結果

問題 No.420 mod2漸化式
ユーザー h-izu
提出日時 2022-06-19 20:02:28
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 1,000 ms
コード長 6,541 bytes
コンパイル時間 4,788 ms
コンパイル使用メモリ 267,624 KB
最終ジャッジ日時 2025-01-29 23:25:28
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
sample AC * 1
other AC * 35
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ソースコード

diff # 

#ifdef __LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>

#include <atcoder/all>
using namespace std;
using namespace atcoder;

typedef unsigned long long ull;
typedef long long ll;

const double PI = 3.14159265358979323846;

#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)

// a^p
// 2^3 = 2 * 2^2
// 2^2 = 2 * (2^1)
// 2^1 = 2
ll modpow(ll a, ll p, ll mod) {
  if (p == 0) return 1;

  if (p % 2 == 0) {
    ll half = modpow(a, p / 2, mod) % mod;
    return half * half % mod;
  } else {
    return a * modpow(a, p - 1, mod) % mod;
  }
}

// a^p
ll powpow(ll a, ll p) {
  if (p == 0) return 1;

  if (p % 2 == 0) {
    ll half = pow(a, p / 2);
    return half * half;
  } else {
    return a * pow(a, p - 1);
  }
}

// a/b
// https://qiita.com/drken/items/3b4fdf0a78e7a138cd9a
ll moddiv(ll a, ll b, ll mod) { return a * modpow(b, mod - 2, mod); }

// nCa を求める
ll modCombination(ll n, ll a, ll mod) {
  if (n < 0 || a < 0 || n < a) return 0;
  if (n - a < a) {
    return modCombination(n, n - a, mod);
  }

  ll denominator = 1;  // 分母
  ll numerator = 1;    // 分子

  for (ll i = 0; i < a; i++) {
    denominator *= a - i;
    numerator *= n - i;
    denominator %= mod;
    numerator %= mod;
  }

  return numerator * modpow(denominator, mod - 2, mod) % mod;
}

vector<vector<ll>> combination(ll n) {
  vector<vector<ll>> C(n + 1, vector<ll>(n + 1));
  C[0][0] = 1;
  rep(i, n) rep(j, i + 1) {
    C[i + 1][j + 1] += C[i][j];
    C[i + 1][j] += C[i][j];
  }

  return C;
}

// ref. https://drken1215.hatenablog.com/entry/2018/06/08/210000
class ModCombinationTale {
 private:
  ll n;
  ll mod;
  vector<ll> fac, finv, inv;

 public:
  ModCombinationTale(ll n, ll mod) : n(n), mod(mod) {
    fac.resize(n + 1);
    finv.resize(n + 1);
    inv.resize(n + 1);

    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;

    for (ll i = 2; i <= n; i++) {
      fac[i] = fac[i - 1] * i % mod;
      inv[i] = mod - inv[mod % i] * (mod / i) % mod;
      finv[i] = finv[i - 1] * inv[i] % mod;
    }
  }

  ll operator()(ll n, ll k) {
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
  }
};

class UnionFind {
 private:
  vector<ll> parents;

 public:
  UnionFind(ll n) : parents(n, -1) {}

  bool issame(ll x, ll y) { return root(x) == root(y); }

  bool merge(ll x, ll y) {
    if (issame(x, y)) return false;

    ll rx = root(x);
    ll ry = root(y);
    if (parents[rx] > parents[ry]) swap(rx, ry);
    // サイズ情報を更新
    parents[rx] += parents[ry];
    // yの親を更新
    parents[ry] = rx;

    return true;
  }

  ll size(ll x) { return -parents[root(x)]; }

  ll root(ll x) {
    if (parents[x] < 0) return x;
    // 根の親の値に木の(-)サイズの情報を入れる
    return parents[x] = root(parents[x]);
  }
};

