N-Queens Solver (upto 25k in 1000ms)

#include <bits/stdc++.h>
// tiom4eg's precompiler options
// POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS
// IO settings
#define fastIO ios_base::sync_with_stdio(false); cin.tie(0)
// Quick types
#define ll long long
#define pii pair <int, int>
#define pll pair <ll, ll>
#define vi vector <int>
#define mi vector <vector <int> >
// Quick functions
#define endl "\n"
#define F first
#define S second
#define all(a) a.begin(), a.end()
#define sz(a) a.size()
#define pb push_back
#define mp make_pair
// Quick fors
#define FOR(i, a, b) for (int i = a; i < b; ++i)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)
// Pragmas
#pragma GCC optimize("O3,unroll-loops") // let the chaos begin!
//#pragma GCC target("avx,avx2,bmi,bmi2,popcnt,lzcnt,tune=native")
#pragma GCC comment(linker, "/stack:200000000")
// PBDS
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ordered_set tree <int, null_type, less <int>, rb_tree_tag, tree_order_statistics_node_update>
#define ook order_of_key
#define fbo find_by_order
// POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS
using namespace std;
using namespace __gnu_pbds;
mt19937 rng(std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now().time_since_epoch()).count());

int randint(int n) { // [0; n)
    return rng() % n;
}

/*
 ██▓     ███▄ ▄███▓ ▄▄▄       ▒█████
▓██▒    ▓██▒▀█▀ ██▒▒████▄    ▒██▒  ██▒
▒██░    ▓██    ▓██░▒██  ▀█▄  ▒██░  ██▒
▒██░    ▒██    ▒██ ░██▄▄▄▄██ ▒██   ██░
░██████▒▒██▒   ░██▒ ▓█   ▓██▒░ ████▓▒░
░ ▒░▓  ░░ ▒░   ░  ░ ▒▒   ▓▒█░░ ▒░▒░▒░
░ ░ ▒  ░░  ░      ░  ▒   ▒▒ ░  ░ ▒ ▒░
  ░ ░   ░      ░     ░   ▒   ░ ░ ░ ▒
    ░  ░       ░         ░  ░    ░ ░
*/
const int ITER = 50000;
vi cnt, rcnt, a;
int n, cur = 0;
void gen() {
    vi p(n); FOR(i, 0, n) p[i] = i;
    FOR(i, 0, n) {
        int k = randint(n - i);
        a[i] = p[k];
        p.erase(p.begin() + k);
    }
}
// all in O(1)
int f(int p) { return cnt[p + a[p]] + rcnt[2 * (n - 1) - a[p] - (n - p - 1)] - 2; }
void add(int p) { cnt[p + a[p]]++, rcnt[2 * (n - 1) - a[p] - (n - p - 1)]++; }
void del(int p) { cnt[p + a[p]]--, rcnt[2 * (n - 1) - a[p] - (n - p - 1)]--; }
void change(int p1, int p2) {
    cur -= 2 * (f(p1) + f(p2));
    del(p1);
    del(p2);
    swap(a[p1], a[p2]);
    add(p1);
    add(p2);
    cur += 2 * (f(p1) + f(p2));
}

int main() {
    cin >> n;
    FOR(att, 0, 100) {
        cur = 0;
        cnt.assign(2 * n, 0);
        rcnt.assign(2 * n, 0);
        a.resize(n);
        gen();
        FOR(i, 0, n) add(i);
        FOR(i, 0, n) cur += f(i);
        FOR(i, 0, ITER) {
            if (!cur) break;
            int now = cur;
            int p1 = randint(n), p2 = randint(n);
            while (p2 == p1) p2 = randint(n);
            change(p1, p2);
            if (cur > now) change(p1, p2);
        }
        if (!cur) {
            for (auto& x : a) cout << x + 1 << ' ';
            return 0;
        }
    }
}