#961316 (C++17) No.2677 Minmax Independent Set

提出ソース

結果

問題	No.2677 Minmax Independent Set
ユーザー	👑 Nachia
提出日時	2024-03-16 15:58:35
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	42 ms / 2,000 ms
コード長	14,659 bytes
コンパイル時間	1,082 ms
コンパイル使用メモリ	90,452 KB
実行使用メモリ	14,660 KB
最終ジャッジ日時	2024-09-30 04:04:12
合計ジャッジ時間	4,305 ms
ジャッジサーバーID （参考情報）	judge5 / judge1

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 6,816 KB
testcase_01	AC	1 ms 6,816 KB
testcase_02	AC	2 ms 6,820 KB
testcase_03	AC	1 ms 6,816 KB
testcase_04	AC	2 ms 6,816 KB
testcase_05	AC	35 ms 14,580 KB
testcase_06	AC	33 ms 14,496 KB
testcase_07	AC	32 ms 14,512 KB
testcase_08	AC	32 ms 14,576 KB
testcase_09	AC	34 ms 14,604 KB
testcase_10	AC	28 ms 14,588 KB
testcase_11	AC	28 ms 14,496 KB
testcase_12	AC	29 ms 14,572 KB
testcase_13	AC	38 ms 14,560 KB
testcase_14	AC	36 ms 14,516 KB
testcase_15	AC	41 ms 14,612 KB
testcase_16	AC	42 ms 14,588 KB
testcase_17	AC	40 ms 14,504 KB
testcase_18	AC	24 ms 10,368 KB
testcase_19	AC	29 ms 11,648 KB
testcase_20	AC	10 ms 6,820 KB
testcase_21	AC	33 ms 12,592 KB
testcase_22	AC	4 ms 6,816 KB
testcase_23	AC	1 ms 6,820 KB
testcase_24	AC	2 ms 6,816 KB
testcase_25	AC	1 ms 6,816 KB
testcase_26	AC	1 ms 6,816 KB
testcase_27	AC	2 ms 6,816 KB
testcase_28	AC	29 ms 14,560 KB
testcase_29	AC	36 ms 14,492 KB
testcase_30	AC	1 ms 6,820 KB
testcase_31	AC	1 ms 6,816 KB
testcase_32	AC	2 ms 6,816 KB
testcase_33	AC	2 ms 6,820 KB
testcase_34	AC	1 ms 6,820 KB
testcase_35	AC	1 ms 6,820 KB
testcase_36	AC	2 ms 6,820 KB
testcase_37	AC	1 ms 6,816 KB
testcase_38	AC	1 ms 6,816 KB
testcase_39	AC	2 ms 6,820 KB
testcase_40	AC	2 ms 6,816 KB
testcase_41	AC	2 ms 6,820 KB
testcase_42	AC	3 ms 6,816 KB
testcase_43	AC	5 ms 6,820 KB
testcase_44	AC	9 ms 6,816 KB
testcase_45	AC	17 ms 8,576 KB
testcase_46	AC	41 ms 14,324 KB
testcase_47	AC	40 ms 14,508 KB
testcase_48	AC	41 ms 14,660 KB
testcase_49	AC	40 ms 14,564 KB
testcase_50	AC	11 ms 7,296 KB
testcase_51	AC	3 ms 6,820 KB
testcase_52	AC	24 ms 12,544 KB
testcase_53	AC	22 ms 11,776 KB
testcase_54	AC	2 ms 6,816 KB
testcase_55	AC	30 ms 14,588 KB
testcase_56	AC	29 ms 14,540 KB
testcase_57	AC	28 ms 14,524 KB
testcase_58	AC	30 ms 14,508 KB
testcase_59	AC	29 ms 14,508 KB
testcase_60	AC	21 ms 14,552 KB
testcase_61	AC	20 ms 14,508 KB
testcase_62	AC	21 ms 14,572 KB
testcase_63	AC	20 ms 14,504 KB

