最大独立集合 (graph/maximum-independent-set.hpp)

• View this file on GitHub
• View document part on GitHub
• Last update: 2025-09-09 22:49:44+09:00
• Include: #include "graph/maximum-independent-set.hpp"
• Link: https://maspypy.github.io/library/graph/maximum_independent_set.hpp
• Link: https://www.slideshare.net/wata_orz/ss-12131479
• Link: https://yukicoder.me/problems/no/382

rem : 未決定頂点集合
cur : 採用する頂点集合
nbd[i]&rem : iと隣接する未決定頂点集合
degが1以下ならその頂点を採用して損しない
そのような頂点がなくなったらdeg最大の頂点を使うor使わないで分岐

LINK

• https://maspypy.github.io/library/graph/maximum_independent_set.hpp
• https://yukicoder.me/problems/no/382

Depends on

• other/fastio.hpp
• other/type-utils.hpp
• template.hpp

Verified with

• test/library_checker/graph/maximum_independent_set.test.cpp

Code

#pragma once
#include "../template.hpp"
// https://maspypy.github.io/library/graph/maximum_independent_set.hpp
// https://yukicoder.me/problems/no/382
// https://www.slideshare.net/wata_orz/ss-12131479 より高速
// n=120 5sec
template <int n_max, class edge_type>
vector<int> max_independent_set(int n, const vector<edge_type> &edges) {
    using BS = bitset<n_max>;
    BS res;
    auto dfs = [&n, &res](auto &&dfs, vector<BS> nbd, BS rem, BS cur) {
        while(1) {
            bool upd = false;
            for(int i : views::iota(0, n) | views::filter([&](int i) {
                            return rem[i] and (rem & nbd[i]).count() <= 1;
                        })) {
                rem[i] = 0;
                cur[i] = 1;
                upd = true;
                rem &= ~nbd[i];
            }
            if(!upd)
                break;
        }
        if(rem.none()) {
            if(res.count() < cur.count())
                res = cur;
            return;
        }
        int max_idx = ranges::max(
            views::iota(0, n) | views::filter([&](int i) { return rem[i]; }),
            {}, [&](int i) { return (rem & nbd[i]).count(); });
        assert(rem[max_idx] and nbd[max_idx].any());
        rem[max_idx] = 0;
        // max_idx 使わない
        if(nbd[max_idx].count() > 2) // 2以下->全部2->どれ使っても一緒
            dfs(dfs, nbd, rem, cur);
        // 使う
        cur[max_idx] = 1;
        rem &= ~nbd[max_idx];
        dfs(dfs, nbd, rem, cur);
    };
    vector<BS> nbd(n);
    BS rem;
    for(int i : views::iota(0, n))
        rem[i] = 1;
    for(auto &e : edges) {
        assert(0 <= min(e, e.from) and max(e, e.from) < n);
        if(e.from == e)
            rem[e] = 0;
        nbd[e.from][e] = nbd[e][e.from] = 1;
    }
    dfs(dfs, nbd, rem, BS(0));
    vector<int> res_v;
    for(int i :
        views::iota(0, n) | views::filter([&](int i) { return res[i]; }))
        res_v.emplace_back(i);
    return res_v;
}

#line 2 "other/fastio.hpp"
// ref: https://maspypy.com/library-checker-many-a-b , Nyaanさん
#line 2 "other/type-utils.hpp"
#include <bits/stdc++.h>
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using vi = std::vector<int>;
using vii = std::vector<std::vector<int>>;
using pii = std::pair<int, int>;
using vl = std::vector<ll>;
using vll = std::vector<vl>;
using pll = std::pair<ll, ll>;

template <class T>
concept extended_integral =
    std::integral<T> || std::same_as<std::remove_cv_t<T>, i128> ||
    std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept extended_signed_integral =
    std::signed_integral<T> || std::same_as<std::remove_cv_t<T>, i128>;
template <class T>
concept extended_unsigned_integral =
    std::unsigned_integral<T> || std::same_as<std::remove_cv_t<T>, u128>;

