For a given number, n, generate all combinations of balanced parentheses.

1-gen-parentheses.js

function generateCombinationsRec(n, numOpen, numClosed, combo, result) {
  // base case - length of the combination is n * 2
  if (combo.length === n * 2) {
    result.push(combo);
    return;
  }

  // can we add an opening bracket to the current combination?
  // yes if number of opening brackets in the combination is less than n
  // so we add it, and pass it further to add more brackets, incrementing numOpen
  if (numOpen < n) {
    generateCombinationsRec(n, numOpen + 1, numClosed, `${combo}(`, result);
  }

  // can we also add a closing bracket?
  // yes if number of closing brackets is less than open brackets
  // add it and pass further
  if (numClosed < numOpen) {
    generateCombinationsRec(n, numOpen, numClosed + 1, `${combo})`, result);
  }
}

export function generateCombinations(n) {
  const result = [];
  generateCombinationsRec(n, 0, 0, "", result);
  return result;
}

2-README.md