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
Your algorithm should run in O(n log n) time and use O(n) extra space.
The core challenge of this problem is to find two distinct indices in the array such that the sum of the elements at these indices equals the target value. 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 that there are multiple solutions or using the same index twice, which is not allowed.
To solve this problem, we can use a hash map to store the difference between the target and each element as we iterate through the array. This allows us to check in constant time whether the complement of the current element exists in the hash map.
Let's discuss a naive solution first:
The naive approach involves using two nested loops to check all possible pairs of elements. This solution has a time complexity of O(n^2), which is not optimal for large arrays.
An optimized solution involves using a hash map to store the indices of the elements as we iterate through the array. This allows us to find the complement of the current element in constant time, resulting in an overall time complexity of O(n).
Here is a step-by-step breakdown of the optimized algorithm:
import java.util.HashMap;
public class TwoSum {
public int[] twoSum(int[] nums, int target) {
// Create a hash map to store the indices of the elements
HashMap<Integer, Integer> map = new HashMap<>();
// Iterate through the array
for (int i = 0; i < nums.length; i++) {
// Calculate the complement
int complement = target - nums[i];
// Check if the complement exists in the hash map
if (map.containsKey(complement)) {
// Return the indices of the current element and its complement
return new int[] { map.get(complement), i };
}
// Add the current element and its index to the hash map
map.put(nums[i], i);
}
// If no solution is found, return [-1, -1]
return new int[] { -1, -1 };
}
}
The time complexity of this solution is O(n) because we iterate through the array once. The space complexity is also O(n) because we store the indices of the elements in a hash map.
Potential edge cases include:
To test the solution comprehensively, consider the following test cases:
When approaching such problems, consider the following tips:
In this blog post, we discussed the Two Sum II problem and provided a detailed solution using a hash map to achieve an optimal time complexity of O(n). We also covered edge cases, testing, and tips for approaching such problems. Understanding and solving such problems is crucial for improving your algorithmic thinking and coding skills.
For further reading and practice, consider the following resources: