Problem p01979 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define stoi stoll
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
#define ALL(c) begin(c), end(c)
#define RALL(c) rbegin(c), rend(c)
#define ITR(i, b, e) for (auto i = (b); i != (e); ++i)
#define FORE(x, c) for (auto &x : c)
#define REPF(i, a, n) for (int i = a, i##len = (int)(n); i < i##len; ++i)
#define REP(i, n) REPF(i, 0, n)
#define REPR(i, n) for (int i = (int)(n); i >= 0; --i)
#define SZ(c) ((int)c.size())
#define CONTAIN(c, x) (c.find(x) != end(c))
#define OUTOFRANGE(y, x, h, w) ((y) < 0 || (x) < 0 || (y) >= (h) || (x) >= (w))
#define dump(...)
const signed INF_ = 1001001001;
const long long INF = 1001001001001001001LL;
const int DX[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0},
          DY[9] = {-1, 0, 1, 0, -1, 1, 1, -1, 0};
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  ITR(i, begin(v), end(v)) os << *i << (i == end(v) - 1 ? "" : " ");
  return os;
}
template <class T> istream &operator>>(istream &is, vector<T> &v) {
  ITR(i, begin(v), end(v)) is >> *i;
  return is;
}
template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> using heap = priority_queue<T, vector<T>, greater<T>>;
struct {
  template <class T> operator T() {
    T x;
    cin >> x;
    return x;
  }
} IN;
struct before_main_function {
  before_main_function() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(15) << fixed;
#define endl "\\n"
  }
} before_main_function;
//------------------8<------------------------------------8<--------------------

string N;
int dp[20][2][10];
int rec(int i, bool less, int state) {
  auto &DP = dp[i][less][state];
  if (DP != INF)
    return DP;

  if (i == SZ(N)) {
    return DP = (state == 4);
  }

  int ret = 0;
  REP(j, less ? 10 : N[i] - '0' + 1) {
    int next_state = state;
    if (state == 0 && j == 5)
      next_state++;
    else if (state == 1 && j == 1)
      next_state++;
    else if (state == 2 && j == 5)
      next_state = 5;
    else if (state == 2 && j != 5)
      next_state = 6;
    else if ((state == 5 || state == 6) && j == 3)
      next_state = 4;
    else if (state == 4)
      ;
    else {
      if (state == 5 && j == 1) {
        next_state = 2;
      } else if (j == 5) {
        next_state = 1;
      } else {
        next_state = 0;
      }
    }
    ret += rec(i + 1, less || j != (N[i] - '0'), next_state);
  }
  return DP = ret;
}
signed main() {
  REP(i, 20) REP(j, 2) REP(k, 10) dp[i][j][k] = INF;
  cin >> N;
  cout << rec(0, 0, 0) << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define stoi stoll
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
#define ALL(c) begin(c), end(c)
#define RALL(c) rbegin(c), rend(c)
#define ITR(i, b, e) for (auto i = (b); i != (e); ++i)
#define FORE(x, c) for (auto &x : c)
#define REPF(i, a, n) for (int i = a, i##len = (int)(n); i < i##len; ++i)
#define REP(i, n) REPF(i, 0, n)
#define REPR(i, n) for (int i = (int)(n); i >= 0; --i)
#define SZ(c) ((int)c.size())
#define CONTAIN(c, x) (c.find(x) != end(c))
#define OUTOFRANGE(y, x, h, w) ((y) < 0 || (x) < 0 || (y) >= (h) || (x) >= (w))
#define dump(...)
const signed INF_ = 1001001001;
const long long INF = 1001001001001001001LL;
const int DX[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0},
          DY[9] = {-1, 0, 1, 0, -1, 1, 1, -1, 0};
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  ITR(i, begin(v), end(v)) os << *i << (i == end(v) - 1 ? "" : " ");
  return os;
}
template <class T> istream &operator>>(istream &is, vector<T> &v) {
  ITR(i, begin(v), end(v)) is >> *i;
  return is;
}
template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> using heap = priority_queue<T, vector<T>, greater<T>>;
struct {
  template <class T> operator T() {
    T x;
    cin >> x;
    return x;
  }
} IN;
struct before_main_function {
  before_main_function() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(15) << fixed;
#define endl "\\n"
  }
} before_main_function;
//------------------8<------------------------------------8<--------------------

string N;
int rec(int i, bool less, int state) {
  if (i == SZ(N)) {
    return (state == 4);
  }

  int ret = 0;
  if (less) {
    REP(j, 10) {
      int next_state = state;
      if (state == 0 && j == 5)
        next_state++;
      else if (state == 1 && j == 1)
        next_state++;
      else if (state == 2 && j == 5)
        next_state = 10;
      else if (state == 2 && j != 5)
        next_state = 11;
      else if ((state == 10 || state == 11) && j == 3)
        next_state = 4;
      else if (state == 4)
        ;
      else {
        if (state == 10 && j == 1) {
          next_state = 2;
        } else if (j == 5) {
          next_state = 1;
        } else {
          next_state = 0;
        }
      }
      ret += rec(i + 1, true, next_state);
    }
  } else {
    REP(j, N[i] - '0' + 1) {
      int next_state = state;
      if (state == 0 && j == 5)
        next_state++;
      else if (state == 1 && j == 1)
        next_state++;
      else if (state == 2 && j == 5)
        next_state = 10;
      else if (state == 2 && j != 5)
        next_state = 11;
      else if ((state == 10 || state == 11) && j == 3)
        next_state = 4;
      else if (state == 4)
        ;
      else {
        if (state == 10 && j == 1) {
          next_state = 2;
        } else if (j == 5) {
          next_state = 1;
        } else {
          next_state = 0;
        }
      }
      ret += rec(i + 1, j != (N[i] - '0'), next_state);
    }
  }
  return ret;
}
signed main() {
  cin >> N;
  cout << rec(0, 0, 0) << endl;
  return 0;
}