Small Multiple

#include <iostream>
#include <string>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <unordered_map>
#include <numeric>
#include <iomanip>
using namespace std;
#define pii pair<int, int>
#define FAST ios_base::sync_with_stdio(false); cin.tie(NULL)
const int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
const int dl[2] = {1, -1};
const int MOD = 1e9;
const int MAX = 100005;


int n, m, dist[MAX], par[MAX];
vector<pii> v[MAX]; // {node, weight}
priority_queue<pii> pq;

void init_dist(){
    for(int i = 0; i <= n; i++){
        dist[i] = 2e9;
    }
    dist[1] = 0;
}

void Dijkstra(){
    pq.push({-1, 1});
    while(!pq.empty()){
        int cur = pq.top().second;
        int d = -pq.top().first;
        // cout << cur << " " << d << "\n";
        pq.pop();
        for(pii a : v[cur]){
            int nxt = a.first;
            int nd = a.second;
            if(d + nd < dist[nxt]){
                dist[nxt] = d + nd;
                par[nxt] = cur;
                pq.push({-(d + nd), nxt});
            }
        }
    }
}


int main() {
    FAST;
    //freopen("gravity.in", "r", stdin);
    //freopen("gravity.out", "w", stdout);
    cin >> n;
    for(int i = 1; i <= n; i++){
        v[i % n].push_back(make_pair((i + 1) % n, 1));
    }
    for(int i = 1; i <= n; i++){
        v[i % n].push_back(make_pair((i * 10) % n, 0));
    }
    init_dist();
    Dijkstra();
    cout << dist[0] << "\n";
}