Problem p02549 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define sz(x) int(x.size())
#define show(x)                                                                \\
  {                                                                            \\
    for (auto i : x) {                                                         \\
      cout << i << " ";                                                        \\
    }                                                                          \\
    cout << endl;                                                              \\
  }
using namespace std;
using ll = long long;
using P = pair<int, int>;

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, mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination MOD prime
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];
  }
  mint p(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[n - k];
  }
}; // comb(10000007);
// comb(5, 2) → 10, comb.p(5, 2) → 20
// comb.fact[4] → 24, 2のN乗 → mint(2).pow(N)

template <typename T> struct BIT {
  int n;
  vector<T> d;
  BIT(int n = 0) : n(n), d(n + 1) {}
  void add(int i, T x = 1) {
    for (i++; i <= n; i += i & -i) {
      // i&-iで最下位bitを足している
      d[i] += x;
    }
  }
  T sum(int i) {
    T x = 0;
    for (i++; i; i -= i & -i) {
      x += d[i];
    }
    return x;
  }
  T semiopenSum(int l, int r) {
    // [l,r)の半開区間
    return sum(r - 1) - sum(l - 1);
  }
}; // BIT<int> bit(N);

mint dp[200005];

int main() {
  // dp、Kが小さい、BIT
  // L と　Rに注目
  int N, K;
  cin >> N >> K;
  vector<P> LR(K);
  rep(i, K) cin >> LR[i].first >> LR[i].second;
  BIT<mint> bit(N);
  bit.add(0);
  dp[0] = 1;
  for (int i = 1; i <= N; i++) {
    for (auto p : LR) {
      if (i - p.first < 0)
        continue;
      int left = i - p.second, right = i - p.first;
      if (left < 0)
        left = 0;
      dp[i] += bit.semiopenSum(left, right + 1);
    }
    bit.add(i, dp[i]);
  }
  cout << dp[N - 1] << '\\n';
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define sz(x) int(x.size())
#define show(x)                                                                \\
  {                                                                            \\
    for (auto i : x) {                                                         \\
      cout << i << " ";                                                        \\
    }                                                                          \\
    cout << endl;                                                              \\
  }
using namespace std;
using ll = long long;
using P = pair<int, int>;

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, mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination MOD prime
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];
  }
  mint p(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[n - k];
  }
}; // comb(10000007);
// comb(5, 2) → 10, comb.p(5, 2) → 20
// comb.fact[4] → 24, 2のN乗 → mint(2).pow(N)

mint dp[200005];
mint imos[200005];

int main() {
  int N, K;
  cin >> N >> K;
  vector<P> LR(N);
  rep(i, K) cin >> LR[i].first >> LR[i].second;
  dp[0] = 1;
  for (int i = 0; i < N; i++) {
    if (i > 0) {
      imos[i] += imos[i - 1];
      dp[i] += imos[i];
    }
    for (auto p : LR) {
      int left = i + p.first;
      if (left >= N)
        continue;
      int right = min(N - 1, i + p.second);
      imos[left] += dp[i];
      imos[right + 1] -= dp[i];
    }
  }
  cout << dp[N - 1] << '\\n';
  return 0;
}