Submission #36451488

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Source Code Expand

// #define NDEBUG
#include <bits/stdc++.h>

#define REP_(i, a_, b_, a, b, ...) for (int i = (a), END_##i = (b); i < END_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using Int = long long;
using Uint = unsigned long long;
using Real = long double;

template<typename T, typename U>
inline bool chmax(T &a, U b) { return a < b and ((a = b), true); }
template<typename T, typename U>
inline bool chmin(T &a, U b) { return a > b and ((a = b), true); }
template<typename T>
constexpr T kBig = std::numeric_limits<T>::max() / 2;
#if __cplusplus < 202002L
template<typename T>
inline int ssize(const T &a) { return (int) a.size(); }
#endif

template<size_t BufSize>
class InputReader {
 public:
  void skip() {
    // Initialize on the first use.
    [[maybe_unused]] static const bool init = [this]() {
      const size_t len = fread(buf, 1, sizeof(buf) - 1, stdin);
      buf[len] = '\0';
      p = buf;
      bufend = buf + len;
      return true;
    }();

    while (isspace(*p)) ++p;
  }

  template<typename T>
  operator T() {
    T x;
    skip();
    assert(not is_eof());  // Couldn't read reached the end of input.
    read_one(x);
    return x;
  }

  struct Sized {
    InputReader<BufSize> &reader;
    int n;
    template<typename T>
    operator T() const {
      T xs(n);
      for (auto &x: xs) {
        reader.skip();
        assert(not reader.is_eof());
        reader.read_one(x);
      }
      return xs;
    }
  };
  Sized operator()(int n) { return {*this, n}; }

  bool is_eof() { return p >= bufend; }

 private:
  static inline char buf[BufSize];
  char *p, *bufend;

  template<class T>
  std::enable_if_t<std::is_integral_v<T>> read_one(T &x) {
    [[maybe_unused]] int sign = 1;
    if constexpr (std::is_signed_v<T>) {
      sign = (*p == '-') ? (++p, -1) : 1;
    }
    x = 0;
    while (isdigit(*p)) x = x * 10 + (*p++ & 0x0F);
    if constexpr (std::is_signed_v<T>) {
      x *= sign;
    }
  }
  void read_one(std::string &s) {
    char *p0 = p;
    while (not isspace(*p)) p++;
    s.assign(p0, p);
  }
  void read_one(std::string_view &s) {
    const char *p0 = p;
    while (not isspace(*p)) p++;
    s = std::string_view(p0, p - p0);
  }
};
InputReader<(1 << 26)> in;

template<typename Container>
std::ostream &out_seq(const Container &seq, const char *sep = " ",
                      const char *ends = "\n", std::ostream &os = std::cout) {
  const auto itl = std::begin(seq), itr = std::end(seq);
  for (auto it = itl; it != itr; ++it) {
    if (it != itl) os << sep;
    os << *it;
  }
  return os << ends;
}

template<typename T>
std::ostream &out_one(const T &x, char endc) {
  if constexpr (std::is_same<T, bool>::value) {
    return std::cout << (x ? "Yes" : "No") << endc;
  } else {
    return std::cout << x << endc;
  }
}
template<typename T>
std::ostream &out(const T &x) {
  return out_one(x, '\n');
}
template<typename T, typename... Ts>
std::ostream &out(const T &head, Ts... tail) {
  return out_one(head, ' '), out(tail...);
}

void init_() {
  // std::ios::sync_with_stdio(false);
  // std::cin.tie(nullptr);
  std::cout << std::fixed << std::setprecision(18);
}

[[noreturn]] void exit_() {
#ifdef MY_DEBUG
  in.skip();
  assert(in.is_eof());  // Some input is left.
#endif
  fflush(stdout), fflush(stderr);
  std::cout.flush(), std::cerr.flush();
  std::_Exit(0);
}

#ifdef MY_DEBUG
#include "debug_dump.hpp"
#include "backward.hpp"
backward::SignalHandling kSignalHandling;
#else
#define DUMP(...)
#define test_case(...)
#define cerr if(false)cerr
#endif

using namespace std;

auto solve() -> bool {
  int H = in, W = in;
  auto A = vector(H, vector(W, 0LL));
  REP(i, H) REP(j, W) A[i][j] = Int(in);
  for (int i = H - 1; i >= 0; --i) {
    bool all_zero = [&]() {
      REP(j, W) if (A[i][j] != 0) return false;
      return true;
    }();
    if (all_zero) {
      swap(A[i], A.back());
      A.pop_back();
      --H;
    }
  }
  if (A.empty()) return true;
  for (int j = W - 1; j >= 0; --j) {
    bool all_zero = [&]() {
      REP(i, H) if (A[i][j] != 0) return false;
      return true;
    }();
    if (all_zero) {
      REP(i, H) {
        swap(A[i][j], A[i].back());
        A[i].pop_back();
      }
      --W;
    }
  }
  if (W == 0) return true;
  DUMP(H, W);
  REP(i, H) {
    DUMP(A[i]);
  }

  vector<Int> rsum(H), rc(H);
  REP(i, H) {
    REP(j, W) {
      rsum[i] += A[i][j];
      if (A[i][j] > 0) ++rc[i];
    }
  }

  {
    vector<int> idx(A.size());
    std::iota(idx.begin(), idx.end(), 0);
    sort(ALL(idx), [&](int i, int j) {
      return rsum[i] * rc[j] < rsum[j] * rc[i];
    });
    DUMP(rsum);
    DUMP(rc);
    DUMP(idx);
    Int maxval = -1;
    for (int i: idx) {
      Int mi = kBig<Int>, ma = -1;
      REP(j, W) {
        if (A[i][j] == 0) continue;
        chmin(mi, A[i][j]);
        chmax(ma, A[i][j]);
      }
      if (mi < maxval) {
        return false;
      }
      chmax(maxval, ma);
    }
  }

  list<map<Int, set<int>>> seq;
  REP(i, H) {
    map<Int, set<int>> si;
    REP(j, W) {
      Int x = A[i][j];
      if (x == 0) continue;
      si[x].insert(j);
    }
    if (si.empty()) continue;
    seq.push_back(si);
  }
  vector<int> bigger(W);
  for (auto it = seq.begin(); it != seq.end(); ++it) {
    assert(not it->empty());
    for (auto jt = next(it->begin()); jt != it->end(); ++jt) {
      for (int k: jt->second) ++bigger[k];
    }
  }
  queue<int> minq;
  REP(i, W) {
    if (bigger[i] == 0) {
      minq.push(i);
    }
  }
  set<int> oks;
  while (not minq.empty()) {
    int v = minq.front();
    minq.pop();
    oks.insert(v);
    for (auto it = seq.begin(); it != seq.end();) {
      bool erased = false;
      it->begin()->second.erase(v);
      if (it->begin()->second.empty()) {
        it->erase(it->begin());
        if (it->empty()) {
          it = seq.erase(it);
          erased = true;
        } else {
          for (int k: it->begin()->second) {
            --bigger[k];
            if (bigger[k] == 0) {
              minq.push(k);
            }
          }
        }
      }
      if (not erased) ++it;
    }
  }
  DUMP(oks);
  return ssize(oks) == W;
}

int main() {
  init_();
  const int T = 1;//in;
  REP(t, T) {
    test_case(t, T);
    out(solve());
  }
  exit_();
}

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