Problem p01941 (C++) — buggy submission, verdict: Time Limit Exceeded

// need
#include <algorithm>
#include <iostream>

// data structure
#include <bitset>
// #include <list>
#include <array>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <tuple>
// #include <unordered_map>
#include <complex>
#include <unordered_set>
// #include <deque>
#include <valarray>

// stream
// #include <istream>
// #include <sstream>
// #include <ostream>
// #include <fstream>

// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
// #include <typeinfo>
#include <chrono>
#include <numeric>
#include <random>

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int i = 0; i < n; ++i) {                                                \\
    MACRO_VEC_ROW_Scan(i, __VA_ARGS__);                                        \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &r : c)                                                            \\
    for (auto &i : r)                                                          \\
      std::cin >> i;

// output
#define OUT(d) std::cout << d;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << d;
#define SOUT(n, c, d) std::cout << std::setw(n) << std::setfill(c) << d;
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(i, n) std::cout << (i + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(d)                                                                \\
  { std::cerr << #d << "\\t:" << d << "\\n"; }
#define SHOWVECTOR(v)                                                          \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWVECTOR2(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << yyy << " ";                                               \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWQUEUE(a)                                                           \\
  {                                                                            \\
    auto tmp(a);                                                               \\
    std::cerr << #a << "\\t:";                                                  \\
    while (!tmp.empty()) {                                                     \\
      std::cerr << tmp.front() << " ";                                         \\
      tmp.pop();                                                               \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }

// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define RREP(i, n) for (int i = int(n) - 1; i >= 0; --i)
#define FORLL(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define RFORLL(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define REPLL(i, n) for (ll i = 0; i < ll(n); ++i)
#define RREPLL(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define IN(a, x, b) (a <= x && x < b)
template <typename T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
#define EXCEPTION(msg)                                                         \\
  throw std::string("Exception : " msg " [ in ") + __func__ + " : " +          \\
      std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg)                                                         \\
  try {                                                                        \\
    if (cond)                                                                  \\
      EXCEPTION(msg);                                                          \\
  } catch (std::string s) {                                                    \\
    std::cerr << s << std::endl;                                               \\
  }
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\\n";
}

// test
template <class T> std::vector<std::vector<T>> VV(int n) {
  return std::vector<std::vector<T>>(n);
}
template <class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

// type/const

// #define int ll
using ll = long long;
using ull = unsigned long long;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                         // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

int dp[2][102][10004];

signed main() {
  INIT;
  VAR(int, n, C);
  VEC_ROW(int, n, a, b, c);

  REP(i, 2) REP(j, 102) REP(k, 10004) dp[i][j][k] = -1;
  dp[0][0][0] = 0;
  REP(i, n) {
    int from = i % 2;
    int to = (i + 1) % 2;
    REP(j, C + 1) {
      REP(k, n * 100 + 1) {
        if (dp[from][j][k] == -1)
          continue;
        CHMAX(dp[to][j][k], dp[from][j][k]);
      }
      if (j + c[i] <= C) {
        REP(k, n * 100 + 1) {
          if (dp[from][j][k] == -1)
            continue;
          CHMAX(dp[to][j + c[i]][k + a[i]], dp[from][j][k] + b[i]);
          CHMAX(dp[to][j + c[i]][k + b[i]], dp[from][j][k] + a[i]);
          CHMAX(dp[to][j + c[i]][dp[from][j][k] + a[i]], k + b[i]);
          CHMAX(dp[to][j + c[i]][dp[from][j][k] + b[i]], k + a[i]);
        }
      }
    }
  }
  int ans = 0;
  REP(j, C + 1) REP(k, n * 100 + 1) {
    if (dp[n % 2][j][k] == -1)
      continue;
    CHMAX(ans, std::min(k, dp[n % 2][j][k]));
  }
  OUT(ans) BR;
  return 0;
}

Error: TLE

Fixed submission:

// need
#include <algorithm>
#include <iostream>

// data structure
#include <bitset>
// #include <list>
#include <array>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <tuple>
// #include <unordered_map>
#include <complex>
#include <unordered_set>
// #include <deque>
#include <valarray>

// stream
// #include <istream>
// #include <sstream>
// #include <ostream>
// #include <fstream>

// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
// #include <typeinfo>
#include <chrono>
#include <numeric>
#include <random>

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int i = 0; i < n; ++i) {                                                \\
    MACRO_VEC_ROW_Scan(i, __VA_ARGS__);                                        \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &r : c)                                                            \\
    for (auto &i : r)                                                          \\
      std::cin >> i;

// output
#define OUT(d) std::cout << d;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << d;
#define SOUT(n, c, d) std::cout << std::setw(n) << std::setfill(c) << d;
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(i, n) std::cout << (i + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(d)                                                                \\
  { std::cerr << #d << "\\t:" << d << "\\n"; }
#define SHOWVECTOR(v)                                                          \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWVECTOR2(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << yyy << " ";                                               \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWQUEUE(a)                                                           \\
  {                                                                            \\
    auto tmp(a);                                                               \\
    std::cerr << #a << "\\t:";                                                  \\
    while (!tmp.empty()) {                                                     \\
      std::cerr << tmp.front() << " ";                                         \\
      tmp.pop();                                                               \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }

// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define RREP(i, n) for (int i = int(n) - 1; i >= 0; --i)
#define FORLL(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define RFORLL(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define REPLL(i, n) for (ll i = 0; i < ll(n); ++i)
#define RREPLL(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define IN(a, x, b) (a <= x && x < b)
template <typename T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
#define EXCEPTION(msg)                                                         \\
  throw std::string("Exception : " msg " [ in ") + __func__ + " : " +          \\
      std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg)                                                         \\
  try {                                                                        \\
    if (cond)                                                                  \\
      EXCEPTION(msg);                                                          \\
  } catch (std::string s) {                                                    \\
    std::cerr << s << std::endl;                                               \\
  }
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\\n";
}

// test
template <class T> std::vector<std::vector<T>> VV(int n) {
  return std::vector<std::vector<T>>(n);
}
template <class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
  return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

// type/const

// #define int ll
using ll = long long;
using ull = unsigned long long;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                         // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

struct P {
  int x, y;
  P() : x(0), y(0) {}
  P(int x, int y) : x(x), y(y) {}
  bool operator<(const P &r) const {
    if (x == r.x)
      return y > r.y;
    else
      return x < r.x;
  }
};
std::set<P> dp[2][102];

signed main() {
  INIT;
  VAR(int, n, C);
  VEC_ROW(int, n, a, b, c);

  dp[0][0].insert(P(0, 0));
  REP(i, n) {
    int from = i % 2;
    int to = (i + 1) % 2;
    REP(j, C + 1) dp[to][j].clear();
    REP(j, C + 1) {
      if (dp[from][j].empty())
        continue;
      P pre = P(-1, -1);
      for (auto &p : dp[from][j]) {
        if (p.x != pre.x) {
          dp[to][j].insert(p);
          if (j + c[i] <= C) {
            P pp(p), pp2(p);
            pp.x += a[i];
            pp.y += b[i];
            if (pp.x > pp.y)
              std::swap(pp.x, pp.y);
            auto &TO = dp[to][j + c[i]];
            {
              auto it = TO.lower_bound(P(pp.x, INFINT));
              if (it != TO.end()) {
                if (it->x == pp.x) {
                  if (it->y < pp.y) {
                    TO.erase(it);
                    TO.insert(pp);
                  }
                } else {
                  TO.insert(pp);
                }
              } else {
                TO.insert(pp);
              }
            }
            pp2.y += a[i];
            pp2.x += b[i];
            if (pp2.x > pp2.y)
              std::swap(pp2.x, pp2.y);
            {
              auto it = TO.lower_bound(P(pp2.x, INFINT));
              if (it != TO.end()) {
                if (it->x == pp2.x) {
                  if (it->y < pp2.y) {
                    TO.erase(it);
                    TO.insert(pp2);
                  }
                } else {
                  TO.insert(pp2);
                }
              } else {
                TO.insert(pp2);
              }
            }
          }
        }
        pre = p;
      }
    }
  }
  int ans = 0;
  REP(j, C + 1) {
    if (dp[n % 2][j].empty())
      continue;
    CHMAX(ans, (int)(dp[n % 2][j].rbegin())->x);
  }
  OUT(ans) BR;
  return 0;
}