// cf. https://qiita.com/drken/items/a14e9af0ca2d857dad23
vector<ll> enum_divisors(ll n) {
  vector<ll> res;
  // sqrt(n)まで試し割り
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      // 重複しないならばiの相方であるn/iも約数
      // e.g. n=25のときのi=5は重複
      if (n / i != i) res.push_back(n / i);
    }
  }

  sort(res.begin(), res.end());
  return res;
}

// cf. https://qiita.com/drken/items/a14e9af0ca2d857dad23
map<ll, ll> prime_factors(ll n) {
  map<ll, ll> res;
  // sqrt(n)まで試し割り
  for (ll a = 2; a * a <= n; a++) {
    if (n % a != 0) continue;

    // nで割れる限り割る
    while (n % a == 0) {
      res[a]++;
      n /= a;
    }
  }
  if (n != 1) res[n]++;

  return res;
}

ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}

ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; }

// cf. https://qiita.com/drken/items/56a6b68edef8fc605821
class AccumSum2D {
 private:
  vector<vector<ll>> sum;
  ll H;
  ll W;

 public:
  AccumSum2D(vector<vector<ll>> &A) {
    H = (ll)A.size();
    W = (ll)A[0].size();
    sum.resize(H + 1, vector<ll>(W + 1));

    for (ll i = 0; i < H; i++) {
      for (ll j = 0; j < W; j++) {
        sum[i + 1][j + 1] = sum[i][j + 1] + sum[i + 1][j] - sum[i][j] + A[i][j];
      }
    }
  }

  // クエリ [x1, x2) × [y1, y2) の長方形区域の和
  ll Sum(ll x1, ll x2, ll y1, ll y2) {
    return sum[x2][y2] - sum[x1][y2] - sum[x2][y1] + sum[x1][y1];
  }
};

// p/q
struct fraction {
  ll p, q;
  fraction(ll _p = 0, ll _q = 1) : p(_p), q(_q) {
    if (q == 0) {
      p = 1;
      return;
    }
    if (q < 0) {
      p = -p;
      q = -q;
    }

    ll g = gcd(p, q);
    p /= g;
    q /= g;
  }

  bool operator<(const fraction &other) const {
    return p * other.q < q * other.p;
  }

  bool operator<=(const fraction &other) const {
    return p * other.q <= q * other.p;
  }

  bool operator==(const fraction &other) const {
    return p == other.p && q == other.q;
  }
};

// res[i][c] := i 文字目以降で最初に文字 c が登場する index (存在しないときは n)
vector<vector<ll>> calcNext(const string &S) {
  ll n = (ll)S.size();
  vector<vector<ll>> res(n + 1, vector<ll>(26, n));
  for (ll i = n - 1; i >= 0; --i) {
    for (ll j = 0; j < 26; ++j) res[i][j] = res[i + 1][j];
    res[i][S[i] - 'a'] = i;
  }
  return res;
}

// ref. https://algo-logic.info/bridge-lowlink/
struct LowLink {
  vector<vector<ll>> G;
  vector<ll> ord, low;
  vector<bool> visited;
  vector<pair<ll, ll>> bridges;

  LowLink(const vector<vector<ll>> &G) : G(G) {
    visited.resize(G.size(), false);
    ord.resize(G.size(), 0);
    low.resize(G.size(), 0);
    ll k = 0;
    rep(i, (ll)G.size()) {
      if (visited[i]) continue;
      k = dfs(i, k);
    }
  }

  ll dfs(ll node, ll k, ll parent = -1) {
    visited[node] = true;
    ord[node] = k;
    low[node] = k;
    k++;
    for (auto g : G[node]) {
      if (!visited[g]) {
        k = dfs(g, k, node);
        low[node] = min(low[node], low[g]);
        if (ord[node] < low[g]) {
          bridges.emplace_back(node, g);
        }
      } else if (g != parent) {
        low[node] = min(low[node], ord[g]);
      }
    }

    return k;
  }
};

int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);

  ll x;
  cin >> x;

  if (x >= 32) {
    cout << 0 << " " << 0 << endl;
    return 0;
  }
  if (x == 0) {
    cout << 1 << " " << 0 << endl;
    return 0;
  }

  auto C = combination(31);
  cout << C[31][x] << " ";
  ll ans = (powpow(2, 31) - 1) * C[30][x - 1];
  cout << ans << endl;

  return 0;
}
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