Submission #956662

#	Time	Username	Problem	Language	Result	Execution time	Memory
956662		nguyennh	Bootfall (IZhO17_bootfall)	C++14	100 / 100	821 ms	7424 KiB

bootfall

#include<bits/stdc++.h>
#define el '\n'
#define int long long
using namespace std ;
 
const int MN = 5e5 + 10;
 
int n;
 
namespace sub_trau{
  int64_t dp[MN];
  
  // check whether existing a way to divide array into 2 parts with sum = x;
  void solve(){
    vector<int> a(n + 5);
    for ( int i = 1 ; i <= n ; i++ ) cin >> a[i];
    if (n & 1){
      cout << 0;
      return;
    }
    bool odd = false , even = false;
    for ( int i = 1 ; i <= n ; i++ ){
      odd |= (a[i] & 1);
      even |= (a[i] % 2 == 0);
    }
    if (odd && even){
      cout << 0;
      return;
    }
    int sum = accumulate(a.begin() + 1 , a.begin() + n + 1 , 0);
    int mn = *min_element(a.begin() + 1 , a.begin() + n + 1); 
    dp[0] = 1;
    for ( int i = 1 ; i <= n ; i++ ){
      for ( int j = sum ; j >= a[i] ; j-- ) dp[j] += dp[j - a[i]];
    }
    if (!dp[sum / 2] || (sum & 1)){
      cout << 0;
      return;
    }
    vector<int> ans , candidates;
    for ( int i = 1 ; i <= n ; i++ ) candidates.push_back(a[i]);
    for ( int val = odd ? 1 : 2 ; val <= sum - mn ; val += 2 ){
      int all = sum + val;
      candidates.push_back(val);
      for ( int j = all ; j >= val ; j-- ) dp[j] += dp[j - val];
      bool check = true;
      for ( int turn = 0 ; turn < n ; turn++ ){
        if (!check) break;
        int need = all - candidates[turn];
        if (need & 1){
          check = false;
          break;  
        }
        for ( int j = candidates[turn] ; j <= need / 2 ; j++ ){
          dp[j] -= dp[j - candidates[turn]];
        }
        if (!dp[need / 2]){
          check = false;
        }
        for ( int j = need / 2 ; j >= candidates[turn] ; j-- ) dp[j] += dp[j - candidates[turn]];
      }
      if (check) ans.push_back(val);
      candidates.pop_back();
      for ( int j = val ; j <= all ; j++ ) dp[j] -= dp[j - val];
    }
    cout << ans.size() << el;
    for ( auto x : ans ) cout << x << " ";
  }
}
 
namespace sub_final{
  const int mod = 1e9 + 7;
  
  int64_t dp[MN];
  bool choose[MN];
  
  void solve(){
    vector<int> a(n + 5);
    for ( int i = 1 ; i <= n ; i++ ) cin >> a[i];
    int sum = accumulate(a.begin() + 1 , a.begin() + n + 1 , 0);
    dp[0] = 1;
    for ( int i = 1 ; i <= n ; i++ ){
      for ( int j = sum ; j >= a[i] ; j-- ){
        dp[j] += dp[j - a[i]];
        dp[j] %= mod;
      }
    }
    if (!dp[sum / 2] || (sum & 1)){
      cout << 0;
      return;
    }
    memset(choose , true , sizeof(choose));
    for ( int i = 1 ; i <= n ; i++ ){
      vector<int64_t> ndp(MN + 5);
      for ( int j = 0 ; j < MN ; j++ ) ndp[j] = dp[j];
      for ( int j = a[i] ; j < MN ; j++ ) (ndp[j] += (mod - ndp[j - a[i]])) %= mod;
      for ( int val = 1 ; val < MN ; val++ ){
        int new_sum = sum - a[i] + val;
        if ((new_sum & 1) || (new_sum / 2 < val) || !ndp[new_sum / 2 - val]) choose[val] = false; 
      }
    }
    vector<int> ans;
    for ( int i = 1 ; i < MN ; i++ ){
      if (choose[i]) ans.push_back(i);
    }
    cout << ans.size() << el;
    for ( auto x : ans ) cout << x << " ";
  }
}
 
int32_t main (){
//  freopen("bootfall.inp" , "r" , stdin);
//  freopen("bootfall.out" , "w" , stdout);
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  if (n <= 30) sub_trau::solve();
  else sub_final::solve();
}

• Subtask 1: 6 / 6
• Subtask 2: 7 / 7
• Subtask 3: 15 / 15
• Subtask 4: 16 / 16
• Subtask 5: 21 / 21
• Subtask 6: 35 / 35