結果
問題 | No.2677 Minmax Independent Set |
ユーザー |
👑 ![]() |
提出日時 | 2024-03-16 15:58:35 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 66 ms / 2,000 ms |
コード長 | 14,659 bytes |
コンパイル時間 | 1,121 ms |
コンパイル使用メモリ | 87,424 KB |
最終ジャッジ日時 | 2025-02-20 06:51:35 |
ジャッジサーバーID (参考情報) |
judge1 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 61 |
ソースコード
#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 nachianamespace 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 nachiaint 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;}