How to find the next larger permutation 1342 in lexicographic order? I followed the algorithm in Next Permutation Algorithm based on Lexicographic ordering and I found 2134. But we know that after 1342 the next larger permutation in fact is 1423, isn't it?
The next permutation of 1342
discrete mathematicspermutations
Best Answer
Following the algorithm given in this answer on $1342$, and using the dreaded 1-indexing to correspond with natural language "$1$st digit, $2$nd digit" etc.:
Find the largest $i$ such that the $i$th digit is less than the $(i+1)$st digit: this is $i=2$ (as $3<4$ but $4>2$).
Find the largest $j>2$ such that the $j$th digit is larger than the $2$nd digit: this is $j=3$ (as $3<4$ but $3>2$).
Swap the $2$nd and $3$rd digit: $1432$.
Reverse the order of all digits from $2$nd onwards (not including $2$nd): $1423$.
This produces $1423$ as expected.