牛ゲー
(typical/others/cow_game.cpp)

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Last update: 2023-09-23 21:29:16+09:00
Link: https://atcoder.jp/contests/abc216/tasks/abc216_g

概要

以下の線形計画問題は最短路問題に帰着して解くことができる $\min_x x_t-x_s \text{s.t. } x_i-x_j \leq w_{ij}$

方法

頂点$i, j$間に長さ$w_{ij}$の辺をはってdijkstraかbellman-fordで$s, t$の最短路を求めるとその長さが上の線形計画問題の最適値で、$x_i = dist[s][i]$が最適解になる。

Depends on

Code

#define PROBLEM "https://atcoder.jp/contests/abc216/tasks/abc216_g"
#include "library/graph/distance/dijkstra.cpp"
#include "library/template/template.cpp"
/**
 * @brief 牛ゲー
 * @docs docs/cow_game.md
 */
int main() {
    int n, m;
    cin >> n >> m;
    Graph<ll> g(n + 1);
    rep(i, n) {
        g.add_directed_edge(i, i + 1, 1);
        g.add_directed_edge(i + 1, i, 0);
    }
    rep(i, m) {
        ll l, r, x;
        cin >> l >> r >> x;
        l--;
        g.add_directed_edge(l, r, r - l - x);
    }
    auto dist = dijkstra(g, 0);
    rep(i, n) {
        if (dist[i + 1] - dist[i])
            cout << "0 ";
        else
            cout << "1 ";
    }
    cout << endl;
}

#line 1 "typical/others/cow_game.cpp"
#define PROBLEM "https://atcoder.jp/contests/abc216/tasks/abc216_g"
#line 2 "library/template/template.cpp"
/* #region header */
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
    for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//入出力
#define print(x) cout << x << endl
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    for (auto &e : v)
        cout << e << " ";
    cout << endl;
    return os;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &a)
{
    for (auto &i : a)
        scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T mypow(T x, ll n)
{
    T ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}
ll modpow(ll x, ll n, const ll mod)
{
    ll ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
        x %= mod;
        ret %= mod;
    }
    return ret;
}
ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; }
int popcnt(ull x) { return __builtin_popcountll(x); }
template <typename T>
vector<int> IOTA(vector<T> a)
{
    int n = a.size();
    vector<int> id(n);
    iota(all(id), 0);
    sort(all(id), [&](int i, int j)
         { return a[i] < a[j]; });
    return id;
}
long long xor64(long long range) {
    static uint64_t x = 88172645463325252ULL;
    x ^= x << 13;
    x ^= x >> 7;
    return (x ^= x << 17) % range;
}
struct Timer
{
    clock_t start_time;
    void start() { start_time = clock(); }
    int lap()
    {
        // return x ms.
        return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
    }
};
template <typename T = int>
struct Edge
{
    int from, to;
    T cost;
    int idx;

    Edge() = default;

    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}

    operator int() const { return to; }
};

template <typename T = int>
struct Graph
{
    vector<vector<Edge<T>>> g;
    int es;

    Graph() = default;

    explicit Graph(int n) : g(n), es(0) {}

    size_t size() const { return g.size(); }

    void add_directed_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es++);
    }

    void add_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }

    void read(int M, int padding = -1, bool weighted = false,
              bool directed = false)
    {
        for (int i = 0; i < M; i++)
        {
            int a, b;
            cin >> a >> b;
            a += padding;
            b += padding;
            T c = T(1);
            if (weighted)
                cin >> c;
            if (directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }
};

/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
#line 3 "library/graph/distance/dijkstra.cpp"
/**
 * @brief dijkstra
 * @docs docs/dijkstra.md
 */
template <typename T>
vector<T> dijkstra(Graph<T> &g, int s) {
    const auto TINF = numeric_limits<T>::max();
    vector<T> dist(g.size(), TINF);
    priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>> que;
    dist[s] = 0;
    que.emplace(dist[s], s);
    while (!que.empty()) {
        T cost;
        int idx;
        tie(cost, idx) = que.top();
        que.pop();
        if (dist[idx] < cost) continue;
        for (auto &e : g.g[idx]) {
            auto next_cost = cost + e.cost;
            if (dist[e.to] <= next_cost) continue;
            dist[e.to] = next_cost;
            que.emplace(dist[e.to], e.to);
        }
    }
    return dist;
}
#line 4 "typical/others/cow_game.cpp"
/**
 * @brief 牛ゲー
 * @docs docs/cow_game.md
 */
int main() {
    int n, m;
    cin >> n >> m;
    Graph<ll> g(n + 1);
    rep(i, n) {
        g.add_directed_edge(i, i + 1, 1);
        g.add_directed_edge(i + 1, i, 0);
    }
    rep(i, m) {
        ll l, r, x;
        cin >> l >> r >> x;
        l--;
        g.add_directed_edge(l, r, r - l - x);
    }
    auto dist = dijkstra(g, 0);
    rep(i, n) {
        if (dist[i + 1] - dist[i])
            cout << "0 ";
        else
            cout << "1 ";
    }
    cout << endl;
}

牛ゲー (typical/others/cow_game.cpp)

概要

方法

Depends on

Code

牛ゲー
(typical/others/cow_game.cpp)