#1152410 (C++17) No.2744 Power! or +1

• 問題: No.2744 Power! or +1
• ユーザー: 👑 AngrySadEight
• 提出日時: 2026-03-14 17:30:07
• 言語: C++17 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 599 ms / 3,000 ms
• コード長: 5,385 bytes
• コンパイル時間: 3,096 ms
• コンパイル使用メモリ: 220,396 KB
• 実行使用メモリ: 432,252 KB
• 最終ジャッジ日時: 2026-03-14 17:30:13
• 合計ジャッジ時間: 6,298 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge3_0

ファイルパターン	結果
sample	AC * 2
other	AC * 9

ソースコード

#include <algorithm>
#include <atcoder/all>
#include <bitset>
#include <cassert>
#include <cmath>
#include <ctime>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using namespace atcoder;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define mod1 1000000007
#define mod2 998244353
#define mod3 100000007
#define vi vector<int>
#define vs vector<string>
#define vc vector<char>
#define vl vector<ll>
#define vb vector<bool>
#define vvi vector<vector<int>>
#define vvc vector<vector<char>>
#define vvl vector<vector<ll>>
#define vvb vector<vector<bool>>
#define vvvi vector<vector<vector<int>>>
#define vvvl vector<vector<vector<ll>>>
#define pii pair<int, int>
#define pil pair<int, ll>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define vpii vector<pair<int, int>>
#define vpll vector<pair<ll, ll>>
#define vvpii vector<vector<pair<int, int>>>
#define vvpll vector<vector<pair<ll, ll>>>

template <typename T>
void debug(T e) {
    cerr << e << endl;
}

template <typename T>
void debug(vector<T> &v) {
    rep(i, v.size()) { cerr << v[i] << " "; }
    cerr << endl;
}

template <typename T>
void debug(vector<vector<T>> &v) {
    rep(i, v.size()) {
        rep(j, v[i].size()) { cerr << v[i][j] << " "; }
        cerr << endl;
    }
}

template <typename T>
void debug(vector<pair<T, T>> &v) {
    rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; }
}

template <typename T>
void debug(set<T> &st) {
    for (auto itr = st.begin(); itr != st.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(multiset<T> &ms) {
    for (auto itr = ms.begin(); itr != ms.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(map<T, T> &mp) {
    for (auto itr = mp.begin(); itr != mp.end(); itr++) {
        cerr << itr->first << " " << itr->second << endl;
    }
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << H << " ";
    debug_out(T...);
}

using mint = modint998244353;

void debug_mint1(vector<mint> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        cerr << vec[i].val() << " ";
    }
    cerr << endl;
}

void debug_mint2(vector<vector<mint>> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        for (int j = 0; j < vec[i].size(); j++) {
            cerr << vec[i][j].val() << " ";
        }
        cerr << endl;
    }
}

bool islarger(ll x, ll n, ll N){
    ll ret = 1;
    for (ll i = 0; i < n; i++){
        ret *= x;
        if (ret >= N) return true;
    }
    return false;
}

void dijkstra(vvpll &graph, ll v, vl &dist) {
    priority_queue<pll, vpll, greater<pll>> pque;
    pque.push(pll(0, v));
    dist[v] = 0;
    while (pque.size()) {
        pll p = pque.top();
        pque.pop();
        if (dist[p.second] != p.first) {
            continue;
        }
        for (auto x : graph[p.second]) {
            if (dist[x.first] > dist[p.second] + x.second) {
                dist[x.first] = dist[p.second] + x.second;
                pque.push(pll(dist[x.first], x.first));
            }
        }
    }
}

int main() {
    ll N, A, B, C;
    cin >> N >> A >> B >> C;

    // ちょうどその値、か N より大きい領域か、に応じて値を分けることにする
    vector<vector<pll>> graph(2 * N, vector<pll>(0));
    for (ll i = 1; i < N; i++){
        graph[i].push_back(make_pair(i + 1, A));
        graph[i + N].push_back(make_pair((i + 1) % N + N, A));
    }
    vector<ll> fact_exact = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880};
    vector<ll> fact_rem(N);
    fact_rem[0] = 1;
    for (ll i = 1; i < N; i++){
        fact_rem[i] = (fact_rem[i - 1] * i) % N;
    }
    ll max_k = 1;
    while (true){
        if (islarger(B, max_k, A * N)) break;
        max_k++;
    }
    for (ll i = 1; i < N; i++){
        ll rem = 1;
        ll cost = 1;
        bool larger = false;
        for (ll j = 1; j < max_k; j++){
            rem = rem * i;
            cost = cost * B;
            if (rem >= N){
                larger = true;
            }
            rem %= N;
            if (larger){
                graph[i].push_back(make_pair(rem + N, cost));
            }
            else{
                graph[i].push_back(make_pair(rem, cost));
            }
            graph[i + N].push_back(make_pair(rem + N, cost));
        }
    }
    for (ll i = 1; i < N; i++){
        if (i < 10){
            if (fact_exact[i] < N){
                graph[i].push_back(make_pair(fact_rem[i], C));
            }
            else{
                graph[i].push_back(make_pair(fact_rem[i] + N, C));
            }
        }
        else{
            graph[i].push_back(make_pair(N + fact_rem[i], C));
        }
        graph[i + N].push_back(make_pair(N, C));
    }
    ll INF = 10000000000000023;
    vector<ll> dist(2 * N, INF);
    dist[1] = 0;
    dijkstra(graph, 1, dist);
    cout << min(dist[N], dist[0]) << endl;
}