#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
const int MAXN = 105;
int n, L, a[MAXN];
long long dp[MAXN][MAXN][1005][3];
int main(){
cin >> n >> L;
for(int i = 1; i <= n; ++i) cin >> a[i];
sort(a + 1, a + n + 1);
if(n == 1){
cout << 1; return 0;
}
dp[0][0][0][0] = 1;
for(int i = 1; i <= n; ++i){
for(int j = 1; j <= i; ++j){
for(int k = 0; k <= L; ++k){
for(int m = 0; m < 3; ++m){
// first i numbers, j components, k is sum, m endpoints filled
int dif = (a[i + 1] - a[i]) * (2 * j - m);
if((i != n && m > j) || k < dif) continue;
// create new component that isnt endpoint
dp[i][j][k][m] += dp[i - 1][j - 1][k - dif][m];
// create new component that is endpoint
if(m) dp[i][j][k][m] += dp[i - 1][j - 1][k - dif][m - 1] * (3 - m);
// append on edge of component
dp[i][j][k][m] += dp[i - 1][j][k - dif][m] * (2 * j - m);
// append end on component
if(m == 1) dp[i][j][k][m] += dp[i - 1][j][k - dif][m - 1] * 2 * j;
else if(m == 2){
if(i < n) dp[i][j][k][m] += dp[i - 1][j][k - dif][m - 1] * (j - 1);
else dp[i][j][k][m] += dp[i - 1][j][k - dif][m - 1];
}
// merge two components
if(i == n){
dp[i][j][k][m] += dp[i - 1][j + 1][k - dif][m];
} else {
dp[i][j][k][m] += dp[i - 1][j + 1][k - dif][m] * (j * (j + 1) - m * j);
}
dp[i][j][k][m] %= MOD;
}
}
}
}
long long ans = 0;
for(int i = 0; i <= L; ++i) ans += dp[n][1][i][2];
cout << ans % MOD;
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
340 KB |
Output is correct |
| 4 |
Correct |
0 ms |
468 KB |
Output is correct |
| 5 |
Correct |
1 ms |
852 KB |
Output is correct |
| 6 |
Correct |
1 ms |
852 KB |
Output is correct |
| 7 |
Correct |
1 ms |
468 KB |
Output is correct |
| 8 |
Correct |
1 ms |
468 KB |
Output is correct |
| 9 |
Correct |
2 ms |
980 KB |
Output is correct |
| 10 |
Correct |
1 ms |
468 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
724 KB |
Output is correct |
| 2 |
Correct |
1 ms |
724 KB |
Output is correct |
| 3 |
Correct |
1 ms |
852 KB |
Output is correct |
| 4 |
Correct |
1 ms |
736 KB |
Output is correct |
| 5 |
Correct |
1 ms |
852 KB |
Output is correct |
| 6 |
Correct |
1 ms |
852 KB |
Output is correct |
| 7 |
Correct |
2 ms |
724 KB |
Output is correct |
| 8 |
Correct |
1 ms |
852 KB |
Output is correct |
| 9 |
Correct |
1 ms |
852 KB |
Output is correct |
| 10 |
Correct |
1 ms |
724 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
340 KB |
Output is correct |
| 4 |
Correct |
0 ms |
468 KB |
Output is correct |
| 5 |
Correct |
1 ms |
852 KB |
Output is correct |
| 6 |
Correct |
1 ms |
852 KB |
Output is correct |
| 7 |
Correct |
1 ms |
468 KB |
Output is correct |
| 8 |
Correct |
1 ms |
468 KB |
Output is correct |
| 9 |
Correct |
2 ms |
980 KB |
Output is correct |
| 10 |
Correct |
1 ms |
468 KB |
Output is correct |
| 11 |
Correct |
1 ms |
724 KB |
Output is correct |
| 12 |
Correct |
1 ms |
724 KB |
Output is correct |
| 13 |
Correct |
1 ms |
852 KB |
Output is correct |
| 14 |
Correct |
1 ms |
736 KB |
Output is correct |
| 15 |
Correct |
1 ms |
852 KB |
Output is correct |
| 16 |
Correct |
1 ms |
852 KB |
Output is correct |
| 17 |
Correct |
2 ms |
724 KB |
Output is correct |
| 18 |
Correct |
1 ms |
852 KB |
Output is correct |
| 19 |
Correct |
1 ms |
852 KB |
Output is correct |
| 20 |
Correct |
1 ms |
724 KB |
Output is correct |
| 21 |
Correct |
2 ms |
3284 KB |
Output is correct |
| 22 |
Correct |
101 ms |
67208 KB |
Output is correct |
| 23 |
Correct |
111 ms |
78724 KB |
Output is correct |
| 24 |
Correct |
102 ms |
76856 KB |
Output is correct |
| 25 |
Correct |
114 ms |
79164 KB |
Output is correct |
| 26 |
Correct |
107 ms |
74008 KB |
Output is correct |
| 27 |
Correct |
47 ms |
42188 KB |
Output is correct |
| 28 |
Correct |
56 ms |
48844 KB |
Output is correct |
| 29 |
Correct |
96 ms |
74372 KB |
Output is correct |
| 30 |
Correct |
119 ms |
79460 KB |
Output is correct |
