#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif
/*
refs:
https://usaco.guide/problems/joi-2016skyscraper/solution
read it long back, recollected the ideas from there when solving the problem
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
void solve(int test_case)
{
ll n,m; cin >> n >> m;
vector<ll> a(n+5);
rep1(i,n) cin >> a[i];
sort(a.begin()+1,a.begin()+n+1);
a[n+1] = inf1;
if(n == 1){
cout << 1 << endl;
return;
}
ll dp[n+5][n+5][m+5][2][2];
memset(dp,0,sizeof dp);
dp[1][0][0][0][0] = 1;
rep1(i,n){
ll d = a[i+1]-a[i];
rep(j,n+1){
rep(k,m+1){
rep(x,2){
rep(y,2){
dp[i][j][k][x][y] %= MOD;
ll val = dp[i][j][k][x][y];
// new
{
ll spaces = 2*(j+1)-x-y;
ll k2 = k+spaces*d;
if(k2 >= 0 and k2 <= m){
dp[i+1][j+1][k2][x][y] += val;
}
}
// connect to 1 comp
{
ll spaces = 2*j-x-y;
ll k2 = k+spaces*d;
if(k2 >= 0 and k2 <= m){
dp[i+1][j][k2][x][y] += val*spaces;
}
}
// connect to 2 comps
{
ll spaces = 2*(j-1)-x-y;
ll k2 = k+spaces*d;
if(k2 >= 0 and k2 <= m){
ll ways = 0;
// both non-spl
ways += (j-x-y)*(j-x-y-1);
amax(ways,0ll);
// x
if(x){
ways += j-1;
}
// y
if(y){
ways += j-1;
}
// x and y
if(x and y){
if(i == n) ways--;
else ways -= 2;
}
dp[i+1][j-1][k2][x][y] += val*ways;
}
}
// left end
if(!x){
// new
{
ll spaces = 2*(j+1)-(x|1)-y;
ll k2 = k+spaces*d;
if(k2 >= 0 and k2 <= m){
dp[i+1][j+1][k2][x|1][y] += val;
}
}
// connect to 1 comp
{
ll spaces = 2*j-(x|1)-y;
ll k2 = k+spaces*d;
ll ways = j;
if(y and i != n) ways--;
if(k2 >= 0 and k2 <= m){
dp[i+1][j][k2][x|1][y] += val*ways;
}
}
}
// right end
if(!y){
// new
{
ll spaces = 2*(j+1)-x-(y|1);
ll k2 = k+spaces*d;
if(k2 >= 0 and k2 <= m){
dp[i+1][j+1][k2][x][y|1] += val;
}
}
// connect to 1 comp
{
ll spaces = 2*j-x-(y|1);
ll k2 = k+spaces*d;
ll ways = j;
if(x and i != n) ways--;
if(k2 >= 0 and k2 <= m){
dp[i+1][j][k2][x][y|1] += val*ways;
}
}
}
}
}
}
}
}
ll ans = 0;
rep(k,m+1){
ans += dp[n+1][1][k][1][1];
}
ans %= MOD;
cout << ans << endl;
}
int main()
{
fastio;
int t = 1;
// cin >> t;
rep1(i, t) {
solve(i);
}
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
1 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
344 KB |
Output is correct |
| 4 |
Correct |
1 ms |
676 KB |
Output is correct |
| 5 |
Correct |
6 ms |
5468 KB |
Output is correct |
| 6 |
Correct |
5 ms |
4700 KB |
Output is correct |
| 7 |
Correct |
2 ms |
1112 KB |
Output is correct |
| 8 |
Correct |
1 ms |
860 KB |
Output is correct |
| 9 |
Correct |
5 ms |
5268 KB |
Output is correct |
| 10 |
Correct |
1 ms |
1116 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
860 KB |
Output is correct |
| 2 |
Correct |
2 ms |
1368 KB |
Output is correct |
| 3 |
Correct |
1 ms |
860 KB |
Output is correct |
| 4 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 5 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 6 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 7 |
Correct |
1 ms |
604 KB |
Output is correct |
| 8 |
Correct |
1 ms |
860 KB |
Output is correct |
| 9 |
Correct |
2 ms |
1112 KB |
Output is correct |
| 10 |
Correct |
2 ms |
1372 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
1 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
344 KB |
Output is correct |
| 4 |
Correct |
1 ms |
676 KB |
Output is correct |
| 5 |
Correct |
6 ms |
5468 KB |
Output is correct |
| 6 |
Correct |
5 ms |
4700 KB |
Output is correct |
| 7 |
Correct |
2 ms |
1112 KB |
Output is correct |
| 8 |
Correct |
1 ms |
860 KB |
Output is correct |
| 9 |
Correct |
5 ms |
5268 KB |
Output is correct |
| 10 |
Correct |
1 ms |
1116 KB |
Output is correct |
| 11 |
Correct |
1 ms |
860 KB |
Output is correct |
| 12 |
Correct |
2 ms |
1368 KB |
Output is correct |
| 13 |
Correct |
1 ms |
860 KB |
Output is correct |
| 14 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 15 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 16 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 17 |
Correct |
1 ms |
604 KB |
Output is correct |
| 18 |
Correct |
1 ms |
860 KB |
Output is correct |
| 19 |
Correct |
2 ms |
1112 KB |
Output is correct |
| 20 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 21 |
Correct |
4 ms |
3160 KB |
Output is correct |
| 22 |
Correct |
340 ms |
178764 KB |
Output is correct |
| 23 |
Correct |
549 ms |
341160 KB |
Output is correct |
| 24 |
Correct |
432 ms |
258132 KB |
Output is correct |
| 25 |
Correct |
563 ms |
345172 KB |
Output is correct |
| 26 |
Correct |
470 ms |
293972 KB |
Output is correct |
| 27 |
Correct |
158 ms |
86356 KB |
Output is correct |
| 28 |
Correct |
194 ms |
105716 KB |
Output is correct |
| 29 |
Correct |
344 ms |
199584 KB |
Output is correct |
| 30 |
Correct |
551 ms |
347016 KB |
Output is correct |