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ソースコード

raw source code

#define NDEBUG
#include <vector>
#include <algorithm>
#include <utility>
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--)
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
#include <cstdio>
#include <cctype>
#include <cstdint>
#include <string>

namespace nachia{

struct CInStream{
private:
	static const unsigned int INPUT_BUF_SIZE = 1 << 17;
	unsigned int p = INPUT_BUF_SIZE;
	static char Q[INPUT_BUF_SIZE];
public:
	using MyType = CInStream;
	char seekChar(){
		if(p == INPUT_BUF_SIZE){
			size_t len = fread(Q, 1, INPUT_BUF_SIZE, stdin);
			if(len != INPUT_BUF_SIZE) Q[len] = '\0';
			p = 0;
		}
		return Q[p];
	}
	void skipSpace(){ while(isspace(seekChar())) p++; }
private:
	template<class T, int sp = 1>
	T nextUInt(){
		if constexpr (sp) skipSpace();
		T buf = 0;
		while(true){
			char tmp = seekChar();
			if('9' < tmp || tmp < '0') break;
			buf = buf * 10 + (tmp - '0');
			p++;
		}
		return buf;
	}
public:
	uint32_t nextU32(){ return nextUInt<uint32_t>(); }
	int32_t nextI32(){
		skipSpace();
		if(seekChar() == '-'){
			p++; return (int32_t)(-nextUInt<uint32_t, 0>());
		}
		return (int32_t)nextUInt<uint32_t, 0>();
	}
	uint64_t nextU64(){ return nextUInt<uint64_t>();}
	int64_t nextI64(){
		skipSpace();
		if(seekChar() == '-'){
			p++; return (int64_t)(-nextUInt<int64_t, 0>());
		}
		return (int64_t)nextUInt<int64_t, 0>();
	}
	template<class T>
	T nextInt(){
		skipSpace();
		if(seekChar() == '-'){
			p++;
			return - nextUInt<T, 0>();
		}
		return nextUInt<T, 0>();
	}
	char nextChar(){ skipSpace(); char buf = seekChar(); p++; return buf; }
	std::string nextToken(){
		skipSpace();
		std::string buf;
		while(true){
			char ch = seekChar();
			if(isspace(ch) || ch == '\0') break;
			buf.push_back(ch);
			p++;
		}
		return buf;
	}
	MyType& operator>>(unsigned int& dest){ dest = nextU32(); return *this; }
	MyType& operator>>(int& dest){ dest = nextI32(); return *this; }
	MyType& operator>>(unsigned long& dest){ dest = nextU64(); return *this; }
	MyType& operator>>(long& dest){ dest = nextI64(); return *this; }
	MyType& operator>>(unsigned long long& dest){ dest = nextU64(); return *this; }
	MyType& operator>>(long long& dest){ dest = nextI64(); return *this; }
	MyType& operator>>(std::string& dest){ dest = nextToken(); return *this; }
	MyType& operator>>(char& dest){ dest = nextChar(); return *this; }
} cin;

struct FastOutputTable{
	char LZ[1000][4] = {};
	char NLZ[1000][4] = {};
	constexpr FastOutputTable(){
		using u32 = uint_fast32_t;
		for(u32 d=0; d<1000; d++){
			LZ[d][0] = ('0' + d / 100 % 10);
			LZ[d][1] = ('0' + d /  10 % 10);
			LZ[d][2] = ('0' + d /   1 % 10);
			LZ[d][3] = '\0';
		}
		for(u32 d=0; d<1000; d++){
			u32 i = 0;
			if(d >= 100) NLZ[d][i++] = ('0' + d / 100 % 10);
			if(d >=  10) NLZ[d][i++] = ('0' + d /  10 % 10);
			if(d >=   1) NLZ[d][i++] = ('0' + d /   1 % 10);
			NLZ[d][i++] = '\0';
		}
	}
};

