Light OJ 1060 – nth Permutation

Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1060


/*
         +-+ +-+ +-+
         |R| |.| |S|
         +-+ +-+ +-+
 */

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             10000
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sfl(a)          scanf("%lld",&a)
#define sff(a,b)        scanf("%d %d",&a,&b)
#define sffl(a,b)       scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)     scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)    scanf("%lld %lld %lld",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<=b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d: ",z)
#define CASE_PRINT      cout<<"Case "<<z<<": ";
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

ll fact[30];

int main()
{
    CIN;
    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    fact[0]=1;

    REP(i,1,22) fact[i]=fact[i-1]*i;

    int t;
    cin>>t;
    TEST_CASE(t)
    {
        string s1;
        int n;
        cin>>s1>>n;
        int cnt[30]= {0};

        loop(i,SZ(s1)) cnt[s1[i]-'a']++;

        int l=SZ(s1);

        ll valid=fact[l];

        loop(i,26)
            valid/=fact[cnt[i]];

        CASE_PRINT;

        if(valid<n)
        {
            cout<<"Impossible"<<endl;
            continue;
        }

        while(l>0)
        {
            ll x=fact[l-1];

            for(int i=0; i<26; i++)
            {
                if(cnt[i])
                {
                    loop(j,26)
                    {
                        if(i==j)
                            x/=fact[cnt[i]-1];
                        else
                            x/=fact[cnt[j]];
                    }


                    if(x>=n)
                    {
                        cout<<(char)('a'+i);
                        l--;
                        cnt[i]--;
                        break;
                    }
                    else
                    {
                        n-=x;
                        x=fact[l-1];
                    }
                }


            }
        }
        cout<<endl;

    }

    return 0;
}

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