// naive version
// assumption: seq == {0, ..., n - 1} as set
bool johnson_trotter(std::vector<int>& seq)
{
assert(seq.size() <= std::numeric_limits<int>::max());
const int n = seq.size();
std::vector<int> invseq(n, 0);
for (int i = 0; i < n; ++i) {
invseq[seq[i]] = i;
}
// step 1
std::vector<int> y(n, 0);
for (int i = 0; i < n; ++i) {
int sign = sgn(invseq.begin(), invseq.begin() + i);
y[i] = invseq[i] - sign;
}
// step 2
int i = n - 1;
while (i >= 0) {
if ((0 <= y[i] && y[i] < n) && seq[y[i]] < i) {
break;
}
i--;
}
// last permutation
if (i < 0) {
return false;
}
std::swap(seq[invseq[i]], seq[y[i]]);
return true;
}
string getPermutation(int n, int k) {
vector<int> invseq(n,0);
for( int i=1;i<k;++i){
int j=n-1;
while(j>=0 && invseq[j]==n-1-j)--j;
if (j==-1)invseq=vector<int>(n,0);
else{
++invseq[j];
while(++j<n)invseq[j]=0;
}
}
string seq(n,0),perm(n,0);
//cout<<vector2string<int>(invseq)<<endl;
for (int i=0;i<n;++i)seq[i]='1'+i;
for (int i=0;i<n;++i){
perm[i]=seq[invseq[i]];
seq.erase(invseq[i],1);
}
return perm;
}