Problem p03134 (C++)

Buggy submission (status: Runtime Error):
#define _CRT_SECURE_NO_WARNINGS
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <float.h>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <string>
#include <time.h>
#include <utility>
#include <vector>
using namespace std;
long long gcd(long long a, long long b) {
  if (a < b)
    gcd(b, a);
  long long r;
  while ((r = a % b)) {
    a = b;
    b = r;
  }
  return b;
}
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
long long modpow(long long a, long long n, long long mod) {
  long long res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}

long long modinv(long long a, long long mod) {
  long long b = mod, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0)
    u += mod;
  return u;
}
namespace NTT {
const int MOD = 998244353; // to be set appropriately
const long long PR = 3;    // to be set appropriately

void trans(vector<long long> &v, bool inv = false) {
  int n = (int)v.size();
  for (int i = 0, j = 1; j < n - 1; j++) {
    for (int k = n >> 1; k > (i ^= k); k >>= 1)
      ;
    if (i > j)
      swap(v[i], v[j]);
  }
  for (int t = 2; t <= n; t <<= 1) {
    long long bw = modpow(PR, (MOD - 1) / t, MOD);
    if (inv)
      bw = modinv(bw, MOD);
    for (int i = 0; i < n; i += t) {
      long long w = 1;
      for (int j = 0; j < t / 2; ++j) {
        int j1 = i + j, j2 = i + j + t / 2;
        long long c1 = v[j1], c2 = v[j2] * w % MOD;
        v[j1] = c1 + c2;
        v[j2] = c1 - c2 + MOD;
        while (v[j1] >= MOD)
          v[j1] -= MOD;
        while (v[j2] >= MOD)
          v[j2] -= MOD;
        w = w * bw % MOD;
      }
    }
  }
  if (inv) {
    long long inv_n = modinv(n, MOD);
    for (int i = 0; i < n; ++i)
      v[i] = v[i] * inv_n % MOD;
  }
}

// C is A*B
vector<long long> mult(vector<long long> A, vector<long long> B) {
  int size_a = 1;
  while (size_a < A.size())
    size_a <<= 1;
  int size_b = 1;
  while (size_b < B.size())
    size_b <<= 1;
  int size_fft = max(size_a, size_b) << 1;

  vector<long long> cA(size_fft, 0), cB(size_fft, 0), cC(size_fft, 0);
  for (int i = 0; i < A.size(); ++i)
    cA[i] = A[i];
  for (int i = 0; i < B.size(); ++i)
    cB[i] = B[i];

  trans(cA);
  trans(cB);
  for (int i = 0; i < size_fft; ++i)
    cC[i] = cA[i] * cB[i] % MOD;
  trans(cC, true);

  vector<long long> res((int)A.size() + (int)B.size() - 1);
  for (int i = 0; i < res.size(); ++i)
    res[i] = cC[i];
  return res;
}
}; // namespace NTT
typedef pair<int, int> p;
typedef pair<int, p> pai;
const int maxn = 1 << 24;
int n2;
long long dat[2 * maxn - 1];
void init(int n_) {
  n2 = 1;
  while (n2 < n_)
    n2 *= 2;
  for (int i = 0; i < 2 * n2 - 1; i++) {
    dat[i] = LLONG_MIN / 2;
  }
}
void update(long long k, long long a) {
  k += n2 - 1;
  dat[k] = a;
  while (k > 0) {
    k = (k - 1) / 2;
    dat[k] = max(dat[k * 2 + 1], dat[k * 2 + 2]);
  }
}
long long query(int a, int b, int k, int l, int r) {
  if (r <= a || b <= l)
    return LLONG_MIN / 2;
  if (a <= l && r <= b)
    return dat[k];
  else {
    long long vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
    long long vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
    return max(vl, vr);
  }
}
long long mod = 998244353;
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  string s;
  cin >> s;
  vector<int> red;
  vector<int> blue;
  long long dp[2003][2003];
  int n = s.length();
  for (int i = 0; i < 2003; i++) {
    for (int j = 0; j < 2003; j++) {
      dp[i][j] = 0;
    }
  }
  dp[0][0] = 1;
  for (int i = 0; i < n; i++) {
    if (s[i] == '0') {
      red.push_back(i);
      red.push_back(i);
    }
    if (s[i] == '1') {
      red.push_back(i);
      blue.push_back(i);
    }
    if (s[i] == '2') {
      blue.push_back(i);
      blue.push_back(i);
    }
  }
  int r = red.size(), b = blue.size();
  for (int i = 0; i <= r; i++) {
    for (int j = 0; j <= b; j++) {
      if (j < b && blue[j] <= i + j)
        dp[i][j + 1] += dp[i][j];
      dp[i][j + 1] %= mod;
      if (i < r && red[i] <= i + j)
        dp[i + 1][j] = dp[i][j];
      dp[i + 1][j] %= mod;
    }
  }
  cout << dp[r][b];
}


