Problem p03184 (C++)

Buggy submission (status: Runtime Error):

#include <bits/stdc++.h>
#define rep(i, n) for (ll i = 0; i < n; ++i)
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
const ll INF = 1e18;

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;

struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
} comb(100005);

// nPk
mint f(int n, int k) {
  if (n < 0)
    return 0;
  // nPk = nCk * k!
  mint res = comb(n, k);
  res *= comb.fact[k];
  return res;
}

// 組み合わせの数nCrを計算
int calcNumOfCombination(int n, int r) {
  int num = 1;
  for (int i = 1; i <= r; i++) {
    num = num * (n - i + 1) / i;
  }
  return num;
}

int main() {
  ll h, w, n;
  cin >> h >> w >> n;
  vector<P> g(n);
  rep(i, n) {
    ll r1, c1;
    cin >> r1 >> c1;
    r1--;
    c1--;
    g[i] = make_pair(r1, c1);
  }
  sort(g.begin(), g.end());
  mint dp[n + 5];
  // mint test=comb(6,2);
  // cout<<test;
  rep(i, n) {
    //  cout<<"i"<<i<<endl;
    ll r1 = g[i].first;
    ll c1 = g[i].second;
    //  cout<<"r"<<r1<<"c"<<c1<<endl;

    mint now = comb(r1 + c1, r1);
    //  cout<<now<<endl;

    rep(j, n) {
      ll r2 = g[j].first;
      ll c2 = g[j].second;
      if (r2 > r1 or c2 > c1)
        continue;
      mint temp = dp[j] * comb((r1 - r2 + c1 - c2), r1 - r2);
      now -= temp;
    }
    //  cout<<now<<endl;
    dp[i] = now;
  }
  mint ans = comb(h + w - 2, w - 1);
  //  cout<<ans<<endl;
  rep(i, n) {
    ll hnow = h - 1 - g[i].first;
    ll cnow = w - 1 - g[i].second;

    mint temp = comb(hnow + cnow, hnow);
    temp *= dp[i];
    ans -= temp;
  }
  cout << ans << endl;
}


Fixed submission:

#include <bits/stdc++.h>
#define rep(i, n) for (ll i = 0; i < n; ++i)
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
const ll INF = 1e18;

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;

struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
} comb(200005);

// nPk
mint f(int n, int k) {
  if (n < 0)
    return 0;
  // nPk = nCk * k!
  mint res = comb(n, k);
  res *= comb.fact[k];
  return res;
}

// 組み合わせの数nCrを計算
int calcNumOfCombination(int n, int r) {
  int num = 1;
  for (int i = 1; i <= r; i++) {
    num = num * (n - i + 1) / i;
  }
  return num;
}

int main() {
  ll h, w, n;
  cin >> h >> w >> n;
  vector<P> g(n);
  rep(i, n) {
    ll r1, c1;
    cin >> r1 >> c1;
    r1--;
    c1--;
    g[i] = make_pair(r1, c1);
  }
  sort(g.begin(), g.end());
  mint dp[n + 5];
  // mint test=comb(6,2);
  // cout<<test;
  rep(i, n) {
    //  cout<<"i"<<i<<endl;
    ll r1 = g[i].first;
    ll c1 = g[i].second;
    //  cout<<"r"<<r1<<"c"<<c1<<endl;

    mint now = comb(r1 + c1, r1);
    //  cout<<now<<endl;

    rep(j, n) {
      ll r2 = g[j].first;
      ll c2 = g[j].second;
      if (r2 > r1 or c2 > c1)
        continue;
      mint temp = dp[j] * comb((r1 - r2 + c1 - c2), r1 - r2);
      now -= temp;
    }
    //  cout<<now<<endl;
    dp[i] = now;
  }
  mint ans = comb(h + w - 2, w - 1);
  //  cout<<ans<<endl;
  rep(i, n) {
    ll hnow = h - 1 - g[i].first;
    ll cnow = w - 1 - g[i].second;

    mint temp = comb(hnow + cnow, hnow);
    temp *= dp[i];
    ans -= temp;
  }
  cout << ans << endl;
}