What is the algorithm of thinking recursive? (on the specific example)

Question

I just can\'t wrap my head around recursion. I understand all of the concepts (breaking solution into smaller cases) and I can understand solutions after I read them over an

Answer 1

I think recursion is the more intuitive way of solving if you get familiar with it. Simple rule is that imagine your function as a combination of the same function with smaller inputs. There are cases where recursion is more visible than others. For example permutations is one such case. Just imagine permut(S) = List{a+permut(S-{a})} for all a in S where S consists of unique characters. Idea is to select a character in string and concatenate it with all permutations of the remaining characters this will give all unique permutations of string starting with that character.

Example pseudo code : -

Permutation(S,List) {

    if(S.length>0) {

        for all a in S {

            Permutation(S.remove(a),List.add(a));
        }

    }

    else  print List;

 }

The above code is according to me most simple to understand for permutation because it directly translates the recurrence relation where in we select a character from string and then concatenate it all other combinations of smaller string.

Note:- This can be done more efficiently using array and swapping but it is more complex for understanding.