Problem p02775 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, a, b) for (int i = a; i < b; i++)
#define rrep(i, a, b) for (int i = b - 1; i >= a; i--)
#define ALL(a) a.begin(), a.end()
#define pii pair<int, int>
#pragma GCC optimize("Ofast")
#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)
#define pb push_back
#define mp make_pair
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
};
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
};
inline void IN(void) { return; }
template <typename First, typename... Rest>
void IN(First &first, Rest &...rest) {
  cin >> first;
  IN(rest...);
  return;
}
inline void OUT(void) {
  cout << "\n";
  return;
}
template <typename First, typename... Rest>
void OUT(First first, Rest... rest) {
  cout << first << " ";
  OUT(rest...);
  return;
}
const double EPS = 1e-9;
const int mod = 1e9 + 7;
const int INF = 1e9;
const long long LLINF = 1e18;
long long lcm(ll a, ll b) { return a * b / __gcd(a, b); }
struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;
template <int mod> struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
using modint = ModInt<mod>;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

const int MAX = 1e5 + 10;
int dp[MAX][2];
// dp[i+1][j] := Aを下からi桁目まで決めた時繰り下がりがjの時の最小値

int main() {
  iosetup;
  string S;
  cin >> S;
  reverse(ALL(S));
  S += '0';
  int N = S.size();
  rep(i, 0, N + 1) rep(j, 0, 2) dp[i][j] = INF;
  dp[0][0] = 0;
  rep(i, 0, N) rep(j, 0, 2) {
    int x = S[i] - '0';
    x += j;
    rep(a, 0, 10) {
      int ni = i + 1, nj = 0;
      int b = a - x;
      if (b < 0) {
        nj = 1;
        b += 10;
      }
      chmin(dp[ni][nj], dp[i][j] + a + b);
    }
  }
  int ans = dp[N][0];
  cout << ans << endl;
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, a, b) for (int i = a; i < b; i++)
#define rrep(i, a, b) for (int i = b - 1; i >= a; i--)
#define ALL(a) a.begin(), a.end()
#define pii pair<int, int>
#pragma GCC optimize("Ofast")
#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)
#define pb push_back
#define mp make_pair
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
};
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
};
inline void IN(void) { return; }
template <typename First, typename... Rest>
void IN(First &first, Rest &...rest) {
  cin >> first;
  IN(rest...);
  return;
}
inline void OUT(void) {
  cout << "\n";
  return;
}
template <typename First, typename... Rest>
void OUT(First first, Rest... rest) {
  cout << first << " ";
  OUT(rest...);
  return;
}
const double EPS = 1e-9;
const int mod = 1e9 + 7;
const int INF = 1e9;
const long long LLINF = 1e18;
long long lcm(ll a, ll b) { return a * b / __gcd(a, b); }
struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;
template <int mod> struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
using modint = ModInt<mod>;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

const int MAX = 1e6 + 10;
int dp[MAX][2];
// dp[i+1][j] := Aを下からi桁目まで決めた時繰り下がりがjの時の最小値

int main() {
  iosetup;
  string S;
  cin >> S;
  reverse(ALL(S));
  S += '0';
  int N = S.size();
  rep(i, 0, N + 1) rep(j, 0, 2) dp[i][j] = INF;
  dp[0][0] = 0;
  rep(i, 0, N) rep(j, 0, 2) {
    int x = S[i] - '0';
    x += j;
    rep(a, 0, 10) {
      int ni = i + 1, nj = 0;
      int b = a - x;
      if (b < 0) {
        nj = 1;
        b += 10;
      }
      chmin(dp[ni][nj], dp[i][j] + a + b);
    }
  }
  int ans = dp[N][0];
  cout << ans << endl;
  return 0;
}