Finding all combinations of well-formed brackets

Question

This came up while talking to a friend and I thought I\'d ask here since it\'s an interesting problem and would like to see other people\'s solutions.

The task is to

Answer 1

An attempt with memoization:

void push_strings(int i, int j ,vector> &T){
    for (int k=0; k< T[j].size(); ++k){
        for (int l=0; l< T[i - 1 - j].size(); ++l){
            string s = "(" + T[j][k] + ")" + T[i-1 - j][l];
            T[i].push_back(s);
        }
    }
}

vector generateParenthesis(int n) {
    vector> T(n+10);
    T[0] = {""};

    for (int i =1; i <=n; ++i){
        for(int j=0; j