#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
struct custom_hash
{
template<class T>
unsigned long long operator()(T v) const
{
unsigned long long x = v;
x += FIXED_RANDOM;
// x += 11400714819323198485ull;
// x = (x ^ (x >> 30)) * 13787848793156543929ull;
x = (x ^ (x >> 27)) * 10723151780598845931ull;
return x ^ (x >> 31);
}
};
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;
template<class T>
T randomize(T mod)
{
return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
template<class T>
void readi(T &x)
{
x = 0;
bool negative = false;
char c = ' ';
while (c < '-')
{
c = getchar();
}
if (c == '-')
{
negative = true;
c = getchar();
}
while (c >= '0')
{
x = x * 10 + (c - '0');
c = getchar();
}
if (negative)
{
x = -x;
}
}
template<class T>
void printi(T output)
{
if (output == 0)
{
putchar('0');
return;
}
if (output < 0)
{
putchar('-');
output = -output;
}
int buf[20], n = 0;
while(output)
{
buf[n] = ((output % 10));
output /= 10;
n++;
}
for (n--; n >= 0; n--)
{
putchar(buf[n] + '0');
}
return;
}
template<class T>
void ckmin(T &a, T b)
{
a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
return (b ? gcd(b, a % b) : a);
}
#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << (x) << endl
#define SZ(x) ((int) ((x).size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) (x).begin(), (x).end()
const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;
#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 113
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;
int N, L;
int arr[MAXN];
hash_table<int, int> dp[MAXN][2][2][MAXN];
int ans;
int states = 0;
int solve(int idx, bool lt, bool rt, int cc, int sum)
{
states++;
if (idx == N)
{
// if (sum <= L && lt == 1 && rt == 1 && cc == 1) DBG(sum);
return ((sum <= L && lt == 1 && rt == 1 && cc == 1) ? 1 : 0);
}
if (dp[idx][lt][rt][cc].find(sum) != dp[idx][lt][rt][cc].end())
{
return dp[idx][lt][rt][cc][sum];
}
ll res = 0;
if (!lt)
{
//latch onto the left!
res += solve(idx + 1, 1, rt, cc, sum + arr[idx]);
//create a new one on the left!
res += solve(idx + 1, 1, rt, cc + 1, sum - arr[idx]);
}
if (!rt)
{
//latch onto the right!
res += solve(idx + 1, lt, 1, cc, sum + arr[idx]);
//create a new one on the right!
res += solve(idx + 1, lt, 1, cc + 1, sum - arr[idx]);
}
//create a new connected component that's by itself!
res += 1ll * (cc + 1 - lt - rt) * solve(idx + 1, lt, rt, cc + 1, sum - 2 * arr[idx]);
//join two connected components!
if (cc > 1) res += 1ll * (cc - 1) * solve(idx + 1, lt, rt, cc - 1, sum + 2 * arr[idx]);
//latch on right!
res += 1ll * (cc - rt) * solve(idx + 1, lt, rt, cc, sum);
//latch on left!
res += 1ll * (cc - lt) * solve(idx + 1, lt, rt, cc, sum);
res %= INF;
dp[idx][lt][rt][cc][sum] = res;
// cerr << idx << ' ' << lt << ' ' << rt << ' ' << cc << ' ' << sum << ' ' << res << endl;
return res;
}
int32_t main()
{
ios_base::sync_with_stdio(0); cin.tie(0);
// cout << fixed << setprecision(10);
// cerr << fixed << setprecision(10);
// if (fopen("file.in", "r"))
// {
// freopen ("file.in", "r", stdin);
// freopen ("file.out", "w", stdout);
// }
cin >> N >> L;
if (N == 1)
{
cout << "1\n";
return 0;
}
FOR(i, 0, N)
{
cin >> arr[i];
}
sort(arr, arr + N);
if (arr[N - 1] - arr[0] > L)
{
cout << "0\n";
return 0;
}
ans = solve(1, 0, 0, 1, -2 * arr[0]); nmod(ans, INF);
ans += solve(1, 1, 0, 1, -arr[0]); nmod(ans, INF);
ans += solve(1, 0, 1, 1, -arr[0]); nmod(ans, INF);
cout << ans << '\n';
//when we place a # down, we can either say: ok new left spot open! ok new right spot open! ok new nothing open!