Fixed submission:
#define _CRT_SECURE_NO_WARNINGS
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <float.h>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <string>
#include <time.h>
#include <utility>
#include <vector>
using namespace std;
long long gcd(long long a, long long b) {
  if (a < b)
    gcd(b, a);
  long long r;
  while ((r = a % b)) {
    a = b;
    b = r;
  }
  return b;
}
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
long long modpow(long long a, long long n, long long mod) {
  long long res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}

long long modinv(long long a, long long mod) {
  long long b = mod, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0)
    u += mod;
  return u;
}
namespace NTT {
const int MOD = 998244353; // to be set appropriately
const long long PR = 3;    // to be set appropriately

void trans(vector<long long> &v, bool inv = false) {
  int n = (int)v.size();
  for (int i = 0, j = 1; j < n - 1; j++) {
    for (int k = n >> 1; k > (i ^= k); k >>= 1)
      ;
    if (i > j)
      swap(v[i], v[j]);
  }
  for (int t = 2; t <= n; t <<= 1) {
    long long bw = modpow(PR, (MOD - 1) / t, MOD);
    if (inv)
      bw = modinv(bw, MOD);
    for (int i = 0; i < n; i += t) {
      long long w = 1;
      for (int j = 0; j < t / 2; ++j) {
        int j1 = i + j, j2 = i + j + t / 2;
        long long c1 = v[j1], c2 = v[j2] * w % MOD;
        v[j1] = c1 + c2;
        v[j2] = c1 - c2 + MOD;
        while (v[j1] >= MOD)
          v[j1] -= MOD;
        while (v[j2] >= MOD)
          v[j2] -= MOD;
        w = w * bw % MOD;
      }
    }
  }
  if (inv) {
    long long inv_n = modinv(n, MOD);
    for (int i = 0; i < n; ++i)
      v[i] = v[i] * inv_n % MOD;
  }
}

// C is A*B
vector<long long> mult(vector<long long> A, vector<long long> B) {
  int size_a = 1;
  while (size_a < A.size())
    size_a <<= 1;
  int size_b = 1;
  while (size_b < B.size())
    size_b <<= 1;
  int size_fft = max(size_a, size_b) << 1;

  vector<long long> cA(size_fft, 0), cB(size_fft, 0), cC(size_fft, 0);
  for (int i = 0; i < A.size(); ++i)
    cA[i] = A[i];
  for (int i = 0; i < B.size(); ++i)
    cB[i] = B[i];

  trans(cA);
  trans(cB);
  for (int i = 0; i < size_fft; ++i)
    cC[i] = cA[i] * cB[i] % MOD;
  trans(cC, true);

  vector<long long> res((int)A.size() + (int)B.size() - 1);
  for (int i = 0; i < res.size(); ++i)
    res[i] = cC[i];
  return res;
}
}; // namespace NTT
typedef pair<int, int> p;
typedef pair<int, p> pai;
const int maxn = 1 << 24;
int n2;
long long dat[2 * maxn - 1];
void init(int n_) {
  n2 = 1;
  while (n2 < n_)
    n2 *= 2;
  for (int i = 0; i < 2 * n2 - 1; i++) {
    dat[i] = LLONG_MIN / 2;
  }
}
void update(long long k, long long a) {
  k += n2 - 1;
  dat[k] = a;
  while (k > 0) {
    k = (k - 1) / 2;
    dat[k] = max(dat[k * 2 + 1], dat[k * 2 + 2]);
  }
}
long long query(int a, int b, int k, int l, int r) {
  if (r <= a || b <= l)
    return LLONG_MIN / 2;
  if (a <= l && r <= b)
    return dat[k];
  else {
    long long vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
    long long vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
    return max(vl, vr);
  }
}
long long mod = 998244353;
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  string s;
  cin >> s;
  vector<int> red;
  vector<int> blue;
  long long dp[4003][4003];
  int n = s.length();
  for (int i = 0; i < 2003; i++) {
    for (int j = 0; j < 2003; j++) {
      dp[i][j] = 0;
    }
  }
  dp[0][0] = 1;
  for (int i = 0; i < n; i++) {
    if (s[i] == '0') {
      red.push_back(i);
      red.push_back(i);
    }
    if (s[i] == '1') {
      red.push_back(i);
      blue.push_back(i);
    }
    if (s[i] == '2') {
      blue.push_back(i);
      blue.push_back(i);
    }
  }
  int r = red.size(), b = blue.size();
  for (int i = 0; i <= r; i++) {
    for (int j = 0; j <= b; j++) {
      if (j < b && blue[j] <= i + j)
        dp[i][j + 1] += dp[i][j];
      dp[i][j + 1] %= mod;
      if (i < r && red[i] <= i + j)
        dp[i + 1][j] = dp[i][j];
      dp[i + 1][j] %= mod;
    }
  }
  cout << dp[r][b];
}