Submission #741180

#	Time	Username	Problem	Language	Result	Execution time	Memory
741180		Sam_a17	Magneti (COCI21_magneti)	C++17	110 / 110	43 ms	26264 KiB

Main

/////////////////////include/////////////////////
//#include <bits/stdc++.h>
#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <string>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <cassert>
#include <set>
#include <map>
#include <unordered_map>
#include <vector>
#include <stack>
#include <queue>
#include <iomanip>
#include <bitset>
#include <stdio.h>
#include <climits>
#include <numeric>
using namespace std;
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//template <typename T>
//using ordered_set = tree <T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
/////////////////////define/////////////////////
#define ci(x) if(x) cout << "YES" << '\n'; else cout << "NO" << '\n';
#define cii(x) if(check(x))
#define MOD 1000000007
#define MOD2 998244353
#define oo 1e9
#define ool 1e18L
#define pii pair<int, int>
#define pll pair<long long, long long>
#define mii map<int, int>
#define vi vector<int>
#define vpi vector<pair<int, int>>
#define vll vector <ll>
#define ff first
#define ss second
#define mp make_pair
#define ll long long
#define ld long double
#define pb push_back
#define eb emplace_back
#define pob pop_back
#define lb lower_bound
#define ub upper_bound
#define bs binary_search
#define sz(x) (int((x).size()))
#define all(x) (x).begin(), (x).end()
#define alll(x) (x), (x) + n
#define clr(x) (x).clear();
#define fri(x) for(int i = 0; i < x; ++i)
#define frj(x) for(int j = 0; j < x; ++j)
#define frp(x) for(int p = 0; p < x; ++p)
#define frr(a, b) for(int i = a; i < b; ++i)
#define frrj(a, b) for(int j = a; j < b; ++j)
#define fra(x) for(int i = 0; i < x; ++i) cin >> a[i];
#define frb(x) for(int i = 0; i < x; ++i) cin >> b[i];
#define frs(x) for(auto it = x.begin(); it != x.end(); ++it)
#define fr(x) for(auto it : x) //el
#define fastio ios_base::sync_with_stdio(false); cin.tie(0);
#define dbg(x) cerr << #x << ": " << x << endl;
#define ce(x) cout << x << endl;
#define uniq(x) x.resize(unique(all(x)) - x.begin()); //make all one after sorting
#define blt __builtin_popcount
/////////////////////print array, vector, deque, set, multiset, pair, map /////////////////////
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(long double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T, class V> void print(T v[],V n) {cerr << "["; for(int i = 0; i < n; i++) {print(v[i]); cerr << " "; } cerr << "]"; cout << endl;}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(stack <T> v) {cerr << "[ "; stack<T> s = v; while(s.size()) {T i = s.top(); print(i); s.pop(); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(queue <T> v) {cerr << "[ "; queue<T> s = v; while(s.size()) {T i = s.front(); print(i); s.pop(); cerr << " ";} cerr << "]"; cout << endl;}
template <class T> void print(deque <T> v) {cerr << "[ "; deque<T> s = v; while(s.size()) {T i = s.front(); print(i); s.pop_front(); cerr << " ";} cerr << "]"; cout << endl;}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
template <class T, class V> void print(unordered_map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]"; cout << endl;}
/////////////////////code/////////////////////
ll a[55], dp[51][51][60002]; //i, j hat xumb ka, p hat tex enq zbaxacrel(datark texery radiusneri hety)
const int N=1e5;
ll fact[N+2], invFact[N+2];
long long power(long long a, int n) {
	if (n == 0) return 1;
	if (n % 2 == 0) {
		long long r = power(a, n / 2);
		return (r * r) % MOD;
	}
	return a * power(a, n - 1) % MOD;
}
ll cnk(int n, int k) {
    return (((fact[n] * invFact[k]) % MOD) * invFact[n - k]) % MOD;
}
void precalc() {
    fact[0] = 1;
    for(int i = 1; i <= N; i++)
        fact[i] = (fact[i - 1] * i) % MOD;
    invFact[N] = power(fact[N], MOD - 2); //(a / b) % p = a * (b ^ (p - 2) % p), 1 / f % p  = f ^ (p - 2) % p
    for(int i = N; i >= 1; i--) //(invF(i-1)^(p-2))%p=((invF(i-1)*i)^(p-2)%p*i)%p=((invF(i)^(p-2)%p)*(i^p-2%p))*i%p=((invF(i)^p-2%p)*(1/i%p)*i)%p=(invF(i)^p-2%p)%p
        invFact[i - 1] = (invFact[i] * i) % MOD;
}
int main() {
    fastio;
    precalc();
    int n, l; 
    cin >> n >> l;
    fra(n) 
    sort(alll(a));
    dp[0][1][1] = 1; //1 voch te 3 vorovhetev heto vor urish ban avelacnenq inqy ed taracqy arden kzbaxacni
    for(int i = 0; i < n - 1; i++) {
        for(ll j = 1; j <= (i + 1); j++) {
            for(int p = 1; p < l; p++) {
                if(!dp[i][j][p]) continue;
                dp[i + 1][j + 1][p + 1] += dp[i][j][p];
                dp[i + 1][j + 1][p + 1] %= MOD;

                dp[i + 1][j][p + a[i + 1]] += dp[i][j][p] * 2 * j;
                dp[i + 1][j][p + a[i + 1]] %= MOD;

                dp[i + 1][j - 1][p + 2 * a[i + 1] - 1] += dp[i][j][p] * (((j * (j - 1)) % MOD));
                dp[i + 1][j - 1][p + 2 * a[i + 1] - 1] %= MOD;
            }
        }
    }
    ll ans = 0;
    for(int d = 1; d <= l; d++) {
        // dbg(d) dbg(dp[n-1][1][d]) dbg(n+l-d) dbg(l-d)
        ans += dp[n-1][1][d] * cnk(n+l-d, l-d); //l-d hat tex a mnacel
        ans %= MOD;
    }
    cout << ans;
    return 0;
}

//	           ♥ ♥ ♥  ♥  ♥    ♥   ♥    ♥
//	           ♥      ♥  ♥     ♥ ♥    ♥ ♥
//	           ♥ ♥ ♥  ♥  ♥      ♥    ♥   ♥
//	           ♥      ♥  ♥      ♥   ♥ ♥ ♥ ♥
//	           ♥      ♥  ♥ ♥ ♥  ♥  ♥       ♥
//
//        God loves Fil, Fil accepts God's will

• Subtask 1: 10 / 10
• Subtask 2: 20 / 20
• Subtask 3: 30 / 30
• Subtask 4: 50 / 50