Problem p02692 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstdio>
#include <ctime>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

namespace {
using Integer = long long; //__int128;
template <class T, class S> istream &operator>>(istream &is, pair<T, S> &p) {
  return is >> p.first >> p.second;
}
template <class T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &val : vec)
    is >> val;
  return is;
}
template <class T> istream &operator,(istream &is, T &val) { return is >> val; }
template <class T, class S>
ostream &operator<<(ostream &os, const pair<T, S> &p) {
  return os << p.first << " " << p.second;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i == vec.size() - 1 ? "" : " ");
  return os;
}
template <class T> ostream &operator,(ostream &os, const T &val) {
  return os << " " << val;
}

template <class H> void print(const H &head) { cout << head; }
template <class H, class... T> void print(const H &head, const T &...tail) {
  cout << head << " ";
  print(tail...);
}
template <class... T> void println(const T &...values) {
  print(values...);
  cout << endl;
}

template <class H> void eprint(const H &head) { cerr << head; }
template <class H, class... T> void eprint(const H &head, const T &...tail) {
  cerr << head << " ";
  eprint(tail...);
}
template <class... T> void eprintln(const T &...values) {
  eprint(values...);
  cerr << endl;
}

class range {
  Integer start_, end_, step_;

public:
  struct range_iterator {
    Integer val, step_;
    range_iterator(Integer v, Integer step) : val(v), step_(step) {}
    Integer operator*() { return val; }
    void operator++() { val += step_; }
    bool operator!=(range_iterator &x) {
      return step_ > 0 ? val < x.val : val > x.val;
    }
  };
  range(Integer len) : start_(0), end_(len), step_(1) {}
  range(Integer start, Integer end) : start_(start), end_(end), step_(1) {}
  range(Integer start, Integer end, Integer step)
      : start_(start), end_(end), step_(step) {}
  range_iterator begin() { return range_iterator(start_, step_); }
  range_iterator end() { return range_iterator(end_, step_); }
};

inline string operator"" _s(const char *str, size_t size) {
  return move(string(str));
}
constexpr Integer my_pow(Integer x, Integer k, Integer z = 1) {
  return k == 0    ? z
         : k == 1  ? z * x
         : (k & 1) ? my_pow(x * x, k >> 1, z * x)
                   : my_pow(x * x, k >> 1, z);
}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z = 1) {
  return k == 0    ? z % M
         : k == 1  ? z * x % M
         : (k & 1) ? my_pow_mod(x * x % M, k >> 1, M, z * x % M)
                   : my_pow_mod(x * x % M, k >> 1, M, z);
}
constexpr unsigned long long operator"" _ten(unsigned long long value) {
  return my_pow(10, value);
}

inline int k_bit(Integer x, int k) { return (x >> k) & 1; } // 0-indexed

mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(
               chrono::steady_clock::now().time_since_epoch())
               .count());

template <class T> string join(const vector<T> &v, const string &sep) {
  stringstream ss;
  for (size_t i = 0; i < v.size(); i++) {
    if (i > 0)
      ss << sep;
    ss << v[i];
  }
  return ss.str();
}

inline string operator*(string s, int k) {
  string ret;
  while (k) {
    if (k & 1)
      ret += s;
    s += s;
    k >>= 1;
  }
  return ret;
}
} // namespace
constexpr long long mod = 9_ten + 7;

int main() {
  int n;
  cin >> n;
  vector<long long> w(3);
  cin >> w;
  vector<string> s(n);
  cin >> s;

  vector<map<array<int, 3>, int>> dp(n + 1);
  for (int i : range(3))
    w[i] = min(2ll, w[i]);

  map<string, vector<int>> x = {
      {"AB"s, {0, 1}},
      {"AC"s, {0, 2}},
      {"BC"s, {1, 2}},
  };

