Java Coding Test Course, What Algorithm Should I Use?

1. Problem Description

The following is a problem of finding indices of two numbers in a given array that sum up to a specific value.

Problem: Given an array nums and an integer target, return the indices of the two numbers such that they add up to target. Each input has exactly one solution, and you may not use the same element twice. The returned indices should be zero-based and returned as an array.

Example:

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

2. Problem Analysis

This problem is a very common one that has been asked multiple times. As we need to find two numbers in the given array, the first method that comes to mind is using a nested loop. However, this method has a time complexity of O(n²) and is inefficient.

Using the optimal method, we can solve the problem with a time complexity of O(n). This method will approach the problem by using a hashmap for searching.

3. Algorithm Design

We will design the algorithm in the following steps:

1. Create an empty hashmap.
2. Iterate through all the numbers.
3. For each number, check if target - current number exists in the hashmap.
4. If it exists, return the two indices; if not, add the current number to the hashmap.

The key point of this algorithm is to find the two numbers in a single iteration.

4. Java Code Implementation

Now, let’s write the code to solve this problem using Java.

import java.util.HashMap;

public class TwoSum {
    public static int[] findTwoSum(int[] nums, int target) {
        HashMap numMap = new HashMap<>();
        for (int i = 0; i < nums.length; i++) {
            int complement = target - nums[i];
            if (numMap.containsKey(complement)) {
                return new int[] { numMap.get(complement), i };
            }
            numMap.put(nums[i], i);
        }
        throw new IllegalArgumentException("No two sum solution");
    }

    public static void main(String[] args) {
        int[] nums = {2, 7, 11, 15};
        int target = 9;
        int[] result = findTwoSum(nums, target);

        System.out.println("Indices: [" + result[0] + ", " + result[1] + "]");
    }
}

The above code solves the problem in a very simple yet efficient way. It uses a HashMap to store the indices of each number and calculates the difference with the target for searching.

5. Time Complexity Analysis

The time complexity of this algorithm is O(n). Here, n is the length of the input array. Both the operations of adding numbers to the hashmap and searching have an average time complexity of O(1), allowing the entire iteration process to be O(n). The space complexity is also O(n) because we store as many numbers as the input numbers in the hashmap.

6. Additional Considerations

When solving this problem, there are a few additional considerations:

• In case of duplicate numbers: the same number should not be used twice.
• Performance of the hashmap: Java's hashmap has an average time complexity of O(1). However, if the input follows a specific pattern, it can reach O(n) in the worst case.
• Exception handling: appropriate exceptions should be thrown in case there is no solution.

7. Conclusion

Today, we learned about using hashmaps as an algorithm to solve a specific programming problem. As the ability to apply such skills in practical situations is important, it is advisable to practice by solving various problems. It is essential to continuously strive to improve your algorithm problem-solving skills for employment.