struct COutStream{
private:
	using u32 = uint32_t;
	using u64 = uint64_t;
	using MyType = COutStream;
	static const u32 OUTPUT_BUF_SIZE = 1 << 17;
	static char Q[OUTPUT_BUF_SIZE];
	static constexpr FastOutputTable TB = FastOutputTable();
	u32 p = 0;
	static constexpr u32 P10(u32 d){ return d ? P10(d-1)*10 : 1; }
	static constexpr u64 P10L(u32 d){ return d ? P10L(d-1)*10 : 1; }
	template<class T, class U> static void Fil(T& m, U& l, U x){ m = l/x; l -= m*x; }
public:
	void next_dig9(u32 x){
		u32 y;
		Fil(y, x, P10(6));
		nextCstr(TB.LZ[y]);
		Fil(y, x, P10(3));
		nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
	}
	void nextChar(char c){
		Q[p++] = c;
		if(p == OUTPUT_BUF_SIZE){ fwrite(Q, p, 1, stdout); p = 0; }
	}
	void nextEoln(){ nextChar('\n'); }
	void nextCstr(const char* s){ while(*s) nextChar(*(s++)); }
	void nextU32(uint32_t x){
		u32 y = 0;
		if(x >= P10(9)){
			Fil(y, x, P10(9));
			nextCstr(TB.NLZ[y]); next_dig9(x);
		}
		else if(x >= P10(6)){
			Fil(y, x, P10(6));
			nextCstr(TB.NLZ[y]);
			Fil(y, x, P10(3));
			nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
		}
		else if(x >= P10(3)){
			Fil(y, x, P10(3));
			nextCstr(TB.NLZ[y]); nextCstr(TB.LZ[x]);
		}
		else if(x >= 1) nextCstr(TB.NLZ[x]);
		else nextChar('0');
	}
	void nextI32(int32_t x){
		if(x >= 0) nextU32(x);
		else{ nextChar('-'); nextU32((u32)-x); }
	}
	void nextU64(uint64_t x){
		u32 y = 0;
		if(x >= P10L(18)){
			Fil(y, x, P10L(18));
			nextU32(y);
			Fil(y, x, P10L(9));
			next_dig9(y); next_dig9(x);
		}
		else if(x >= P10L(9)){
			Fil(y, x, P10L(9));
			nextU32(y); next_dig9(x);
		}
		else nextU32(x);
	}
	void nextI64(int64_t x){
		if(x >= 0) nextU64(x);
		else{ nextChar('-'); nextU64((u64)-x); }
	}
	template<class T>
	void nextInt(T x){
		if(x < 0){ nextChar('-'); x = -x; }
		if(!(0 < x)){ nextChar('0'); return; }
		std::string buf;
		while(0 < x){
			buf.push_back('0' + (int)(x % 10));
			x /= 10;
		}
		for(int i=(int)buf.size()-1; i>=0; i--){
			nextChar(buf[i]);
		}
	}
	void writeToFile(bool flush = false){
		fwrite(Q, p, 1, stdout);
		if(flush) fflush(stdout);
		p = 0;
	}
	COutStream(){ Q[0] = 0; }
	~COutStream(){ writeToFile(); }
	MyType& operator<<(unsigned int tg){ nextU32(tg); return *this; }
	MyType& operator<<(unsigned long tg){ nextU64(tg); return *this; }
	MyType& operator<<(unsigned long long tg){ nextU64(tg); return *this; }
	MyType& operator<<(int tg){ nextI32(tg); return *this; }
	MyType& operator<<(long tg){ nextI64(tg); return *this; }
	MyType& operator<<(long long tg){ nextI64(tg); return *this; }
	MyType& operator<<(const std::string& tg){ nextCstr(tg.c_str()); return *this; }
	MyType& operator<<(const char* tg){ nextCstr(tg); return *this; }
	MyType& operator<<(char tg){ nextChar(tg); return *this; }
} cout;

char CInStream::Q[INPUT_BUF_SIZE];
char COutStream::Q[OUTPUT_BUF_SIZE];

} // namespace nachia

int main(){
    using nachia::cin;
    using nachia::cout;
    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';
    return 0;
}

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結果

テストケース

ソースコード