cp/cses/introductory-problems/chessboard-and-queens.cc
2025-02-26 12:02:28 -05:00

98 lines
1.9 KiB
C++

#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;
}
// }}}