//dp of:
//total sum,
// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
return 0;
}
/* READ READ READ
* int overflow, maxn too small, special cases (n=1?, two distinct?), cin.tie() interactive
* reread the problem, try small cases
* note down possible sources of error as you go
* do smth instead of nothing
*/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
16 ms |
11136 KB |
Output is correct |
| 2 |
Correct |
17 ms |
11136 KB |
Output is correct |
| 3 |
Correct |
22 ms |
11128 KB |
Output is correct |
| 4 |
Correct |
21 ms |
11256 KB |
Output is correct |
| 5 |
Correct |
20 ms |
11520 KB |
Output is correct |
| 6 |
Correct |
21 ms |
11520 KB |
Output is correct |
| 7 |
Correct |
18 ms |
11136 KB |
Output is correct |
| 8 |
Correct |
22 ms |
11264 KB |
Output is correct |
| 9 |
Correct |
24 ms |
11520 KB |
Output is correct |
| 10 |
Correct |
16 ms |
11264 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
22 ms |
11512 KB |
Output is correct |
| 2 |
Correct |
42 ms |
13796 KB |
Output is correct |
| 3 |
Correct |
19 ms |
11684 KB |
Output is correct |
| 4 |
Correct |
32 ms |
13820 KB |
Output is correct |
| 5 |
Correct |
48 ms |
14328 KB |
Output is correct |
| 6 |
Correct |
29 ms |
12920 KB |
Output is correct |
| 7 |
Correct |
23 ms |
12152 KB |
Output is correct |
| 8 |
Correct |
24 ms |
11648 KB |
Output is correct |
| 9 |
Correct |
24 ms |
11748 KB |
Output is correct |
| 10 |
Correct |
33 ms |
13148 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
16 ms |
11136 KB |
Output is correct |
| 2 |
Correct |
17 ms |
11136 KB |
Output is correct |
| 3 |
Correct |
22 ms |
11128 KB |
Output is correct |
| 4 |
Correct |
21 ms |
11256 KB |
Output is correct |
| 5 |
Correct |
20 ms |
11520 KB |
Output is correct |
| 6 |
Correct |
21 ms |
11520 KB |
Output is correct |
| 7 |
Correct |
18 ms |
11136 KB |
Output is correct |
| 8 |
Correct |
22 ms |
11264 KB |
Output is correct |
| 9 |
Correct |
24 ms |
11520 KB |
Output is correct |
| 10 |
Correct |
16 ms |
11264 KB |
Output is correct |
| 11 |
Correct |
22 ms |
11512 KB |
Output is correct |
| 12 |
Correct |
42 ms |
13796 KB |
Output is correct |
| 13 |
Correct |
19 ms |
11684 KB |
Output is correct |
| 14 |
Correct |
32 ms |
13820 KB |
Output is correct |
| 15 |
Correct |
48 ms |
14328 KB |
Output is correct |
| 16 |
Correct |
29 ms |
12920 KB |
Output is correct |
| 17 |
Correct |
23 ms |
12152 KB |
Output is correct |
| 18 |
Correct |
24 ms |
11648 KB |
Output is correct |
| 19 |
Correct |
24 ms |
11748 KB |
Output is correct |
| 20 |
Correct |
33 ms |
13148 KB |
Output is correct |
| 21 |
Correct |
434 ms |
45192 KB |
Output is correct |
| 22 |
Execution timed out |
2076 ms |
180728 KB |
Time limit exceeded |
| 23 |
Halted |
0 ms |
0 KB |
- |