template <class T>
concept Streamable =
    requires(std::ostream &os, T &x) { os << x; } || extended_integral<T>;
template <class mint>
concept is_modint = requires(mint &x) {
    { x.val() } -> std::convertible_to<int>;
};
#line 4 "other/fastio.hpp"
namespace fastio {
constexpr int SZ = 1 << 17;
constexpr int offset = 64;
constexpr int mod = 10000;
char in_buf[SZ];
int in_left{}, in_right{};
char out_buf[SZ];
char out_tmp[offset];
int out_right{};
struct Pre {
    char num[4 * mod]{};
    constexpr Pre() {
        for(int i = 0; i < mod; ++i) {
            for(int n = i, j = 3; j >= 0; --j, n /= 10)
                num[4 * i + j] = '0' + n % 10;
        }
    }
    constexpr const char *operator[](int i) const { return &num[4 * i]; }
} constexpr pre;
void load() {
    memmove(in_buf, in_buf + in_left, in_right - in_left);
    in_right += -in_left + std::fread(in_buf + in_right - in_left, 1,
                                      SZ - (in_right - in_left), stdin);
    in_left = 0;
    if(in_right < SZ)
        in_buf[in_right++] = '\n';
}
void read(char &c) {
    do {
        if(in_left == in_right)
            load();
        c = in_buf[in_left++];
    } while(isspace(c));
}
void read(std::string &s) {
    s.clear();
    char c;
    do {
        if(in_left == in_right)
            load();
        c = in_buf[in_left++];
    } while(isspace(c));
    do {
        s += c;
        if(in_left == in_right)
            load();
        c = in_buf[in_left++];
    } while(!isspace(c));
}
template <extended_integral T> void read(T &x) {
    if(in_right - in_left < offset)
        load();
    char c;
    do
        c = in_buf[in_left++];
    while(c < '-'); // \n:10 space:32 -:45 '0':48
    bool minus{};
    if constexpr(extended_signed_integral<T>) {
        if(c == '-') {
            c = in_buf[in_left++];
            minus = true;
        }
    }
    x = 0;
    while(c >= '0') {
        x = 10 * x + (c & 15);
        c = in_buf[in_left++];
    }
    if constexpr(extended_signed_integral<T>) {
        if(minus)
            x = -x;
    }
}
void flush() { fwrite(out_buf, 1, std::exchange(out_right, 0), stdout); }
void write_range(const char *c, int n) {
    int pos{};
    while(pos < n) {
        if(out_right == SZ)
            flush();
        int len = std::min(n - pos, SZ - out_right);
        memcpy(out_buf + out_right, c + pos, len);
        out_right += len;
        pos += len;
    }
}

