JavaScript Coding Test Course, Exploring Combinations

1. Introduction

Many developers prepare for coding tests to solve algorithm problems while preparing for employment. In particular, when using JavaScript, combination problems are one of the frequently encountered topics. Combinations deal with how to select a specific number of elements from a given set. In this article, we will clarify the concept of combinations and present algorithm problems utilizing this concept, detailing the solution process.

2. Concept of Combinations

A combination refers to the method of selecting a specific number of elements without regard to the order. For example, the combinations of selecting 2 elements from the set {A, B, C} are {A, B}, {A, C}, and {B, C}, totaling 3. Combinations can be calculated using the following mathematical formula.

  • nCk = n! / (k! * (n-k)!)

Here, n is the size of the set, k is the number of elements to be selected, and ! denotes factorial.

3. Algorithm Problem

Problem: Sum of Combinations

Given an integer array arr and an integer target. Find all combinations of elements from the array that sum up to target. Each combination should be considered the same even if the order of elements is different.

Input Example

  • arr = [2, 3, 6, 7]
  • target = 7

Output Example

  • Result: [[7], [2, 2, 3]]

4. Problem Solving Process

To solve this problem, we can use recursion and the backtracking technique. The considerations when designing the function are as follows.

  • If the sum of the currently selected elements equals the target, save that combination.
  • If the sum of the currently selected elements exceeds the target, terminate the function.
  • Iteratively select each element to create combinations.

4.1. JavaScript Code


function combinationSum(arr, target) {
    const results = [];
    
    function backtrack(start, path, sum) {
        if (sum === target) {
            results.push([...path]);
            return;
        }
        if (sum > target) {
            return;
        }
        
        for (let i = start; i < arr.length; i++) {
            path.push(arr[i]);
            backtrack(i, path, sum + arr[i]);
            path.pop();
        }
    }
    
    backtrack(0, [], 0);
    return results;
}

const arr = [2, 3, 6, 7];
const target = 7;
console.log(combinationSum(arr, target));

4.2. Code Analysis

The above code solves the problem through the following steps.

  1. Function Definition: Define the combinationSum function and declare the backtrack function internally to generate combinations.
  2. Recursive Call: After selecting each element, continue to explore combinations including that element recursively. Here, the variable start is used to ensure that already selected elements are not selected again.
  3. Sum Comparison: If the current sum sum equals the target, add the current combination path to the results array.
  4. Backtracking: After the recursive call, remove the selected element and move to the next element.

5. Time Complexity

The time complexity of this problem is O(2^n) in the worst case. This is because it involves deciding whether or not to include each element, leading to exploration of all possible combinations. Even though a worst-case scenario exists, if the number of combinations is relatively small, this method can still effectively solve the problem.

6. Conclusion

Today, we explored how to solve combination problems using JavaScript. We demonstrated that by understanding the concept of combinations and utilizing a recursive approach through backtracking, it is possible to effectively solve these problems. Since combination problems frequently appear in coding tests, understanding and practicing these problems is essential. I hope you enhance your skills by tackling various problems.

7. References

  • LeetCode - Algorithm problem-solving platform
  • GeeksforGeeks - Various data structures and algorithm courses