Problem p02827 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using gpp_set = tree<T, null_type, less<T>, rb_tree_tag,
tree_order_statistics_node_update>; template<typename T, typename L> using
gpp_map = tree<T, L, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using gpp_multiset = tree<T, null_type, less_equal<T>,
rb_tree_tag, tree_order_statistics_node_update>;*/
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  {                                                                            \
    cout << #v << "=" << endl;                                                 \
    REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                      \
    cout << endl;                                                              \
  }
#define mdebug(m)                                                              \
  {                                                                            \
    cout << #m << "=" << endl;                                                 \
    REP(i_debug, m.size()) {                                                   \
      REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }  \
      cout << endl;                                                            \
    }                                                                          \
  }
#define Return(ans)                                                            \
  {                                                                            \
    cout << (ans) << endl;                                                     \
    return 0;                                                                  \
  }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void Ans(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
// const int mod = 998244353;
// #define Add(x, y) x = (x + (y)) % mod
// #define Mult(x, y) x = (x * (y)) % mod

using bset = bitset<50000>;

signed main() {

  int N, M, T;
  cin >> N >> M >> T;
  vec x(M), y(M);
  REP(i, M) {
    cin >> x[i] >> y[i];
    x[i]--;
    y[i]--;
  }

  if (T == 1) {
    vector<bset> b(N);
    REP(i, N) b[i][i] = 1;
    REP(i, M) {
      b[x[i]] |= b[y[i]];
      b[y[i]] = b[x[i]];
    }

    int f = -1;
    REP(i, N) if (b[i].count() == N) f = i;
    if (f == -1)
      Out(-1);
    else {
      // debug(f);
      string ans(M, '.');
      bset s;
      s[f] = 1;
      IREP(i, M) {
        if (s[y[i]])
          ans[i] = 'v';
        else
          ans[i] = '^';
        if (s[x[i]])
          s[y[i]] = 1;
        if (s[y[i]])
          s[x[i]] = 1;
      }
      Out(ans);
    }

  } else {
    assert(false);
  }

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using gpp_set = tree<T, null_type, less<T>, rb_tree_tag,
tree_order_statistics_node_update>; template<typename T, typename L> using
gpp_map = tree<T, L, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using gpp_multiset = tree<T, null_type, less_equal<T>,
rb_tree_tag, tree_order_statistics_node_update>;*/
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  {                                                                            \
    cout << #v << "=" << endl;                                                 \
    REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                      \
    cout << endl;                                                              \
  }
#define mdebug(m)                                                              \
  {                                                                            \
    cout << #m << "=" << endl;                                                 \
    REP(i_debug, m.size()) {                                                   \
      REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }  \
      cout << endl;                                                            \
    }                                                                          \
  }
#define Return(ans)                                                            \
  {                                                                            \
    cout << (ans) << endl;                                                     \
    return 0;                                                                  \
  }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void Ans(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
// const int mod = 998244353;
// #define Add(x, y) x = (x + (y)) % mod
// #define Mult(x, y) x = (x * (y)) % mod

using bset = bitset<50000>;

signed main() {

  int N, M, T;
  cin >> N >> M >> T;
  vec x(M), y(M);
  REP(i, M) {
    cin >> x[i] >> y[i];
    x[i]--;
    y[i]--;
  }

  if (T == 1) {
    vector<bset> b(N);
    REP(i, N) b[i][i] = 1;
    REP(i, M) {
      b[x[i]] |= b[y[i]];
      b[y[i]] = b[x[i]];
    }

    int f = -1;
    REP(i, N) if (b[i].count() == N) f = i;
    if (f == -1)
      Out(-1);
    else {
      // debug(f);
      string ans(M, '.');
      bset s;
      s[f] = 1;
      IREP(i, M) {
        if (s[y[i]])
          ans[i] = 'v';
        else
          ans[i] = '^';
        if (s[x[i]])
          s[y[i]] = 1;
        if (s[y[i]])
          s[x[i]] = 1;
      }
      Out(ans);
    }

  } else {
    if (N == 2) {
      Out(-1);
      return 0;
    }
    string ans(M, '.');
    REP(i, M) {
      if (y[i] <= 2) {
        int i0 = -1;
        FOR(j, i + 1, M) if (y[j] <= 2) {
          i0 = j;
          break;
        }
        if (i0 == -1)
          ans[i] = '^';
        else {
          if (y[i] != x[i0] && y[i] != y[i0])
            ans[i] = 'v';
          else
            ans[i] = '^';
        }
      } else
        ans[i] = '^';
    }
    Out(ans);
  }

  return 0;
}