Solving the Two Sum Problem: Three Approaches in Java

The Two Sum problem is a classic algorithmic challenge that appears frequently in coding interviews and competitive programming. The problem statement is simple: given an array of integers and a target sum, find the indices of the two numbers that add up to the target sum. In this post, we'll explore three different approaches to solve this problem in Java.

Problem Statement

Given an array of integers nums and an integer target, return the indices of the two numbers such that they add up to the target.

Example

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

Best Approach

• Best way to solve this problem is using HashMap.
• Compute the difference between the target and the current element.
• If the difference exists in the HashMap, return the indices.

Approach 1: Two Pointer Technique

If the array is sorted, we can use the two-pointer technique to solve this problem efficiently.

Algorithm

1. Initialize two pointers: left at the start of the array and right at the end.
2. While left is less than right:
   • If the sum of nums[left] and nums[right] equals the target, return the indices.
   • If the sum is greater than the target, decrement the right pointer.
   • If the sum is less than the target, increment the left pointer.
3. If no solution is found, return [0, 0].

Code

public int[] twoSum(int[] nums, int target) {
    int left = 0;
    int right = nums.length - 1;

    while (left < right) {
        if (nums[left] + nums[right] == target) {
            return new int[]{left, right};
        } else if (nums[left] + nums[right] > target) {
            right--;
        } else {
            left++;
        }
    }
    return new int[]{0, 0};
}

Time Complexity

• Time Complexity: O(n)
• Space Complexity: O(1)

Approach 2: Brute Force

The brute force approach involves checking all possible pairs of numbers to find the solution. This approach has a time complexity of O(n^2).

Algorithm

1. Iterate through each element in the array.
2. For each element, iterate through the remaining elements to check if their sum equals the target.
3. If a pair is found, return their indices.
4. If no solution is found, return [0, 0].

Code

public int[] twoSum_2(int[] nums, int target) {
    for (int i = 0; i < nums.length; i++) {
        for (int j = i + 1; j < nums.length; j++) {
            if (nums[i] + nums[j] == target) {
                return new int[]{i, j};
            }
        }
    }
    return new int[]{0, 0};
}

Time Complexity

• Time Complexity: O(n^2)
• Space Complexity: O(1)

Approach 3: HashMap

The optimized approach uses a HashMap to store the elements and their indices. This approach has a time complexity of O(n).

Algorithm

1. Create a HashMap to store the elements and their indices.
2. Iterate through the array:
   • Calculate the difference between the target and the current element.
   • If the difference exists in the HashMap, return the indices.
   • Otherwise, add the current element and its index to the HashMap.
3. If no solution is found, return null.

Code

public int[] twoSum_3(int[] nums, int target) {
    Map<Integer, Integer> map = new HashMap<>();
    for (int i = 0; i < nums.length; i++) {
        int num = nums[i];
        int diff = target - num;
        if (map.containsKey(diff)) {
            return new int[]{i, map.get(diff)};
        }
        map.put(nums[i], i);
    }
    return null;
}

Time Complexity

• Time Complexity: O(n)
• Space Complexity: O(n)