  dp[0][{w[0], w[1], w[2]}] = 1;
  for (int i = 0; i < n; i++) {
    auto &y = x[s[i]];
    for (auto p : dp[i]) {
      auto v = p.first;
      v[y[0]]++;
      v[y[1]]--;
      if (v[y[1]] >= 0) {
        dp[i + 1][v] = 0;
      }
      v[y[0]] -= 2;
      v[y[1]] += 2;
      if (v[y[0]] >= 0) {
        dp[i + 1][v] = 1;
      }
    }
  }

  if (dp[n].size() == 0) {
    puts("No");
    return 0;
  }
  auto v = dp[n].begin()->first;
  vector<string> ans;
  for (int i = n - 1; i >= 0; i--) {
    int prev = dp[i + 1][v];
    ans.push_back(""s + s[i][prev]);
    auto &y = x[s[i]];
    v[y[prev]]--;
    v[y[prev ^ 1]]++;
  }
  reverse(begin(ans), end(ans));
  puts("Yes");
  println(join(ans, "\\n"));

  return 0;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstdio>
#include <ctime>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

namespace {
using Integer = long long; //__int128;
template <class T, class S> istream &operator>>(istream &is, pair<T, S> &p) {
  return is >> p.first >> p.second;
}
template <class T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &val : vec)
    is >> val;
  return is;
}
template <class T> istream &operator,(istream &is, T &val) { return is >> val; }
template <class T, class S>
ostream &operator<<(ostream &os, const pair<T, S> &p) {
  return os << p.first << " " << p.second;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i == vec.size() - 1 ? "" : " ");
  return os;
}
template <class T> ostream &operator,(ostream &os, const T &val) {
  return os << " " << val;
}

template <class H> void print(const H &head) { cout << head; }
template <class H, class... T> void print(const H &head, const T &...tail) {
  cout << head << " ";
  print(tail...);
}
template <class... T> void println(const T &...values) {
  print(values...);
  cout << endl;
}

template <class H> void eprint(const H &head) { cerr << head; }
template <class H, class... T> void eprint(const H &head, const T &...tail) {
  cerr << head << " ";
  eprint(tail...);
}
template <class... T> void eprintln(const T &...values) {
  eprint(values...);
  cerr << endl;
}

class range {
  Integer start_, end_, step_;

public:
  struct range_iterator {
    Integer val, step_;
    range_iterator(Integer v, Integer step) : val(v), step_(step) {}
    Integer operator*() { return val; }
    void operator++() { val += step_; }
    bool operator!=(range_iterator &x) {
      return step_ > 0 ? val < x.val : val > x.val;
    }
  };
  range(Integer len) : start_(0), end_(len), step_(1) {}
  range(Integer start, Integer end) : start_(start), end_(end), step_(1) {}
  range(Integer start, Integer end, Integer step)
      : start_(start), end_(end), step_(step) {}
  range_iterator begin() { return range_iterator(start_, step_); }
  range_iterator end() { return range_iterator(end_, step_); }
};

inline string operator"" _s(const char *str, size_t size) {
  return move(string(str));
}
constexpr Integer my_pow(Integer x, Integer k, Integer z = 1) {
  return k == 0    ? z
         : k == 1  ? z * x
         : (k & 1) ? my_pow(x * x, k >> 1, z * x)
                   : my_pow(x * x, k >> 1, z);
}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z = 1) {
  return k == 0    ? z % M
         : k == 1  ? z * x % M
         : (k & 1) ? my_pow_mod(x * x % M, k >> 1, M, z * x % M)
                   : my_pow_mod(x * x % M, k >> 1, M, z);
}
constexpr unsigned long long operator"" _ten(unsigned long long value) {
  return my_pow(10, value);
}

inline int k_bit(Integer x, int k) { return (x >> k) & 1; } // 0-indexed

mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(
               chrono::steady_clock::now().time_since_epoch())
               .count());

template <class T> string join(const vector<T> &v, const string &sep) {
  stringstream ss;
  for (size_t i = 0; i < v.size(); i++) {
    if (i > 0)
      ss << sep;
    ss << v[i];
  }
  return ss.str();
}

inline string operator*(string s, int k) {
  string ret;
  while (k) {
    if (k & 1)
      ret += s;
    s += s;
    k >>= 1;
  }
  return ret;
}
} // namespace
constexpr long long mod = 9_ten + 7;

typedef struct {
  int to;
  long long cap;
  int rev;
  bool is_rev;
} edge;