void write(char c) {
    if(SZ == out_right)
        flush();
    out_buf[out_right++] = c;
}
void write(const char *c) { write_range(c, strlen(c)); }
void write(const std::string &s) { write_range(s.data(), s.size()); }
template <std::floating_point T> void write(T x) {
    int n = std::snprintf(out_tmp, sizeof(out_tmp), "%.16g", x);
    write_range(out_tmp, n);
}
void write(bool x) { write(x ? '1' : '0'); }
template <extended_integral T> void write(T x) {
    if(x == 0) {
        write('0');
    }
    if constexpr(extended_signed_integral<T>) {
        if(x < 0) {
            write('-');
            x = -x;
        }
    }
    if(SZ - out_right < offset)
        flush();
    int cur = offset;
    for(; x >= 1000; x /= mod) {
        cur -= 4;
        memcpy(out_tmp + cur, pre[x % mod], 4);
    }
    if(x >= 100) {
        cur -= 3;
        memcpy(out_tmp + cur, pre[x % mod] + 1, 3);
    } else if(x >= 10) {
        cur -= 2;
        memcpy(out_tmp + cur, pre[x % mod] + 2, 2);
    } else if(x >= 1) {
        cur -= 1;
        memcpy(out_tmp + cur, pre[x % mod] + 3, 1);
    }
    write_range(out_tmp + cur, offset - cur);
}
struct Dummy {
    // プログラム終了時に出力
    ~Dummy() { flush(); }
} dummy;
} // namespace fastio
using fastio::write;
#line 4 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#line 8 "template.hpp"
using namespace std;
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...)
#endif
template <Streamable T> void print_one(const T &value) { fastio::write(value); }
template <is_modint T> void print_one(const T &value) {
    print_one(value.val());
}
void print() { print_one('\n'); }
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
    print_one(a);
    ((print_one(' '), print_one(b)), ...);
    print();
}
template <ranges::range Iterable>
    requires(!Streamable<Iterable>)
void print(const Iterable &v) {
    for(auto it = v.begin(); it != v.end(); ++it) {
        if(it != v.begin())
            print_one(' ');
        print_one(*it);
    }
    print();
}
#define all(v) begin(v), end(v)
template <class T> void UNIQUE(T &v) {
    ranges::sort(v);
    v.erase(unique(all(v)), end(v));
}
template <typename T> inline bool chmax(T &a, T b) {
    return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
    return ((a > b) ? (a = b, true) : (false));
}
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
    return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
    return max(initializer_list<common_type_t<T...>>{a...});
}
void input() {}
template <class Head, class... Tail> void input(Head &head, Tail &...tail) {
#ifdef LOCAL
    cin >> head;
#else
    fastio::read(head);
#endif
    input(tail...);
}
template <class T> void input(vector<T> &a) {
    for(T &x : a)
        input(x);
}
#define INT(...)                                                               \
    int __VA_ARGS__;                                                           \
    input(__VA_ARGS__)
#define LL(...)                                                                \
    long long __VA_ARGS__;                                                     \
    input(__VA_ARGS__)
#define STR(...)                                                               \
    string __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#define REP1_0(n, c) REP1_1(n, c)
#define REP1_1(n, c)                                                           \
    for(ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(n); REP_COUNTER_##c++)
#define REP1(n) REP1_0(n, __COUNTER__)
#define REP2(i, a) for(ll i = 0; i < (ll)(a); i++)
#define REP3(i, a, b) for(ll i = (ll)(a); i < (ll)(b); i++)
#define REP4(i, a, b, c) for(ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
template <class T> constexpr T floor(T x, T y) noexcept {
    return x / y - ((x ^ y) < 0 and x % y);
}
template <class T> constexpr T ceil(T x, T y) noexcept {
    return x / y + ((x ^ y) >= 0 and x % y);
}
// yの符号に関わらず非負で定義 \bmod:texコマンド
template <class T> constexpr T bmod(T x, T y) noexcept {
    T m = x % y;
    return (m < 0) ? m + (y > 0 ? y : -y) : m;
}
template <std::signed_integral T> constexpr int bit_width(T x) noexcept {
    return std::bit_width((uint64_t)x);
}
template <std::signed_integral T> constexpr int popcount(T x) noexcept {
    return std::popcount((uint64_t)x);
}
constexpr bool kth_bit(auto n, auto k) { return (n >> k) & 1; }
#line 3 "graph/maximum-independent-set.hpp"
// https://maspypy.github.io/library/graph/maximum_independent_set.hpp
// https://yukicoder.me/problems/no/382
// https://www.slideshare.net/wata_orz/ss-12131479 より高速
// n=120 5sec
template <int n_max, class edge_type>
vector<int> max_independent_set(int n, const vector<edge_type> &edges) {
    using BS = bitset<n_max>;
    BS res;
    auto dfs = [&n, &res](auto &&dfs, vector<BS> nbd, BS rem, BS cur) {
        while(1) {
            bool upd = false;
            for(int i : views::iota(0, n) | views::filter([&](int i) {
                            return rem[i] and (rem & nbd[i]).count() <= 1;
                        })) {
                rem[i] = 0;
                cur[i] = 1;
                upd = true;
                rem &= ~nbd[i];
            }
            if(!upd)
                break;
        }
        if(rem.none()) {
            if(res.count() < cur.count())
                res = cur;
            return;
        }
        int max_idx = ranges::max(
            views::iota(0, n) | views::filter([&](int i) { return rem[i]; }),
            {}, [&](int i) { return (rem & nbd[i]).count(); });
        assert(rem[max_idx] and nbd[max_idx].any());
        rem[max_idx] = 0;
        // max_idx 使わない
        if(nbd[max_idx].count() > 2) // 2以下->全部2->どれ使っても一緒
            dfs(dfs, nbd, rem, cur);
        // 使う
        cur[max_idx] = 1;
        rem &= ~nbd[max_idx];
        dfs(dfs, nbd, rem, cur);
    };
    vector<BS> nbd(n);
    BS rem;
    for(int i : views::iota(0, n))
        rem[i] = 1;
    for(auto &e : edges) {
        assert(0 <= min(e, e.from) and max(e, e.from) < n);
        if(e.from == e)
            rem[e] = 0;
        nbd[e.from][e] = nbd[e][e.from] = 1;
    }
    dfs(dfs, nbd, rem, BS(0));
    vector<int> res_v;
    for(int i :
        views::iota(0, n) | views::filter([&](int i) { return res[i]; }))
        res_v.emplace_back(i);
    return res_v;
}

Back to top page