1463A - Dungeon

Note that the total health of enemies has to be a multiple of 9 (6 + 3), if you want to pass the dungeon beautifully.

In such case, the total amount of enhance shots done will be $x = \frac{s}{9}$, where $s$ denotes the total health of enemies.

Note that the actual amount of enhanced shots possible is bounded by the minimum health of all monsters (every enhanced shot forces us to reduce all monster’s health by 1). So, if $x \leq \min(a, b, c)$, there’s always a way to reduce the excess health with normal shots (given our previous assumption that $s$ is a multiple of $9$).

Time complexity: $O(1)$

Memory complexity: $O(1)$

using namespace std;
using ll = long long;
using ii = pair<int, int>;
using vi = vector<int>;
bool solve(int a, int b, int c)
{
    int total = a + b + c;
    if (total % 9)
        return false;
    int shots = total / 9;
    return min({a, b, c}) >= shots;
}
int main(void)
{
    ios::sync_with_stdio(false), cin.tie(NULL);
    int t;
    cin >> t;
    while (t--)
    {
        int a, b, c;
        cin >> a >> b >> c;
        cout << (solve(a, b, c) ? "YES" : "NO") << endl;
    }
    return 0;
}