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cses/introductory-problems/chessboard-and-queens.cc

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+#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>
+constexpr T MIN = std::numeric_limits<T>::min();
+
+template <typename T>
+constexpr T MAX = 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());
+}
+
+using ll = long long;
+using ld = long double;
+template <typename T>
+using vec = std::vector<T>;
+template <typename T, size_t N>
+using arr = std::array<T, N>;
+
+#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 int N = 8;
+
+vec<string> board(N);
+
+// SC: O(n) for recursive space + queens
+// TC: O(n*n*n) - every row every col check all queens
+
+// NOTE: pruning
+ll backtrack(vec<int> &queens) {
+  if (queens.size() == N) {
+    return 1;
+  }
+
+  ll r = queens.size();
+  ll ans = 0;
+  for (int C = 0; C < N; ++C) {
+    if (board[r][C] == '*')
+      continue;
+    bool bad = false;
+    for (int qr = 0; qr < sz<int>(queens); ++qr) {
+      int qc = queens[qr];
+      // Q: does it fall on the DIAGONAL?
+      // for each line, is there an integer sol'n?
+      // y - qr = x - qc -> x - qc + qr <- n queens
+      // or y - qr = -x + qc -> y = -x + qc + qr
+      if (qc == C || abs(r - qr) == abs(C - qc)) {
+        bad = true;
+        break;
+      }
+    }
+    if (bad)
+      continue;
+    queens.eb(C);
+    ans += backtrack(queens);
+    queens.pop_back();
+  }
+  return ans;
+}
+
+void solve() {
+  for (int i = 0; i < N; ++i) {
+    cin >> board[i];
+  }
+
+  vec<int> queens;
+  ll ans = backtrack(queens);
+
+  cout << ans << endl;
+}
+
+int main() {  // {{{
+  cin.tie(nullptr)->sync_with_stdio(false);
+
+  solve();
+
+  return 0;
+}
+// }}}