Problem p03128 (C++)

Buggy submission (status: Time Limit Exceeded):

// include
//------------------------------------------
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;

// conversion
//------------------------------------------
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}

// math
//-------------------------------------------
template <class T> inline T sqr(T x) { return x * x; }

// typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;

// container util
//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i, c)                                                             \
  for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define EXISTch(s, c)                                                          \
  ((((s).find_first_of(c)) != std::string::npos) ? 1 : 0) // cがあれば1 if(1)
#define SORT(c) sort((c).begin(), (c).end())

#define REP(i, n) for (int i = 0; i < (int)n; ++i)
#define FOR(i, c)                                                              \
  for (__typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)

// constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int INF = (int)1000000007;
const LL MOD = (LL)1000000007;          // 10^9+7
const LL INF2 = (LL)100000000000000000; // 10^18

int main() {

  int n, m;
  cin >> n >> m;
  vector<int> a(m);

  for (int i = 0; i < m; i++) {
    cin >> a[i];
  }

  sort(a.rbegin(), a.rend());

  vector<int> num = {-1, 2, 5, 5, 4, 5, 6, 3, 7, 6};
  vector<int> digit(5010, -1000000);

  digit[0] = 0;

  for (int i = 1; i < n + 1; i++) {

    for (int j = 0; j < m; j++) {

      int from = i - num[a[j]];
      if (from < 0)
        continue;

      digit[i] = max(digit[i], digit[from] + 1);
    }
  }

  while (n > 0) {
    for (int i = 0; i < m; i++) {
      if (n - num[a[i]] < 0)
        continue;

      if (digit[n - num[a[i]]] == (digit[n] - 1)) {
        cout << a[i];
        n -= num[a[i]];
        break;
      }
    }
  }

  cout << endl;

  return 0;
}

Fixed submission:

// include
//------------------------------------------
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;

// conversion
//------------------------------------------
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}

// math
//-------------------------------------------
template <class T> inline T sqr(T x) { return x * x; }

// typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;

// container util
//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i, c)                                                             \
  for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define EXISTch(s, c)                                                          \
  ((((s).find_first_of(c)) != std::string::npos) ? 1 : 0) // cがあれば1 if(1)
#define SORT(c) sort((c).begin(), (c).end())

#define REP(i, n) for (int i = 0; i < (int)n; ++i)
#define FOR(i, c)                                                              \
  for (__typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)

// constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int INF = (int)1000000007;
const LL MOD = (LL)1000000007;          // 10^9+7
const LL INF2 = (LL)100000000000000000; // 10^18

int main() {

  int n, m;
  cin >> n >> m;
  vector<int> a(m);

  for (int i = 0; i < m; i++) {
    cin >> a[i];
  }

  sort(a.rbegin(), a.rend());

  vector<int> num = {-1, 2, 5, 5, 4, 5, 6, 3, 7, 6};
  vector<int> digit(n + 1, -1000000);

  digit[0] = 0;

  for (int i = 1; i < n + 1; i++) {

    for (int j = 0; j < m; j++) {

      int from = i - num[a[j]];
      if (from < 0)
        continue;

      digit[i] = max(digit[i], digit[from] + 1);
    }
  }

  while (n > 0) {
    for (int i = 0; i < m; i++) {
      if (n - num[a[i]] < 0)
        continue;

      if (digit[n - num[a[i]]] == (digit[n] - 1)) {
        cout << a[i];
        n -= num[a[i]];
        break;
      }
    }
  }

  cout << endl;

  return 0;
}