Bittilista

#include <iostream>
#include <vector>
#include <string>
#include <utility>

using namespace std;
typedef long long LL;

LL DP[60][2][120];

LL count(LL L, LL b, LL d){
    if(DP[L][b][d + 60] == -1){
        if(b == 1)
            DP[L][b][d + 60] = count(L-1,1,d) + count(L-1,0,d-1);
        else
            DP[L][b][d + 60] = count(L-1,0,d) + count(L-1,1,d+1);
    }
    return DP[L][b][d + 60];
}

int main(){
    
    for(int i = 0; i < 60; i++)
        for(int j = 0; j < 2; j++)
            for(int k = 0; k < 120; k++)
                DP[i][j][k] = -1;
    
    for(int i = 0; i < 120; i++) DP[1][0][i] = 0;
    for(int i = 0; i < 120; i++) DP[1][1][i] = 0;
    DP[1][0][0 + 60] = 1;
    DP[1][1][0 + 60] = 1;
    
    //cout << "total: " << count(6,0,0) << " " << count(5,0,-1) << " " << count(3,0,0) << endl;    
    //return 0;
    
    LL n, k;
    cin >> n >> k;
    
    // 10 -> +
    // 01 -> -
    string s = "";
    LL balance = 0;
    LL skipped = 0;
    
    if(count(n, 0, 0) >= k){
        s += '0';
    } else{
        s += '1';
        skipped += count(n, 0, 0);
    }
    
    for(int i = 1; i < n; i++){
        //cout << skipped << " " << balance << " " << s << endl;
        if(s.back() == '0'){
            if(skipped + count(n-i,0,-balance) >= k){
                s += '0';
            }
            else{
                s += '1';
                skipped += count(n-i,0,-balance);
                balance--;
            }
        }
        else if(s.back() == '1'){
            if(skipped + count(n-i,0,-(balance+1)) >= k){
                s += '0';
                balance++;
            }
            else{
                s += '1';
                skipped += count(n-i,0,-(balance+1));
            }
        }
    }
    
    cout << s << endl;
}

Test 1

Group: 1

Verdict: ACCEPTED

Test 2

Group: 1

Verdict: ACCEPTED

Test 3

Group: 1

Verdict: ACCEPTED

Test 4

Group: 1

Verdict: ACCEPTED

Test 5

Group: 1

Verdict: ACCEPTED

Test 6

Group: 2

Verdict: ACCEPTED

Test 7

Group: 2

Verdict: ACCEPTED

Test 8

Group: 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: ACCEPTED

Test 10

Group: 2

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: ACCEPTED

Test 15

Group: 3

Verdict: ACCEPTED