feat(cf/895): nonlazy prop soln

codeforces/1013/f.cc

@@ -0,0 +1,181 @@
+#include <bits/stdc++.h>  // {{{
+
+// https://codeforces.com/blog/entry/96344
+
+#pragma GCC optimize("O2,unroll-loops")
+#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
+
+using namespace std;
+
+template <typename T>
+[[nodiscard]] static T MIN() {
+  return std::numeric_limits<T>::min();
+}
+
+template <typename T>
+[[nodiscard]] static T MAX() {
+  return std::numeric_limits<T>::max();
+}
+
+template <typename T>
+[[nodiscard]] static T sc(auto&& x) {
+  return static_cast<T>(x);
+}
+
+template <typename T>
+[[nodiscard]] static T sz(auto&& x) {
+  return static_cast<T>(x.size());
+}
+
+#define prln(...) std::println(__VA_ARGS__)
+#define pr(...) std::print(__VA_ARGS__)
+
+#ifdef LOCAL
+#define dbgln(...) std::println(__VA_ARGS__)
+#define dbg(...) std::print(__VA_ARGS__)
+#endif
+
+inline static void NO() {
+  prln("NO");
+}
+
+inline static void YES() {
+  prln("YES");
+}
+
+using ll = long long;
+using ld = long double;
+template <typename T>
+using ve = std::vector<T>;
+template <typename T, size_t N>
+using ar = std::array<T, N>;
+template <typename T1, typename T2>
+using pa = std::pair<T1, T2>;
+template <typename... Ts>
+using tu = std::tuple<Ts...>;
+template <typename... Ts>
+using dq = std::deque<Ts...>;
+template <typename... Ts>
+using qu = std::queue<Ts...>;
+template <typename... Ts>
+using pq = std::priority_queue<Ts...>;
+template <typename... Ts>
+using st = std::stack<Ts...>;
+auto lb = [](auto... args) {
+  return std::lower_bound(args...);
+};
+auto ub = [](auto... args) {
+  return std::upper_bound(args...);
+};
+
+#define ff first
+#define ss second
+#define eb emplace_back
+#define pb push_back
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+//  }}}
+
+constexpr static ll MOD = 998244353;
+
+void solve() {
+  int n, m;
+  ld d;
+  cin >> n >> m >> d;
+  ll d_squared = ll(d * d + 0.5);  // Round to nearest integer
+
+  auto dist = [](pair<ll, ll> p1, pair<ll, ll> p2) {
+    return (p1.first - p2.first) * (p1.first - p2.first) +
+           (p1.second - p2.second) * (p1.second - p2.second);
+  };
+
+  vector<string> grid(n);
+  for (int i = 0; i < n; ++i) {
+    cin >> grid[i];
+  }
+
+  reverse(grid.begin(), grid.end());
+
+  vector<vector<pair<ll, ll>>> holds(n);
+  for (int i = 0; i < n; ++i) {
+    for (int j = 0; j < m; ++j) {
+      if (grid[i][j] == 'X') {
+        holds[i].emplace_back(j, i);
+      }
+    }
+  }
+
+  // Check if starting level has holds
+  if (holds[0].empty()) {
+    cout << "0\n";
+    return;
+  }
+
+  vector<ll> prev(holds[0].size(), 1);
+  for (int level = 1; level < n; ++level) {
+    if (holds[level].empty()) {
+      cout << "0\n";
+      return;
+    }
+    vector<ll> dp1(holds[level].size(), 0);
+    vector<ll> dp2(holds[level].size(), 0);
+    // First pass: transition from previous level
+    int l = 0, r = 0;
+    ll total = 0;
+    for (int i = 0; i < holds[level].size(); ++i) {
+      auto& h = holds[level][i];
+      // Expand r to include holds with dist <= d_squared
+      while (r < prev.size() && dist(holds[level - 1][r], h) <= d_squared) {
+        total = (total + prev[r]) % MOD;
+        r++;
+      }
+      // Shrink l to exclude holds with dist > d_squared
+      while (l < r && dist(holds[level - 1][l], h) > d_squared) {
+        total = (total - prev[l] + MOD) % MOD;
+        l++;
+      }
+      dp1[i] = total;
+    }
+    // Second pass: same-level transitions (pairs)
+    l = 0, r = 0;
+    total = 0;
+    for (int i = 0; i < holds[level].size(); ++i) {
+      auto& h = holds[level][i];
+      // Expand r to include holds with dist <= d_squared
+      while (r < holds[level].size() && dist(holds[level][r], h) <= d_squared) {
+        total = (total + dp1[r]) % MOD;
+        r++;
+      }
+      // Shrink l to exclude holds with dist > d_squared
+      while (l < r && dist(holds[level][l], h) > d_squared) {
+        total = (total - dp1[l] + MOD) % MOD;
+        l++;
+      }
+      // Subtract dp1[i] to avoid self-pairing
+      dp2[i] = (total - dp1[i] + MOD) % MOD;
+    }
+    // Combine dp1 and dp2
+    for (int i = 0; i < holds[level].size(); ++i) {
+      dp1[i] = (dp1[i] + dp2[i]) % MOD;
+    }
+    prev = dp1;
+  }
+
+  ll ans = accumulate(prev.begin(), prev.end(), 0LL) % MOD;
+  cout << ans << "\n";
+}
+
+int main() {  // {{{
+  cin.tie(nullptr)->sync_with_stdio(false);
+  cin.exceptions(cin.failbit);
+
+  int t = 1;
+  cin >> t;
+
+  while (t--) {
+    solve();
+  }
+
+  return 0;
+}
+// }}}