Problem p03179 (C++)

Buggy submission (status: Time Limit Exceeded):
// HTTF.cpp : このファイルには 'main'
// 関数が含まれています。プログラム実行の開始と終了がそこで行われます。
//

#include "bits/stdc++.h"
#define YES "YES"
#define NO "NO"
#define YESNO OUT(three(solve(), YES, NO))
#define ECHO OUT(solve())
#define three(A, B, C) ((A) ? (B) : (C))
#define FOR(i, a, b) for (LL i = (a); i < (LL)(b); i++)
#define EFOR(i, a, b) for (LL i = (a); i <= (LL)(b); i++)
#define RFOR(i, a, b) for (LL i = (a); i >= (LL)(b); i--)
#define REP(i, b) FOR(i, zero, b)
#define EREP(i, b) EFOR(i, zero, b)
#define RREP(i, b) RFOR(i, b, zero)
#define ALL(c) c.begin(), c.end()
#define UNIQUE(c)                                                              \
  sort(ALL(c));                                                                \
  c.erase(unique(ALL(c)), c.end())
#define MAX(c) (*max_element(ALL(c)))
#define MIN(c) (*min_element(ALL(c)))
#define MP make_pair
#define FI first
#define SE second
#define SI(x) (LL(x.size()))
#define PB push_back
#define DEBUG(a) OUT(a)
#define DEBUG2(a, b) OUT2(a, b)
#define cat cout << __LINE__ << endl
#define OUT(a) cout << (a) << endl
#define OUT2(a, b) cout << (a) << " " << (b) << endl
#define zero 0LL
#define int LL
#define pb emplace_back
#define eb pb

using namespace std;
template <typename T> inline void maximize(T &a, T b) { a = max(a, b); }
template <typename T> inline void minimize(T &a, T b) { a = min(a, b); }
template <typename T> inline bool middle(T a, T b, T c) {
  return b <= a && a <= c;
}
template <class T> inline bool MX(T &l, const T &r) {
  return l < r ? l = r, 1 : 0;
}
template <class T> inline bool MN(T &l, const T &r) {
  return l > r ? l = r, 1 : 0;
}
typedef long long LL;
typedef double ld;
typedef int ut;
typedef vector<ut> VI;
typedef vector<VI> VII;
typedef pair<ut, ut> pr;
typedef pair<ut, pr> ppr;
typedef vector<pr> Vpr;
typedef vector<ppr> Vppr;
typedef priority_queue<pr, Vpr, greater<pr>> PQ;
inline void outputVI(VI x) {
  REP(i, SI(x)) { cout << three(i, " ", "") << x[i]; }
  OUT("");
}
const int SIZE1 = 5e5 + 1000;
const int SIZE2 = 3010;
const int SIZE3 = 330;
const int SIZE = SIZE1;
const int MAPSIZE = 40;
const LL p = 7 + 1e9;
const LL INF = 1LL << 60;
const long double EPS = 1e-7;
typedef pair<ld, ut> pld;
#define endl "\n" // インタラクティブでは消す
ut N, M, K, L, Q, D, H, W;
// ut A,B,C,D,E,F,G,H,I,J,O,P,Q,R,T,U;

VI edges[SIZE];
LL vals[SIZE], maps2[SIZE2][SIZE2], answer = zero;
LL maps[SIZE2][SIZE2];
LL DP[SIZE2][SIZE2];
bool finished[SIZE2][SIZE2];
LL A[SIZE2][SIZE2];
string s;
LL sums[SIZE2][SIZE2];
bool finished2[SIZE2][SIZE2];
LL solve2(LL, LL);
LL sum(LL n, LL x) {
  if (x == 0)
    return 0;
  if (finished2[n][x])
    return sums[n][x];
  finished2[n][x];
  return sums[n][x] = (sum(n, x - 1) + solve2(n, x)) % p;
}
LL sum(LL n, LL a, LL b) {
  if (a > b)
    return 0;
  return (p + sum(n, b) - sum(n, a - 1)) % p;
}
LL solve2(LL n, LL k) {
  if (n == 0)
    return k == 1;
  if (finished[n][k])
    return DP[n][k];
  finished[n][k] = true;
  if (s[n - 1] == '<') {
    DP[n][k] = sum(n - 1, 1, k - 1);
  } else {
    DP[n][k] = sum(n - 1, k, n);
  }
  //	cout << n << " " << k << " " << DP[n][k] << endl;
  return DP[n][k];
}
LL solve() {
  cin >> N;
  cin >> s;
  s += '<';
  cout << solve2(N, N + 1) << endl;
  return 0;
}

//!!!!!!!!!!!!!!!!!!!実装を詰める!!!!!!!!!!!!!!!!!!!!!!!!!
signed main() {

  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(0);
  solve();
  cin >> N;
  return 0;
}


Fixed submission:
// HTTF.cpp : このファイルには 'main'
// 関数が含まれています。プログラム実行の開始と終了がそこで行われます。
//

#include "bits/stdc++.h"
#define YES "YES"
#define NO "NO"
#define YESNO OUT(three(solve(), YES, NO))
#define ECHO OUT(solve())
#define three(A, B, C) ((A) ? (B) : (C))
#define FOR(i, a, b) for (LL i = (a); i < (LL)(b); i++)
#define EFOR(i, a, b) for (LL i = (a); i <= (LL)(b); i++)
#define RFOR(i, a, b) for (LL i = (a); i >= (LL)(b); i--)
#define REP(i, b) FOR(i, zero, b)
#define EREP(i, b) EFOR(i, zero, b)
#define RREP(i, b) RFOR(i, b, zero)
#define ALL(c) c.begin(), c.end()
#define UNIQUE(c)                                                              \
  sort(ALL(c));                                                                \
  c.erase(unique(ALL(c)), c.end())
#define MAX(c) (*max_element(ALL(c)))
#define MIN(c) (*min_element(ALL(c)))
#define MP make_pair
#define FI first
#define SE second
#define SI(x) (LL(x.size()))
#define PB push_back
#define DEBUG(a) OUT(a)
#define DEBUG2(a, b) OUT2(a, b)
#define cat cout << __LINE__ << endl
#define OUT(a) cout << (a) << endl
#define OUT2(a, b) cout << (a) << " " << (b) << endl
#define zero 0LL
#define int LL
#define pb emplace_back
#define eb pb

using namespace std;
template <typename T> inline void maximize(T &a, T b) { a = max(a, b); }
template <typename T> inline void minimize(T &a, T b) { a = min(a, b); }
template <typename T> inline bool middle(T a, T b, T c) {
  return b <= a && a <= c;
}
template <class T> inline bool MX(T &l, const T &r) {
  return l < r ? l = r, 1 : 0;
}
template <class T> inline bool MN(T &l, const T &r) {
  return l > r ? l = r, 1 : 0;
}
typedef long long LL;
typedef double ld;
typedef int ut;
typedef vector<ut> VI;
typedef vector<VI> VII;
typedef pair<ut, ut> pr;
typedef pair<ut, pr> ppr;
typedef vector<pr> Vpr;
typedef vector<ppr> Vppr;
typedef priority_queue<pr, Vpr, greater<pr>> PQ;
inline void outputVI(VI x) {
  REP(i, SI(x)) { cout << three(i, " ", "") << x[i]; }
  OUT("");
}
const int SIZE1 = 5e5 + 1000;
const int SIZE2 = 3010;
const int SIZE3 = 330;
const int SIZE = SIZE1;
const int MAPSIZE = 40;
const LL p = 7 + 1e9;
const LL INF = 1LL << 60;
const long double EPS = 1e-7;
typedef pair<ld, ut> pld;
#define endl "\n" // インタラクティブでは消す
ut N, M, K, L, Q, D, H, W;
// ut A,B,C,D,E,F,G,H,I,J,O,P,Q,R,T,U;

VI edges[SIZE];
LL vals[SIZE], maps2[SIZE2][SIZE2], answer = zero;
LL maps[SIZE2][SIZE2];
LL DP[SIZE2][SIZE2];
bool finished[SIZE2][SIZE2];
LL A[SIZE2][SIZE2];
string s;
LL sums[SIZE2][SIZE2];
bool finished2[SIZE2][SIZE2];
LL solve2(LL, LL);
LL sum(LL n, LL x) {
  if (x == 0)
    return 0;
  if (finished2[n][x])
    return sums[n][x];
  finished2[n][x] = true;
  return sums[n][x] = (sum(n, x - 1) + solve2(n, x)) % p;
}
LL sum(LL n, LL a, LL b) {
  if (a > b)
    return 0;
  return (p + sum(n, b) - sum(n, a - 1)) % p;
}
LL solve2(LL n, LL k) {
  if (n == 0)
    return k == 1;
  if (finished[n][k])
    return DP[n][k];
  finished[n][k] = true;
  if (s[n - 1] == '<') {
    DP[n][k] = sum(n - 1, 1, k - 1);
  } else {
    DP[n][k] = sum(n - 1, k, n);
  }
  //	cout << n << " " << k << " " << DP[n][k] << endl;
  return DP[n][k];
}
LL solve() {
  cin >> N;
  cin >> s;
  s += '<';
  cout << solve2(N, N + 1) << endl;
  return 0;
}

//!!!!!!!!!!!!!!!!!!!実装を詰める!!!!!!!!!!!!!!!!!!!!!!!!!
signed main() {

  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(0);
  solve();
  cin >> N;
  return 0;
}