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Submission #867191

# Submission time Handle Problem Language Result Execution time Memory
867191 2023-10-27T20:24:18 Z NotLinux Magneti (COCI21_magneti) C++17
110 / 110
 950 ms 35920 KB 
#include "bits/stdc++.h"
using namespace std;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#define pb push_back
#define endl "\n" 
#define int long long
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()


constexpr int MOD = (int) 1e9 + 7;

inline int add(int a,int b){
  if(a+b >= MOD)return a+b-MOD;
  else return a+b;
}

inline int mult(int a,int b){
  return (a*b)%MOD;
}

inline int fast(int a,int b){
  if(b==0) return 1;
  int res=fast(a,b/2);
  res=mult(res,res);
  if(b&1) res=mult(res,a);
  return res;
}

void solve(){

  int n,l;
  cin >> n >> l;
  
  vector<int> ar;

  int fact[10005];
  int inv_fact[10005];
  fact[0]=1;
  for(int i=1;i<10005;i++) fact[i]=mult(i,fact[i-1]);
  
  inv_fact[10004]=fast(fact[10004],MOD-2);

  for(int i=10003;i>=0;i--) inv_fact[i]=mult(inv_fact[i+1],i+1);

  for(int i=1;i<=n;i++){
    int a;
    cin >> a;
    ar.pb(a);
  }

  if(n==1){
    cout << l << endl;
    return;
  }

  sort(all(ar));
  reverse(all(ar));

  int dp[n+6][l+6][4];
  int ndp[n+6][l+6][4];
  
  memset(dp,0,sizeof(dp));
  memset(ndp,0,sizeof(ndp));

  dp[0][0][0]=1;

  for(int i=0;i<n;i++){

    // merge 
    for(int j=2;j<=n;j++){
       for(int x=0;x<l;x++){
         for(int fl=0;fl<=2;fl++){
           ndp[j-1][x+1][fl]=add(ndp[j-1][x+1][fl],mult(j-1,dp[j][x][fl]));
         }
       }
    }

    // extend
    for(int j=1;j<=n;j++){
       for(int x=0;x<=l;x++){
         for(int fl=0;fl<=2;fl++){
           if(x+ar[i]<=l) ndp[j][x+ar[i]][fl]=add(ndp[j][x+ar[i]][fl],mult(2*j-fl,dp[j][x][fl]));
           if(fl+1<=2 && x+1<=l) ndp[j][x+1][fl+1]=add(ndp[j][x+1][fl+1],mult(2-fl,dp[j][x][fl]));
         }
       }
    }
  
    // create1
    for(int j=0;j<n;j++){
      for(int x=0;x+2*ar[i]-1<=l;x++){
        for(int fl=0;fl<=2;fl++){
          ndp[j+1][x+2*ar[i]-1][fl]=add(ndp[j+1][x+2*ar[i]-1][fl],mult(j+1-fl,dp[j][x][fl]));
        }
      }
    }

    // create2
    for(int j=0;j<n;j++){
      for(int x=0;x+ar[i]<=l;x++){
        for(int fl=0;fl<2;fl++){
          ndp[j+1][x+ar[i]][fl+1]=add(ndp[j+1][x+ar[i]][fl+1],mult(2-fl,dp[j][x][fl]));
        }
      }
    }

    //swap values

    memset(dp,0,sizeof(dp));

    for(int j=0;j<=n;j++)
      for(int x=0;x<=l;x++)
        for(int fl=0;fl<=2;fl++)
          dp[j][x][fl]=ndp[j][x][fl];

    memset(ndp,0,sizeof(ndp));
  }
  
  int ans=0;
  for(int x=0;x<=l;x++){
    ans=add(ans,mult(mult(fact[n+l-x],mult(inv_fact[n],inv_fact[l-x])),dp[1][x][2]));
  }

  cout << ans << '\n';
}

int32_t main(){

  cin.tie(0); ios::sync_with_stdio(0);
  
  int t=1;//cin >> t;
  while(t--) solve();

