 2024-09-13 23:31:09
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 19 ms / 2,000 ms
コード長 10,228 bytes
コンパイル時間 1,362 ms
コンパイル使用メモリ 96,744 KB
最終ジャッジ日時 2025-02-24 08:16:47
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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 * 1
other AC * 49
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 # 

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
const i64 INF = 1001001001001001001;
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; }
#include <atcoder/modint>
//#include <atcoder/string>
#include <utility>
#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

namespace nachia{

auto EulerianTrail(const Graph& graph){
    struct Result {
        int length;
        int start;
        std::vector<int> edges;
    } res;
    res.length = -1;
    auto adj = graph.getEdgeIndexArray();
    int n = graph.numVertices();
    int m = graph.numEdges();
    if(m == 0){
        res.length = 0;
        res.start = 0;
        return res;
    }
    int s = -1;
    if(graph.isUndirected()){
        int codd = 0;
        for(int v=0; v<n; v++) if(adj[v].size() % 2 == 1) codd++;
        if(codd > 2) return res;
        if(codd == 2) for(int v=0; v<n; v++) if(adj[v].size() % 2 == 1) s = v;
    } else {
        std::vector<int> di(n);
        for(auto [v,w] : graph) di[w]++;
        int codd = 0;
        for(int v=0; v<n; v++) codd += std::abs(adj[v].size() - di[v]);
        if(codd > 2) return res;
        if(codd == 2) for(int v=0; v<n; v++) if(adj[v].size() > di[v]) s = v;
    }
    if(s < 0) for(int v=0; v<n; v++) if(adj[v].size() > 0) s = v;
    std::vector<int> ep(n);
    std::vector<int> edges(m);
    std::vector<bool> alive(m, true);
    int pp = 0;
    int pq = m;
    int v = s;
    while(pp < pq){
        if(ep[v] >= adj[v].size()){
            if(pp == 0) return res;
            edges[--pq] = edges[--pp];
            v ^= graph[edges[pq]].xorval();
        } else {
            int e = adj[v][ep[v]++];
            if(!alive[e]) continue;
            alive[e] = false;
            edges[pp++] = e;
            v ^= graph[e].xorval();
        }
    }
    res.length = m;
    res.start = s;
    res.edges = std::move(edges);
    return res;
}

} // namespace nachia
using Modint = atcoder::static_modint<998244353>;
using namespace std;

void testcase(){
    int N; cin >> N;
    if(N <= 4){ cout << string("abba").substr(0, N) << '\n'; return; }
    string et = "";
    int p = 0;
    while((2 << p) + p <= N) p++;
    p--;
    {
        nachia::Graph graph(1<<p, false);
        rep(i,1<<p) rep(t,2) graph.addEdge(i, (i*2+t)&((1<<p)-1));
        auto circuit = nachia::EulerianTrail(graph).edges;
        rep(i,(2<<p)+p) et.push_back('0' + circuit[i&((2<<p)-1)]%2);
    }
    if(int(et.size()) != N){
        et.push_back('0');
    }
    if(int(et.size()) != N){
        p++;
        vector<int> A;
        vector<int> used(2<<p);
        rep(i,1<<p){
            int t = 0;
            rep(j,p+1) t = t * 2 + (et[i+j] - '0');
            A.push_back(t);
            used[t] = 1;
        }
        //for(auto a : used) cout << a;
        //cout << endl;
        vector<int> nx(1<<p);
        rep(i,2<<p) if(used[i] == 0) nx[i/2] = i & ((1<<p)-1);
        //for(auto a : nx) cout << a << " ";
        //cout << endl;
        //for(auto a : A) cout << a << " ";
        //cout << endl;
        vector<int> B;
        int lcnt = N - int(et.size());
        int ap = 0;
        for( ; ap<int(A.size()); ap++){
            int a = A[ap];
            int s = a / 2;
            while(nx[s] >= 0){
                int nxs = nx[s];
                B.push_back(s * 2 + (nxs % 2));
                nx[s] = -1;
                s = nxs;
                lcnt--;
                if(lcnt == 0) break;
            }
            if(lcnt == 0) break;
            B.push_back(a);
        }
        A = vector<int>(A.begin() + ap, A.end());
        for(auto b : B) A.push_back(b);
        //for(auto a : A) cout << a << " ";
        //cout << endl;
        et = "";
        for(int i=p; i>=1; i--) et.push_back('0' + (A[0] >> i) % 2);
        for(int a : A) et.push_back('0' + a % 2);
    }
    //{
    //    auto sa = atcoder::suffix_array(et);
    //    auto lcp = atcoder::lcp_array(et, sa);
    //    for(auto a : lcp) cout << a << " ";
    //    cout << endl;
    //    vector<int> cnt(N+1);
    //    for(auto x : lcp) cnt[x] += 1;
    //    for(auto a : cnt) cout << a << " ";
    //    cout << endl;
    //}
    for(char& c : et){
        if(c == '0') c = 'a'; else c = 'b';
    }
    cout << et << '\n';
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    int T; cin >> T;
    rep(t,T) testcase();
    return 0;
}
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