Problem p03914 (C++)

Buggy submission (status: Runtime Error):

/* -------------------------------- Template -------------------------------- */

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()

using ll = long long;
using ld = long double;

template <typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }
template <typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }

template <typename T> constexpr T inf = []() { assert(false); };
// template<> constexpr int inf<int> = 1e9;
// template<> constexpr ll inf<ll> = 1e18;
// template<> constexpr ld inf<ld> = 1e30;

struct yes_no : std::numpunct<char> {
  string_type do_truename() const { return "Yes"; }
  string_type do_falsename() const { return "No"; }
};

void solve();

int main() {
  std::locale loc(std::locale(), new yes_no);
  std::cout << std::boolalpha << std::setprecision(12) << std::fixed;
  std::cout.imbue(loc);
  solve();
  return 0;
}

using namespace std;

/* -------------------------------- Library -------------------------------- */

template <int M, bool IsPrime = false> class Modulo {
  using ll = long long;
  int n;
  static enable_if_t<IsPrime, ll> inv(ll a, ll p) {
    return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
  }

public:
  Modulo() : n(0) { ; }
  Modulo(int m) : n(m) {
    if (n >= M)
      n %= M;
    else if (n < 0)
      n = (n % M + M) % M;
  }
  Modulo(ll m) {
    if (m >= M)
      m %= M;
    else if (m < 0)
      m = (m % M + M) % M;
    n = m;
  }
  explicit operator int() const { return n; }
  explicit operator ll() const { return n; }
  bool operator==(const Modulo &a) const { return n == a.n; }
  Modulo operator+=(const Modulo &a) {
    n += a.n;
    if (n >= M)
      n -= M;
    return *this;
  }
  Modulo operator-=(const Modulo &a) {
    n -= a.n;
    if (n < 0)
      n += M;
    return *this;
  }
  Modulo operator*=(const Modulo &a) {
    n = (ll(n) * a.n) % M;
    return *this;
  }
  Modulo operator+(const Modulo &a) const {
    Modulo res = *this;
    return res += a;
  }
  Modulo operator-(const Modulo &a) const {
    Modulo res = *this;
    return res -= a;
  }
  Modulo operator*(const Modulo &a) const {
    Modulo res = *this;
    return res *= a;
  }
  Modulo operator^(int n) const {
    if (n == 0)
      return Modulo(1);
    const Modulo a = *this;
    Modulo res = (a * a) ^ (n / 2);
    return n % 2 ? res * a : res;
  }
  enable_if_t<IsPrime, Modulo> operator/(const Modulo &a) const {
    return *this * inv(ll(a), M);
  }
};

template <int M> Modulo<M, true> fact(int n, bool sw = true) {
  static vector<Modulo<M, true>> v1 = {1}, v2 = {1};
  if (n >= (int)v1.size()) {
    const int from = v1.size(), to = n + 1024;
    v1.reserve(to);
    v2.reserve(to);
    for (int i = from; i < to; ++i) {
      v1.push_back(v1.back() * Modulo<M, true>(i));
      v2.push_back(v2.back() / Modulo<M, true>(i));
    }
  }
  return sw ? v1[n] : v2[n];
}

template <int M> Modulo<M, true> comb(int a, int b) {
  if (b < 0 || b > a)
    return fact<M>(0);
  return fact<M>(a, true) * fact<M>(b, false) * fact<M>(a - b, false);
}

const int mod = 1000000007;
using Mod = Modulo<mod, true>;

/* ---------------------------------- Main ---------------------------------- */

Mod dp[2][512][512];

void solve() {
  int N, M;
  cin >> M >> N;
  dp[0][1][0] = 1;
  REP(i, N) {
    REP(j, M + 2) REP(k, M + 1) { dp[(i + 1) & 1][j][k] = 0; }
    REP(j, M + 1) REP(k, M + 1) {
      // cout << i << " " << j << " " << k << " " << int(dp[i][j][k]) << endl;
      dp[(i + 1) & 1][j][k + 1] += dp[i & 1][j][k] * (M - j - k);
      dp[(i + 1) & 1][j][k] += dp[i & 1][j][k] * k;
      dp[(i + 1) & 1][j + k][0] += dp[i & 1][j][k] * j;
    }
  }
  // REP(i,20) { REP(j,20) cout << int(dp[i][j]) << " "; cout << endl; }
  cout << int(dp[N & 1][M][0]) << endl;
  return;
}