  return 0;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 938 ms 35920 KB Output is correct
2 Correct 4 ms 600 KB Output is correct
3 Correct 33 ms 9380 KB Output is correct
4 Correct 8 ms 6492 KB Output is correct
5 Correct 40 ms 5468 KB Output is correct
6 Correct 260 ms 19804 KB Output is correct
7 Correct 260 ms 18820 KB Output is correct
8 Correct 1 ms 600 KB Output is correct
9 Correct 86 ms 12380 KB Output is correct
10 Correct 1 ms 600 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 32 ms 10784 KB Output is correct
2 Correct 3 ms 3420 KB Output is correct
3 Correct 32 ms 10588 KB Output is correct
4 Correct 6 ms 5212 KB Output is correct
5 Correct 33 ms 10612 KB Output is correct
6 Correct 7 ms 3924 KB Output is correct
7 Correct 32 ms 10504 KB Output is correct
8 Correct 5 ms 1372 KB Output is correct
9 Correct 5 ms 4188 KB Output is correct
10 Correct 0 ms 348 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 1112 KB Output is correct
2 Correct 3 ms 860 KB Output is correct
3 Correct 8 ms 1296 KB Output is correct
4 Correct 4 ms 1124 KB Output is correct
5 Correct 8 ms 1116 KB Output is correct
6 Correct 1 ms 1112 KB Output is correct
7 Correct 9 ms 1292 KB Output is correct
8 Correct 1 ms 860 KB Output is correct
9 Correct 3 ms 860 KB Output is correct
10 Correct 1 ms 860 KB Output is correct

Subtask #4
50.0 / 50.0

# Verdict Execution time Memory Grader output
1 Correct 938 ms 35920 KB Output is correct
2 Correct 4 ms 600 KB Output is correct
3 Correct 33 ms 9380 KB Output is correct
4 Correct 8 ms 6492 KB Output is correct
5 Correct 40 ms 5468 KB Output is correct
6 Correct 260 ms 19804 KB Output is correct
7 Correct 260 ms 18820 KB Output is correct
8 Correct 1 ms 600 KB Output is correct
9 Correct 86 ms 12380 KB Output is correct
10 Correct 1 ms 600 KB Output is correct
11 Correct 32 ms 10784 KB Output is correct
12 Correct 3 ms 3420 KB Output is correct
13 Correct 32 ms 10588 KB Output is correct
14 Correct 6 ms 5212 KB Output is correct
15 Correct 33 ms 10612 KB Output is correct
16 Correct 7 ms 3924 KB Output is correct
17 Correct 32 ms 10504 KB Output is correct
18 Correct 5 ms 1372 KB Output is correct
19 Correct 5 ms 4188 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 8 ms 1112 KB Output is correct
22 Correct 3 ms 860 KB Output is correct
23 Correct 8 ms 1296 KB Output is correct
24 Correct 4 ms 1124 KB Output is correct
25 Correct 8 ms 1116 KB Output is correct
26 Correct 1 ms 1112 KB Output is correct
27 Correct 9 ms 1292 KB Output is correct
28 Correct 1 ms 860 KB Output is correct
29 Correct 3 ms 860 KB Output is correct
30 Correct 1 ms 860 KB Output is correct
31 Correct 942 ms 35672 KB Output is correct
32 Correct 531 ms 23964 KB Output is correct
33 Correct 948 ms 35672 KB Output is correct
34 Correct 153 ms 14736 KB Output is correct
35 Correct 950 ms 35676 KB Output is correct
36 Correct 44 ms 9272 KB Output is correct
37 Correct 917 ms 35676 KB Output is correct
38 Correct 119 ms 6236 KB Output is correct
39 Correct 918 ms 35680 KB Output is correct
40 Correct 268 ms 20288 KB Output is correct
41 Correct 945 ms 35672 KB Output is correct
42 Correct 6 ms 2396 KB Output is correct
43 Correct 912 ms 35920 KB Output is correct
44 Correct 69 ms 10840 KB Output is correct
45 Correct 927 ms 35664 KB Output is correct
46 Correct 4 ms 5212 KB Output is correct
47 Correct 167 ms 18128 KB Output is correct
48 Correct 66 ms 6996 KB Output is correct
49 Correct 12 ms 7260 KB Output is correct
50 Correct 2 ms 860 KB Output is correct