Submission #598577

#	Time	Username	Problem	Language	Result	Execution time	Memory
598577		CaroLinda	NoM (RMI21_nom)	C++14	100 / 100	229 ms	204868 KiB

Main

#include <bits/stdc++.h>

#define ll long long

const ll MOD = 1e9+7LL;
const int MAX = 4010;

using namespace std;

int N, M;
int qtdMod[MAX], moduloHere[MAX];
ll dp[MAX][MAX][2]; //flag pra falar se devo escolher livres ou duplas
ll bin[MAX][MAX];
ll fat[MAX], pot[MAX];

void calcBin(){
    bin[0][0] = 1;

    for(int i = 1; i <= 2*N; i++){
        bin[i][0]=1;

        for(int j = 1; j <= 2*N; j++){
            bin[i][j] = (bin[i-1][j]+bin[i-1][j-1]);
            if(bin[i][j] >= MOD)
                bin[i][j] -= MOD;
        }
    }
}

void calcFat(){
    fat[0] = 1;
    for(int i = 1; i <= 2*N; i++)
        fat[i] = (fat[i-1] * i) % MOD;
}

void calcPot(){
    pot[0] = 1;
    for(int i = 1; i <= 2*N; i++)
        pot[i] = (pot[i-1] << 1LL) % MOD;
}

int getQuantity(int x){
    return qtdMod[moduloHere[x]%M]-x;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    cin >> N >> M;

    calcBin();
    calcFat();
    calcPot();

    for(int i = 0; i < 2*N; i++)
        qtdMod[i%M]++;

    int ant = 0;
    for(int i = 0; i < M; i++){
        for(int q = qtdMod[i]; q > 0; q--,ant++ )
            moduloHere[ant] = i;
    }

    for(int i = 1; i < M; i++)
        qtdMod[i] += qtdMod[i-1];

    dp[2*N][0][0] = dp[2*N][0][1] = 1;

    for(int i = 2*N-1; i >= 0; i--)
        for(int j = 0; j <= min(i,N); j++){
            int foram = ((i-j)>>1)+j;

            if(foram > N)
                continue;

            int faltam = N-foram;
            int qtdModLeft = getQuantity(i);

            if(faltam >= qtdModLeft){
                ll jeito = (bin[faltam][qtdModLeft] * fat[qtdModLeft] ) % MOD;
                jeito *= pot[qtdModLeft];
                jeito %= MOD;

                ll qMod = qtdMod[moduloHere[i]]-(moduloHere[i] == 0 ? 0 : qtdMod[moduloHere[i]-1]);
                qMod = bin[qMod][qtdModLeft];

                (jeito *= qMod) %= MOD;

                dp[i][j][1] = jeito  * dp[qtdMod[moduloHere[i]]][j+qtdModLeft][0];
                dp[i][j][1] %= MOD;
            }


            dp[i][j][0] = dp[i][j][1];

            if(j){
                dp[i][j][0] += ( dp[i+1][j-1][0] * j ) % MOD;
                if(dp[i][j][0] >= MOD)
                    dp[i][j][0] -= MOD;
            }
        }

    cout << dp[0][0][0] << "\n";
}

• Subtask 1: 9 / 9
• Subtask 2: 12 / 12
• Subtask 3: 13 / 13
• Subtask 4: 18 / 18
• Subtask 5: 48 / 48