Submission #683418

#	Time	Username	Problem	Language	Result	Execution time	Memory
683418		nifeshe	Energetic turtle (IZhO11_turtle)	C++17	40 / 100	2087 ms	24172 KiB

turtle

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

//#pragma GCC target ("avx2")
//#pragma GCC optimize ("O3")
//#pragma GCC optimize ("unroll-loops")
//#pragma comment (linker, "/STACK: 16777216")

#define f first
#define s second
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define mp make_pair
#define int long long

using namespace std;
using namespace __gnu_pbds;

template <typename T> inline bool umax(T &a, const T &b) { if(a < b) { a = b; return 1; } return 0; }
template <typename T> inline bool umin(T &a, const T &b) { if(a > b) { a = b; return 1; } return 0; }
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
template <typename T> using oset = tree<T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;

ll mod = 998244353;
const ll base = 1e6 + 5;
const ll inf = 1e18;
const int MAX = 1e6;
const int lg = 20;

random_device rd;
mt19937 gen(rd());
uniform_int_distribution<ll> dis(1, inf);

int binpow(int x, int n) {
    int ans = 1;
    while(n) {
        if(n & 1) ans = (ans * x) % mod;
        n /= 2;
        x = (x * x) % mod;
    }
    return ans;
}

void add(int &a, int b) {
    a += b;
    if(a >= mod) a -= mod;
    if(a < 0) a += mod;
}

vector<int> primes;
int phi = 1;
int fact[MAX], inv[MAX];

void precalc() {
    map<int, int> r;
    int x = mod;
    for(int i = 2; i * i <= x; i++) {
        while(x % i == 0) {
            r[i]++;
            x /= i;
        }
    }
    if(x > 1) r[x]++;
    for(auto [p, cnt] : r) {
        phi *= binpow(p, cnt) - binpow(p, cnt - 1);
        primes.pb(p);
    }
    fact[0] = inv[0] = fact[1] = inv[1] = 1;
    for(int i = 2; i < MAX; i++) {
        int x = i;
        for(auto p : primes) {
            while(x % p == 0) x /= p;
        }
        fact[i] = (fact[i - 1] * x) % mod;
        inv[i] = binpow(fact[i], phi - 1);
    }
}

int C(int n, int k) {
    auto get = [&](int x, int p) {
        int ans = 0;
        int pw = p;
        while(pw <= x) {
            ans += x / pw;
            pw *= p;
        }
        return ans;
    };
    int ans = fact[n] * inv[k] % mod * inv[n - k] % mod;
    for(auto p : primes) {
        int cnt = get(n, p) - get(k, p) - get(n - k, p);
        ans = (ans * binpow(p, cnt)) % mod;
    }
//    cout << n << " choose " << k << " = " << ans << endl;
    return ans;
}

void solve() {
    int n, m, k, t;
    cin >> n >> m >> k >> t >> mod; precalc();
    vector<pair<int, int>> a(k);
    for(auto &[x, y] : a) {
        cin >> x >> y;
    }
    sort(all(a));
    int ans = 0;
    vector<int> ways((1 << k));
    for(int mask = 0; mask < (1 << k); mask++) {
        vector<pair<int, int>> need = {{0, 0}};
        for(int i = 0; i < k; i++) {
            if(mask >> i & 1) {
                need.pb(a[i]);
            }
        }
        need.pb({n, m});
        int sz = sz(need);
        int add = 1;
        for(int i = 1; i < sz; i++) {
            if(need[i - 1].s > need[i].s) {
                add = 0;
                break;
            }
            int x = need[i].f - need[i - 1].f, y = need[i].s - need[i - 1].s;
            add = (add * C(x + y, y)) % mod;
        }
        int sign = (__builtin_popcount(mask) & 1? -1 : 1);
        ways[mask] = sign * add;
    }
    for(int i = 0; i < k; i++) {
        for(int mask = 0; mask < (1 << k); mask++) {
            if(mask >> i & 1) continue;
            add(ways[mask], ways[mask | (1 << i)]);
        }
    }
    for(int mask = 0; mask < (1 << k); mask++) {
        if(__builtin_popcount(mask) > t) continue;
        int sign = (__builtin_popcount(mask) & 1? -1 : 1);
        add(ans, sign * ways[mask]);
    }
    cout << ans << '\n';
}

signed main() {
//    freopen("turtle.in", "r", stdin); freopen("turtle.out", "w", stdout);
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int ttt = 1;
//    cin >> ttt;
    while(ttt--) {
        solve();
    }
    return 0;
}

• Subtask 1: 40 / 100