Problem p02685 (C++) — buggy submission, verdict: Time Limit Exceeded


#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
using ll = long long;
const long long INF = 1LL << 60;

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 998244353;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
} comb(200001);

int main() {

  int N, M, K;
  cin >> N >> M >> K;

  mint n, m, k;
  n = N;
  m = M;
  k = K;

  mint summation = 0;
  mint ans = 0;

  rep(i, K + 1) { ans += m * (m - 1).pow(N - i - 1) * comb(N - 1, i); }

  cout << ans << endl;

  return 0;
}


Error: TLE

Fixed submission:


#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
using ll = long long;
const long long INF = 1LL << 60;

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

ll modpow(ll a, ll n, ll mod) {
  ll rtn = 1;
  while (n > 0) {
    if (n & 1)
      rtn = rtn * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return rtn;
}

ll cmb_mod(ll n, ll r, ll mod) {
  ll x = 1;
  ll y = 1;
  if (n / 2 < r) {
    r = n - r;
  }

  rep(i, r) {
    x *= (n - i);
    if (x > mod) {
      x %= mod;
    }
    y *= (r - i);
    if (y > mod) {
      y %= mod;
    }
  }
  ll val = x * modpow(y, mod - 2, mod) % mod;
  return val;
}

int main() {

  ll N, M, K;
  cin >> N >> M >> K;

  ll ans = M;
  ll summation = 0;

  ll MOD = 998244353;

  rep(i, K + 1) {
    summation += modpow(M - 1, N - i - 1, MOD) * cmb_mod(N - 1, i, MOD);
    summation %= MOD;
  }

  cout << (ans * summation % MOD) << endl;

  return 0;
}