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Submission #853286

# Submission time Handle Problem Language Result Execution time Memory
853286 2023-09-23T22:37:14 Z golions Skyscraper (JOI16_skyscraper) C++14
100 / 100
 124 ms 5148 KB 
#include <bits/stdc++.h>
//connected components dp practice

using namespace std;

const long long MOD = 1000000007LL;

void add(long long& x, long long y){
   x += y;
   if(x >= MOD) x -= MOD;
}

long long mul(long long a, long long b){
   return (a*b + MOD)%MOD;
}

//# of ways for n (mod 2), # of components, L, # of ends used(0, 1, or 2)
long long dp[2][101][1001][3];

int main(){
   ios::sync_with_stdio(false);
   cin.tie(0);
   
   int n, L;
   cin >> n >> L;
   
   vector<int> array(n);
   for(int k = 0; k < n; k++){
      cin >> array[k];
   }
   
   sort(array.begin(),array.end());
   
   if(n == 1){
      cout << 1 << endl;
      return 0;
   }
   if(n == 2){
      if(array[1] - array[0] <= L){
         cout << 2 << endl;
      } else {
         cout << 0 << endl;
      }
      return 0;
   }
   
   //n >= 3
   //add first element in middle
   dp[0][1][0][0] = 1LL;
   //add on either end
   dp[0][1][0][1] = 2LL;
   
   int newcost;
   for(int k = 0; k < n-1; k++){
      int from = k&1;
      int to = from^1;
      
      int diff = array[k+1] - array[k];
      for(int j = 1; j <= n; j++){
         long long jl = (long long)j;
         for(int h = 0; h <= L; h++){
            //# of ends used
            for(int g = 0; g <= 2; g++){
               newcost = h + diff * (j*2 - g);
               
               if(newcost <= L){
                  //add new component
                  if(j+1 <= n){
                     //add to middle (not an end)
                     add(dp[to][j+1][newcost][g], mul(dp[from][j][h][g],jl+1 - g));
                     
                     //add to end
                     if(g == 0){
                        //2 ends open, add once for each end
                        add(dp[to][j+1][newcost][1], dp[from][j][h][0]);
                        add(dp[to][j+1][newcost][1], dp[from][j][h][0]);
                     } else if(g == 1){
                        //1 end open
                        add(dp[to][j+1][newcost][2], dp[from][j][h][1]);
                     }
                  }
                  
                  //add to endpoint of component
                  
                  //add to middle (not an end)
                  add(dp[to][j][newcost][g], mul(dp[from][j][h][g], jl*2LL - g));
                  
                  //add to end
                  if(g == 0){
                     //2 ends open
                     add(dp[to][j][newcost][1], dp[from][j][h][0]);
                     add(dp[to][j][newcost][1], dp[from][j][h][0]);
                  } else if(g == 1){
                     //1 end open
                     add(dp[to][j][newcost][2], dp[from][j][h][1]);
                  }
                  
                  //join components
                  if(j >= 2){
                     add(dp[to][j-1][newcost][g], mul(dp[from][j][h][g], jl-1));
                  }
                     
               }
               
               //clear
               dp[from][j][h][g] = 0LL;
            }
            
            
         }
      }
   }
   
   long long answer = 0LL;
   for(int l = 0; l <= L; l++){
      add(answer,dp[n&1^1][1][l][2]);
   }
   
   cout << answer << endl;
   
   
   return 0;
}

Compilation message

skyscraper.cpp: In function 'int main()':
skyscraper.cpp:116:22: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
  116 |       add(answer,dp[n&1^1][1][l][2]);
      |                     ~^~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 2652 KB Output is correct
6 Correct 1 ms 2652 KB Output is correct
7 Correct 1 ms 2512 KB Output is correct
8 Correct 1 ms 344 KB Output is correct
9 Correct 1 ms 2652 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 1 ms 604 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 1 ms 604 KB Output is correct
6 Correct 1 ms 604 KB Output is correct
7 Correct 1 ms 2392 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 604 KB Output is correct
10 Correct 1 ms 604 KB Output is correct

Subtask #3
80.0 / 80.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 2652 KB Output is correct
6 Correct 1 ms 2652 KB Output is correct
7 Correct 1 ms 2512 KB Output is correct
8 Correct 1 ms 344 KB Output is correct
9 Correct 1 ms 2652 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 1 ms 344 KB Output is correct
12 Correct 1 ms 604 KB Output is correct
13 Correct 1 ms 604 KB Output is correct
14 Correct 1 ms 2652 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 604 KB Output is correct
17 Correct 1 ms 2392 KB Output is correct
18 Correct 1 ms 604 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 1 ms 604 KB Output is correct
21 Correct 1 ms 856 KB Output is correct
22 Correct 115 ms 4088 KB Output is correct
23 Correct 120 ms 5148 KB Output is correct
24 Correct 109 ms 4700 KB Output is correct
25 Correct 123 ms 5140 KB Output is correct
26 Correct 114 ms 4956 KB Output is correct
27 Correct 40 ms 2392 KB Output is correct
28 Correct 54 ms 2652 KB Output is correct
29 Correct 104 ms 3932 KB Output is correct
30 Correct 124 ms 4952 KB Output is correct