Painfull_Bases.md

Algorithm: DP , Bitmask

Problem: Painfull Bases

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define vi vector<int>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vvi vector<vi>
#define vll vector<ll>
#define vvll vector<vector<ll>>
#define vpii vector<pair<int,int>>
#define vpll vector<pair<ll,ll>>
#define vb vector<bool>
#define vs vector<string>
///............x...........///
#define all(a) a.begin(), a.end()
#define allr(a) a.rbegin(), a.rend()
#define mp(a, b) make_pair(a, b)
#define pb push_back
#define ff first
#define ss second
#define bg begin()
#define UNIQUE(X) (X).erase(unique(all(X)), (X).end())
#define ft cout << "for test"<<endl;
#define read(v, a, n) for (int i = a; i<n; i++)cin>>v[i];
#define print(v) for (auto it : v)cout << it<<' ';cout << endl;
#define PI acos(-1.0)
#define yes cout <<"Yes"<< endl
#define no cout<<"No"<<endl
#define FIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define t_c int test, cs = 1;cin>>test;while (test--)
#define casep cout<<"Case "<< cs++<<": ";
///................function.....................///

#define D(a) (double)(a)
#define sqr(a) (a * a)
#define siz(s) (int)(s.size())
#define max3(a, b, c) max(a, max(b, c))
#define min3(a, b, c) min(a, min(b, c))
#define Min(a) *min_element(all(a))
///#define mod 1000000007
///.........Graph.........///
int X[] = {1, -1, 0, 0};
int Y[] = {0, 0, 1, -1};
///........constant........///
const ll N = (1<<13);
ll dp[N+5][20],n,k,base;
string s;
map<char,int>cast;
ll Fun(int bit, ll val){
	if(bit==(1<<n)-1)return (val==0);
	ll &ret=dp[bit][val];
	if(~ret)return ret;
	ret=0;
	for(int i=0; i<n; i++){
		if(bit&(1<<i))continue;
		ret += Fun(bit|(1<<i),(val*base+cast[s[i]])%k);
	}
	return ret;
}
int main(){
	FIO;
	for(char ch='0'; ch<='9'; ch++)cast[ch]=ch-'0';
	for(char ch='A'; ch<'G'; ch++)cast[ch]=ch-'A'+10;
	t_c{
		memset(dp,-1,sizeof dp);
		cin>>base>>k;
		cin>>s;
		n = siz(s);
		casep;
		cout<<Fun(0,0)<<endl;
	}
}