Small Multiple

题目描述

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.
Constraints
2≤K≤105
K is an integer.

输入

Input is given from Standard Input in the following format:
K

输出

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

样例输入

6

样例输出

3

提示

12=6×2 yields the smallest sum.

 

#include<bits/stdc++.h>
#define ll long long
#define inf 0x3f3f3f3f
using namespace std;
const int N=3e5+50;
const int p=1e9+7;
int k,cnt;
int dis[N],last[N];
bool vis[N];
struct orz{
    int v,nex,s;}e[N*5];
queue<int>q;
void add(int x,int y,int z)
{
    cnt++;
    e[cnt].v=y;
    e[cnt].nex=last[x];
    last[x]=cnt;
    e[cnt].s=z;
}
void spfa()
{
    for (int i=0;i<k;i++) dis[i]=inf;
    dis[1]=0; vis[1]=1;
    q.push(1);
    while (!q.empty())
    {
        int now=q.front(); q.pop();
        for (int i=last[now];i;i=e[i].nex)
        {
            if (dis[e[i].v]>dis[now]+e[i].s)
            {
                dis[e[i].v]=dis[now]+e[i].s;
                if (!vis[e[i].v])
                {
                    vis[e[i].v]=1;
                    q.push(e[i].v);
                }
            }
        }
        vis[now]=0;
    }
}
int main()
{
    scanf("%d",&k);
    for (int i=0;i<k;i++)
    {
        add(i,(i+1)%k,1);
        add(i,i*10%k,0);
    }
 
    spfa();
 
    printf("%d\n",dis[0]+1);
    return 0;
}