# Two Sum

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

You may assume that each input would have exactly one solution, and you may not use the same element twice.

You can return the answer in any order.

**Example 1:**

**Input: **nums = [2,7,11,15], target = 9

**Output: **[0,1]

**Output:** Because nums[0] + nums[1] == 9, we return [0, 1].

**Example 2:**

**Input: **nums = [3,2,4], target = 6

**Output:** [1,2]

**Example 3:**

**Input: **nums = [3,3], target = 6

**Output: **[0,1]

**Constraints:**

- 2 <= nums.length <= 104
- -109 <= nums[i] <= 109
- -109 <= target <= 109
**Only one valid answer exists.**

**Follow-up: **Can you come up with an algorithm that is less than O(n2) time complexity?

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## All replies

Brute ForceThe brute force approach is simple. Loop through each element xx and find if there is another value that equals to target - x

Java code:`public int[] twoSum(int[] nums, int target) { for (int i = 0; i < nums.length; i++) { for (int j = i + 1; j < nums.length; j++) { if (nums[j] == target - nums[i]) { return new int[] { i, j }; } } } throw new IllegalArgumentException("No two sum solution"); }`

Complexity Analysis

Time complexity : O(n^2). For each element, we try to find its complement by looping through the rest of array which takes O(n) time. Therefore, the time complexity is O(n^2).

Space complexity : O(1).

One-pass Hash TableIt turns out we can do it in one-pass. While we iterate and inserting elements into the table, we also look back to check if current element's complement already exists in the table. If it exists, we have found a solution and return immediately.

Java code:`public int[] twoSum(int[] nums, int target) { Map<Integer, Integer> map = new HashMap<>(); for (int i = 0; i < nums.length; i++) { int complement = target - nums[i]; if (map.containsKey(complement)) { return new int[] { map.get(complement), i }; } map.put(nums[i], i); } throw new IllegalArgumentException("No two sum solution"); }`

Complexity Analysis:Time complexity :O(n). We traverse the list containing nn elements only once. Each look up in the table costs only O(1) time.Space complexity :O(n). The extra space required depends on the number of items stored in the hash table, which stores at most nn elements.good!