Two Sum IV - O(n) Time Complexity in JavaScript

Given an array of integers, return indices of the two numbers such that they add up to a specific target.

You may assume that each input will have at most one solution, and you may not use the same index twice.

In case no solution exists, return [-1, -1]

Example:

Input: nums = [2, 7, 11, 15], target = 9
Output: [0, 1]
Explanation: nums[0] + nums[1] = 2 + 7 = 9

Note:

Your algorithm should run in O(n) time and use O(n) space.

Understanding the Problem

The core challenge of this problem is to find two indices in an array such that the sum of the elements at these indices equals a given target. This problem is significant in various applications, such as financial transactions, where you need to find pairs of transactions that sum up to a specific amount.

Potential pitfalls include assuming multiple solutions or using the same index twice, which the problem explicitly forbids.

Approach

To solve this problem, we can start with a naive approach and then optimize it:

Naive Solution

The naive solution involves using two nested loops to check all possible pairs of indices. This approach has a time complexity of O(n^2), which is not optimal for large arrays.

Optimized Solution

To achieve an O(n) time complexity, we can use a hash map (or dictionary) to store the elements and their indices as we iterate through the array. This allows us to check in constant time whether the complement of the current element (i.e., target - current element) exists in the hash map.

Algorithm

Here is a step-by-step breakdown of the optimized algorithm:

Initialize an empty hash map.
Iterate through the array.
For each element, calculate its complement (target - current element).
Check if the complement exists in the hash map.
If it exists, return the indices of the current element and its complement.
If it doesn't exist, add the current element and its index to the hash map.
If no solution is found, return [-1, -1].

Code Implementation

/**
 * Function to find two indices such that their elements sum up to the target.
 * @param {number[]} nums - Array of integers.
 * @param {number} target - Target sum.
 * @return {number[]} - Indices of the two numbers.
 */
function twoSum(nums, target) {
    // Initialize an empty hash map
    const indexMap = new Map();

    // Iterate through the array
    for (let j = 0; j < nums.length; j++) {
        // Calculate the complement
        const complement = target - nums[j];

        // Check if the complement exists in the hash map
        if (indexMap.has(complement)) {
            // Return the indices of the current element and its complement
            return [indexMap.get(complement), j];
        }

        // Add the current element and its index to the hash map
        indexMap.set(nums[j], j);
    }

    // If no solution is found, return [-1, -1]
    return [-1, -1];
}

// Example usage:
const nums = [2, 7, 11, 15];
const target = 9;
console.log(twoSum(nums, target)); // Output: [0, 1]

Complexity Analysis

The time complexity of this approach is O(n) because we iterate through the array once. The space complexity is also O(n) due to the hash map storing up to n elements.

Edge Cases

Potential edge cases include:

Empty array: The function should return [-1, -1].
Array with one element: The function should return [-1, -1].
No solution exists: The function should return [-1, -1].

To test these edge cases, you can use the following examples:

console.log(twoSum([], 9)); // Output: [-1, -1]
console.log(twoSum([1], 9)); // Output: [-1, -1]
console.log(twoSum([1, 2, 3], 7)); // Output: [-1, -1]

Testing

To test the solution comprehensively, you can use a variety of test cases, from simple to complex. Here are some examples:

console.log(twoSum([2, 7, 11, 15], 9)); // Output: [0, 1]
console.log(twoSum([3, 2, 4], 6)); // Output: [1, 2]
console.log(twoSum([3, 3], 6)); // Output: [0, 1]

Thinking and Problem-Solving Tips

When approaching such problems, it's essential to:

Understand the problem requirements and constraints.
Start with a brute force solution to understand the basic logic.
Think about how to optimize the solution using data structures like hash maps.
Practice similar problems to improve problem-solving skills.

Conclusion

In this blog post, we discussed the Two Sum problem, its significance, and how to solve it optimally using a hash map. We also covered edge cases, testing, and provided tips for problem-solving. Understanding and solving such problems is crucial for improving algorithmic thinking and coding skills.

Additional Resources

For further reading and practice, consider the following resources: