JavaScript: Bracket Combinations challenge

Introduction

Brackets are an essential component of programming languages and are commonly used for grouping expressions. In this coding challenge, we will focus on generating all possible combinations of valid brackets using JavaScript and recursion.

Problem Statement

Given a number n, we need to generate all possible combinations of n pairs of brackets. For example, when n is 3, the possible combinations are:

• “((()))”
• “(()())”
• “(())()”
• “()(())”
• “()()()”

Approach

To solve this problem, we can use a recursive approach. We will define a recursive function that takes three parameters: the current bracket combination, the number of opening brackets used, and the number of closing brackets used.

1. Start the recursive function with an empty string and both opening and closing brackets count set to 0.
2. If the combined length of opening and closing brackets equal to 2 * n, we have generated a valid combination. Add it to the result array and return.
3. If the number of opening brackets is less than n, we can add an opening bracket and recursively call the function with an updated combination and increment the count of opening brackets.
4. If the number of closing brackets is less than the number of opening brackets, we can add a closing bracket and recursively call the function with an updated combination and increment the count of closing brackets.

JavaScript Implementation

Here’s the JavaScript implementation for the bracket combinations challenge:

function generateBracketCombinations(n) {
  const combinations = [];

  function generate(current, open, close) {
    if (current.length === 2 * n) {
      combinations.push(current);
      return;
    }

    if (open < n) {
      generate(current + "(", open + 1, close);
    }

    if (close < open) {
      generate(current + ")", open, close + 1);
    }
  }

  generate("", 0, 0);
  return combinations;
}

const n = 3;
const combinations = generateBracketCombinations(n);
console.log(combinations);

Example Output

For n = 3, the output will be:

[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]

Complexity Analysis

The time complexity for this approach is O(2^n) as there are 2^n combinations possible. The space complexity is O(n) to store the valid combinations.

Conclusion

In this coding challenge, we explored how to generate all possible combinations of brackets using JavaScript and recursion. This problem can be solved by using a recursive approach and carefully keeping track of the count of opening and closing brackets. By understanding this concept, you can improve your problem-solving skills and understanding of recursion in JavaScript.