Dice Combinations

#include <bits/stdc++.h>
using namespace std;
// clang-format off
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) { os << '{'; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << '}'; }
void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }
template <typename T> istream &operator>>(istream &is, vector<T> &v) { T value; is >> value; v.push_back(value); return is; }
#define preamble ios::sync_with_stdio(0); cin.tie(0); dbg("INIT");
// clang-format on
#ifdef DO_DBG
#define dbg(...) cerr << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef vector<ll> vi;
typedef vector<bool> vb;
typedef set<ll> si;
typedef pair<ll, ll> pi;
typedef vector<pair<ll, ll>> vpi;
#define F first
#define S second
#define PB push_back
#define MP make_pair
const int MAX_N = 1e5 + 5;
const ll MOD = 1e9 + 7;
const ll INF = 1e9;
const ld EPS = 1e-9;
#define loop(n) for (ll i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()

vb ready;
vi value;

si coins{1, 2, 3, 4, 5, 6};

int solve(int x) {
  if (x == 0)
    return 1;
  if (ready[x])
    return value[x];
  int ways = 0;
  for (auto c : coins) {
    if (x - c < 0) {
      continue;
    }
    ways += solve(x - c);
  }
  value[x] = ways;
  ready[x] = true;
  dbg(x, ways);
  return ways;
}

int main() {
  preamble;
  ll n;
  cin >> n;
  dbg(n);
  ready.resize(n + 1);
  value.resize(n + 1);
  cout << solve(n) << "\n";
}

/*
n=1
1

n=2
1+1
2


n=2
1+1
2

n=3
1+1+1
2+1
1+2
3








n=3
1+1+1
1+2
2+1
3

n=4
1+1+1+1
1+2+1
2+1+1
3+1

2+2
4

n=5
1+1+1+1+1
1+2+1+1
2+1+1+1
3+1+1
4+1
2+2+1
5
2+3

n=6
1+1+1+1+1+1
1+2+1+1+1
2+1+1+1+1
3+1+1+1
4+1+1
2+2+1+1
5+1
2+3+1
6
2+2+2
3+3

n=7
1+1+1+1+1+1+1
1+2+1+1+1+1
2+1+1+1+1+1
3+1+1+1+1
4+1+1+1
2+2+1+1+1
5+1+1
2+3+1+1
6
2+2+2
3+3

*/

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: WRONG ANSWER

Test 12

Verdict: WRONG ANSWER

Test 13

Verdict: WRONG ANSWER

Test 14

Verdict: WRONG ANSWER

Test 15

Verdict: WRONG ANSWER

Test 16

Verdict: WRONG ANSWER

Test 17

Verdict: WRONG ANSWER

Test 18

Verdict: WRONG ANSWER

Test 19

Verdict: WRONG ANSWER

Test 20

Verdict: WRONG ANSWER