Fixed submission:

/* -------------------------------- Template -------------------------------- */

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()

using ll = long long;
using ld = long double;

template <typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }
template <typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }

template <typename T> constexpr T inf = []() { assert(false); };
// template<> constexpr int inf<int> = 1e9;
// template<> constexpr ll inf<ll> = 1e18;
// template<> constexpr ld inf<ld> = 1e30;

struct yes_no : std::numpunct<char> {
  string_type do_truename() const { return "Yes"; }
  string_type do_falsename() const { return "No"; }
};

void solve();

int main() {
  std::locale loc(std::locale(), new yes_no);
  std::cout << std::boolalpha << std::setprecision(12) << std::fixed;
  std::cout.imbue(loc);
  solve();
  return 0;
}

using namespace std;

/* -------------------------------- Library -------------------------------- */

template <int M, bool IsPrime = false> class Modulo {
  using ll = long long;
  int n;
  static enable_if_t<IsPrime, ll> inv(ll a, ll p) {
    return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
  }

public:
  Modulo() : n(0) { ; }
  Modulo(int m) : n(m) {
    if (n >= M)
      n %= M;
    else if (n < 0)
      n = (n % M + M) % M;
  }
  Modulo(ll m) {
    if (m >= M)
      m %= M;
    else if (m < 0)
      m = (m % M + M) % M;
    n = m;
  }
  explicit operator int() const { return n; }
  explicit operator ll() const { return n; }
  bool operator==(const Modulo &a) const { return n == a.n; }
  Modulo operator+=(const Modulo &a) {
    n += a.n;
    if (n >= M)
      n -= M;
    return *this;
  }
  Modulo operator-=(const Modulo &a) {
    n -= a.n;
    if (n < 0)
      n += M;
    return *this;
  }
  Modulo operator*=(const Modulo &a) {
    n = (ll(n) * a.n) % M;
    return *this;
  }
  Modulo operator+(const Modulo &a) const {
    Modulo res = *this;
    return res += a;
  }
  Modulo operator-(const Modulo &a) const {
    Modulo res = *this;
    return res -= a;
  }
  Modulo operator*(const Modulo &a) const {
    Modulo res = *this;
    return res *= a;
  }
  Modulo operator^(int n) const {
    if (n == 0)
      return Modulo(1);
    const Modulo a = *this;
    Modulo res = (a * a) ^ (n / 2);
    return n % 2 ? res * a : res;
  }
  enable_if_t<IsPrime, Modulo> operator/(const Modulo &a) const {
    return *this * inv(ll(a), M);
  }
};

template <int M> Modulo<M, true> fact(int n, bool sw = true) {
  static vector<Modulo<M, true>> v1 = {1}, v2 = {1};
  if (n >= (int)v1.size()) {
    const int from = v1.size(), to = n + 1024;
    v1.reserve(to);
    v2.reserve(to);
    for (int i = from; i < to; ++i) {
      v1.push_back(v1.back() * Modulo<M, true>(i));
      v2.push_back(v2.back() / Modulo<M, true>(i));
    }
  }
  return sw ? v1[n] : v2[n];
}

template <int M> Modulo<M, true> comb(int a, int b) {
  if (b < 0 || b > a)
    return fact<M>(0);
  return fact<M>(a, true) * fact<M>(b, false) * fact<M>(a - b, false);
}

const int mod = 1000000007;
using Mod = Modulo<mod, true>;

/* ---------------------------------- Main ---------------------------------- */

Mod dp[2][1024][1024];

void solve() {
  int N, M;
  cin >> M >> N;
  dp[0][1][0] = 1;
  REP(i, N) {
    REP(j, M + 2) REP(k, M + 1) { dp[(i + 1) & 1][j][k] = 0; }
    REP(j, M + 1) REP(k, M + 1) {
      // cout << i << " " << j << " " << k << " " << int(dp[i][j][k]) << endl;
      dp[(i + 1) & 1][j][k + 1] += dp[i & 1][j][k] * (M - j - k);
      dp[(i + 1) & 1][j][k] += dp[i & 1][j][k] * k;
      dp[(i + 1) & 1][j + k][0] += dp[i & 1][j][k] * j;
    }
  }
  // REP(i,20) { REP(j,20) cout << int(dp[i][j]) << " "; cout << endl; }
  cout << int(dp[N & 1][M][0]) << endl;
  return;
}