// node v : distance from s => level[v]
void bfs(vector<vector<edge>> &G, vector<int> &level, int s) {
  fill(level.begin(), level.end(), -1);
  queue<int> q;
  q.push(s);
  level[s] = 0;
  while (!q.empty()) {
    int e = q.front();
    q.pop();
    for (int i = 0; i < G[e].size(); i++) {
      if (G[e][i].cap > 0 && level[G[e][i].to] < 0) {
        level[G[e][i].to] = level[e] + 1;
        q.push(G[e][i].to);
      }
    }
  }
}

long long dfs(vector<vector<edge>> &G, vector<int> &level, vector<bool> &used,
              vector<int> &iter, int s, long long f, int t) {
  if (s == t)
    return f;
  else {
    // iter[e] : done searching from v[0] to v[ iter[e]-1 ]
    for (int &i = iter[s]; i < G[s].size(); i++) {
      // distance from s to v[e][i].to must be longer than dist from s to v
      if (G[s][i].cap > 0 && level[s] < level[G[s][i].to]) {
        long long d =
            dfs(G, level, used, iter, G[s][i].to, min(f, G[s][i].cap), t);
        if (d > 0) {
          G[s][i].cap -= d;
          G[G[s][i].to][G[s][i].rev].cap += d;
          return d;
        }
      }
    }
    return 0;
  }
}

long long dinic_maxflow(vector<vector<edge>> &G, int s, int t) {
  const long long INF = 1000000000000000000ll;
  long long flow = 0;
  while (true) {
    vector<int> level(G.size(), -1);
    vector<int> iter(G.size(), 0);
    vector<bool> used(G.size(), false);
    bfs(G, level, s);
    if (level[t] < 0)
      return flow; // unable to achieve to t
    while (true) {
      long long f = dfs(G, level, used, iter, s, INF, t);
      if (f == 0)
        break;
      else
        flow += f;
    }
  }
}

void add_edge(vector<vector<edge>> &G, int from, int to, int cap) {
  G[from].push_back((edge){to, cap, (int)G[to].size(), false});
  G[to].push_back((edge){from, 0, (int)G[from].size() - 1, true});
}

int main() {
  int n;
  cin >> n;
  vector<long long> w(3);
  cin >> w;
  vector<string> s(n);
  cin >> s;

  vector<vector<int>> t(n);
  string abc = "ABC";

  vector<vector<edge>> G((n + 1) * 4 + 2);
  int source = G.size() - 2;
  int sink = G.size() - 1;
  auto w_ = w;
  for (int i = 0; i < n; i++) {
    int v = 4 * i + 3;
    add_edge(G, source, v, 1);
    for (int j = 0; j < 3; j++) {
      int u = 4 * i + j;
      if (find(begin(s[i]), end(s[i]), abc[j]) != end(s[i])) {
        w_[j]++;
        add_edge(G, v, u, 1);
      }
      add_edge(G, u, u + 4, w_[j] / 2);
    }
  }
  for (int j : range(3))
    add_edge(G, 4 * n + j, sink, n);

  int f = dinic_maxflow(G, source, sink);
  if (f < n) {
    puts("No");
  } else {
    puts("Yes");
    for (int i = 0; i < n; i++) {
      int v = 4 * i + 3;
      for (auto e : G[v]) {
        if (e.is_rev)
          continue;
        if (e.cap == 1) {
          int j = e.to % 4;
          print(abc[j] + "\\n"s);
        }
      }
    }
  }

  return 0;
}