CSES-solutions/CSES Problem Set/Investigation.cpp

/* Problem URL: https://cses.fi/problemset/task/1202 */

#include <bits/stdc++.h>

using namespace std;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m;
    cin >> n >> m;

    V<V<pair<int, ll>>> graph(n);
    V<V<pair<int, ll>>> rev(n);

    while (m--) {
        int a, b, c;
        cin >> a >> b >> c;
        a--, b--;

        graph[a].emplace_back(b, c);
        rev[b].emplace_back(a, c);
    }

    ll inf = INT64_MAX >> 1;
    vl dis(n, inf);

    auto dijkstra = [&]() {
        priority_queue<pair<ll, int>, V<pair<ll, int>>, greater<>> pq;
        dis[0] = 0;
        pq.emplace(0, 0);

        while (!pq.empty()) {
            auto [c, i] = pq.top();
            pq.pop();

            if (c > dis[i]) {
                continue;
            }

            for (auto [j, cc] : graph[i]) {
                if (dis[j] > c + cc) {
                    dis[j] = c + cc;
                    pq.emplace(dis[j], j);
                }
            }
        }

        return dis.back();
    };

    ll ans = dijkstra();

    vl dp1(n, -1);

    ll mod = 1e9 + 7;

    function<ll(int, ll)> dfs1 = [&](int i, ll c) {
        if (i == 0) {
            dp1[i] = 1;
            return dp1[i];
        }

        if (dp1[i] != -1) {
            return dp1[i];
        }

        dp1[i] = 0;

        for (auto [j, cc] : rev[i]) {
            if (dis[j] == c - cc) {
                dp1[i] += dfs1(j, c - cc);
                dp1[i] %= mod;
            }
        }

        return dp1[i];
    };

    vi dp2(n, -1);
    function<int(int, ll)> dfsmax = [&](int i, ll c) {
        if (i == 0) {
            dp2[i] = 1;
            return dp2[i];
        }

        if (dp2[i] != -1) {
            return dp2[i];
        }

        dp2[i] = 0;

        for (auto [j, cc] : rev[i]) {
            if (dis[j] == c - cc) {
                int res = dfsmax(j, c - cc);
                if (res > 0) {
                    rmax(dp2[i], res + 1);
                }
            }
        }

        return dp2[i];
    };

    vi dp3(n, -1);
    function<int(int, ll)> dfsmin = [&](int i, ll c) {
        if (i == 0) {
            dp3[i] = 1;
            return dp3[i];
        }

        if (dp3[i] != -1) {
            return dp3[i];
        }

        dp3[i] = INT32_MAX >> 1;

        for (auto [j, cc] : rev[i]) {
            if (dis[j] == c - cc) {
                rmin(dp3[i], dfsmin(j, c - cc) + 1);
            }
        }

        return dp3[i];
    };

    cout << ans << ' ' << dfs1(n - 1, ans) << ' ' << dfsmin(n - 1, ans) - 1 << ' ' << dfsmax(n - 1, ans) - 1 << '\n';
}