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XII Maratona Mineira de Programação/F. Fome de Queijo.cpp

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+/* Problem URL: https://codeforces.com/group/YgJmumGtHD/contest/105936/problem/F */
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define V vector
+
+#define rmin(a, b) a = min(a, b)
+#define rmax(a, b) a = max(a, b)
+
+#define rep(i, lim) for (int i = 0; i < (lim); i++)
+#define nrep(i, s, lim) for (int i = s; i < (lim); i++)
+
+#define repv(i, v) for (auto &i : (v))
+#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
+#define sortv(v) sort(v.begin(), v.end())
+#define all(v) (v).begin(), (v).end()
+
+using vi = vector<int>;
+using vvi = vector<vi>;
+using vvvi = vector<vvi>;
+using vvvvi = vector<vvvi>;
+
+using ll = long long;
+
+using vl = vector<ll>;
+using vvl = vector<vl>;
+using vvvl = vector<vvl>;
+using vvvvl = vector<vvvl>;
+
+template<class v>
+auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
+    os << vec[0];
+    for (size_t i = 1; i < vec.size(); i++) {
+        os << ' ' << vec[i];
+    }
+    os << '\n';
+    return os;
+}
+
+template<class v>
+auto operator>>(istream &is, vector<v> &vec)->istream& {
+    for (auto &i : vec) {
+        is >> i;
+    }
+    return is;
+}
+
+template<class v>
+auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
+    for (auto &i : vec) {
+        os << i[0];
+        for (size_t j = 1; j < i.size(); j++) {
+            os << ' ' << i[j];
+        }
+        os << '\n';
+    }
+    return os;
+}
+
+template<class v>
+auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
+    for (auto &i : vec) {
+        for (auto &j : i) {
+            is >> j;
+        }
+    }
+    return is;
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n, m, k;
+    cin >> n >> m >> k;
+
+    V<string> fds(n);
+    cin >> fds;
+
+    ll valids = 0;
+
+    int ri = -1;
+    int rj = -1;
+
+    rep(i, n) {
+        rep(j, m) {
+            if (fds[i][j] == 'R') {
+                ri = i;
+                rj = j;
+                continue;
+            }
+
+            if (fds[i][j] == '.') {
+                valids++;
+            }
+        }
+    }
+
+    ll inf = INT64_MAX >> 1;
+    vl discount(n * m + 1, 0);
+
+    ll minimal_cheese = inf;
+    ll maximal = 0;
+
+    auto bfs = [&](int i, int j) {
+        vvl dis(n, vl(m, inf));
+        dis[i][j] = 0;
+        queue<pair<int, int>> q;
+        q.emplace(i, j);
+
+        while (!q.empty()) {
+            auto [i, j] = q.front();
+            q.pop();
+
+            rmax(maximal, dis[i][j]);
+
+            if (fds[i][j] == 'Q') {
+                rmin(minimal_cheese, dis[i][j]);
+            } else {
+                discount[dis[i][j]]++;
+            }
+
+            int add[][2] = {{0, -1}, {0, 1}, {-1, 0}, {1, 0}};
+
+            repv(k, add) {
+                int id = i + k[0];
+                int jd = j + k[1];
+                
+                if (id >= 0 && id < n && jd >= 0 && jd < m && fds[id][jd] != '#' && dis[id][jd] > dis[i][j] + 1) {
+                    dis[id][jd] = dis[i][j] + 1;
+                    q.emplace(id, jd);
+                }
+            }
+        }
+    };
+
+    bfs(ri, rj);
+
+    vl suf(n * m + 1);
+    for (int i = n * m - 1; i >= 0; i--) {
+        suf[i] = suf[i + 1] + discount[i];
+    }
+
+    const ll mod = 998244353;
+
+    ll divs = valids;
+    nrep(i, 1, k) {
+        divs *= (valids - i);
+        divs %= mod;
+    }
+
+    vl fact(n * m + 1);
+    fact[0] = 1;
+
+    nrep(i, 1, n * m + 1) {
+        fact[i] = fact[i - 1] * i;
+        fact[i] %= mod;
+    }
+
+    auto fastpow = [&](ll a, ll b) {
+        ll ans = 1;
+        ll fds = a;
+
+        rep(i, 31) {
+            if ((b >> i) & 1) { ans *= fds;
+                ans %= mod;
+            }
+
+            fds *= fds;
+            fds %= mod;
+        }
+
+        return ans;
+    };
+
+    auto comb = [&](ll a, ll k) {
+        return (fact[a] * fastpow((fact[k] * fact[a - k]) % mod, mod - 2)) % mod;
+    };
+
+    auto perm = [&](ll a, ll k) {
+        return (fact[a] * fastpow(fact[a - k], mod - 2)) % mod;
+    };
+
+    ll ans = 0;
+
+    for (ll i = 1; i <= maximal && i < minimal_cheese; i++) {
+        if (suf[i] < k) {
+            break;
+        }
+
+        if (suf[i + 1] < k) {
+            ans += perm(suf[i], k) * i;
+            ans %= mod;
+            break;
+        }
+
+        // ans += ((comb(suf[i], k) - comb(suf[i + 1], k)) % mod + mod) % mod * i;
+        ans += ((perm(suf[i], k) - perm(suf[i + 1], k)) % mod + mod) % mod * i;
+        ans %= mod;
+    }
+
+    if (minimal_cheese != inf && suf[minimal_cheese] >= k) {
+        ans += perm(suf[minimal_cheese], k) * minimal_cheese;
+        ans %= mod;
+    }
+    
+    cerr << ans << '\n';
+
+    cout << (ans * fastpow(divs, mod - 2)) % mod << '\n';
+}