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

Alex Brothers Posted on 3/7/2022 Hello coders! Today we will be discussing the various solutions to the Problem Statement 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] Explanation: 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 map = new HashMap(); 9 for ( int i = 0 ; i < nums.length; i++) Time Complexity If the number of elements in the array is n, in the worst case we are visiting n elements. We are simply visiting every element at most one time, meaning the time complexity is linear, or O(n). Space Complexity In this solution, we are using an auxiliary data structure to keep track of the elements and their index. This means that in the worst case, we are storing n elements, meaning the space complexity is linear, or O(n). Conclusion The two sum problem can be solved in O(n) time and O(n) space. All the code can be found on Recommended Blogs • •

@Test fun twoSum () public int [] twoSum ( int [] nums , int target )

• Archive • About This Blog • Source Code & Binaries • • • Hot Articles • Coding • • • • • • • • • • • • • • Linux • List of Online Tools • • • • List of Software (Freeware) • Forum • • • SEO, WordPress, Coding for the Web • Data Structure & Algorithms • Shell Scripting & Database • Programming Languages • • Algorithms • • • • • • Teaching Kids Programming • Hardware • • • • 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] Two Sum Algorithm using Hash Table Using Hashmap is very common in accelerating solutions and reducing algorithm complexity. A Hashmap is a data structure that is aimed for high performance lookup, indexing items etc. In C++, you can use std::map to create a hash map, also known as associate array that maps a key to a value (keypair). In Java, this is similar via java.util.Hashtable We use hash map to make solutions faster. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 class Solution ; class Solution ; However, the same solution, rewritten in Java gets accepted in 684ms. ( why?) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 public class Solution public class Solution With Hashmap, we can reduce the running time to O(n) (and O(n) space). In C++, the following code is accepted in 60ms. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 #include using namespace std ; ...

• • • • Question: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] Explanation: Because nums 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 ] Explanation: 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 <= 1 0 4 - − 1 0 9 <= nums [ i ] <= 1 0 9 - − 1 0 9 <= target <= 1 0 9 - Only one valid answer exists. We discussed this problem at the start of the semester and gave a naïve answer to it that ran in O ( n 2 ) time. Your job now is to write a new solution that runs in O ( n ) time. Test your answer by submitting it to leetcode and ensuring that your answer runs faster than at least 90% of the submissions ever uploaded there (this problem has over 16 million submissions so far). Previous question Next question

@Test fun twoSum () public int [] twoSum ( int [] nums , int target )

• • • • Question: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] Explanation: Because nums 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 ] Explanation: 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 <= 1 0 4 - − 1 0 9 <= nums [ i ] <= 1 0 9 - − 1 0 9 <= target <= 1 0 9 - Only one valid answer exists. We discussed this problem at the start of the semester and gave a naïve answer to it that ran in O ( n 2 ) time. Your job now is to write a new solution that runs in O ( n ) time. Test your answer by submitting it to leetcode and ensuring that your answer runs faster than at least 90% of the submissions ever uploaded there (this problem has over 16 million submissions so far). Previous question Next question

• Archive • About This Blog • Source Code & Binaries • • • Hot Articles • Coding • • • • • • • • • • • • • • Linux • List of Online Tools • • • • List of Software (Freeware) • Forum • • • SEO, WordPress, Coding for the Web • Data Structure & Algorithms • Shell Scripting & Database • Programming Languages • • Algorithms • • • • • • Teaching Kids Programming • Hardware • • • • 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] Two Sum Algorithm using Hash Table Using Hashmap is very common in accelerating solutions and reducing algorithm complexity. A Hashmap is a data structure that is aimed for high performance lookup, indexing items etc. In C++, you can use std::map to create a hash map, also known as associate array that maps a key to a value (keypair). In Java, this is similar via java.util.Hashtable We use hash map to make solutions faster. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 class Solution ; class Solution ; However, the same solution, rewritten in Java gets accepted in 684ms. ( why?) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 public class Solution public class Solution With Hashmap, we can reduce the running time to O(n) (and O(n) space). In C++, the following code is accepted in 60ms. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 #include using namespace std ; ...

• • • • Question: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] Explanation: Because nums 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 ] Explanation: 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 <= 1 0 4 - − 1 0 9 <= nums [ i ] <= 1 0 9 - − 1 0 9 <= target <= 1 0 9 - Only one valid answer exists. We discussed this problem at the start of the semester and gave a naïve answer to it that ran in O ( n 2 ) time. Your job now is to write a new solution that runs in O ( n ) time. Test your answer by submitting it to leetcode and ensuring that your answer runs faster than at least 90% of the submissions ever uploaded there (this problem has over 16 million submissions so far). Previous question Next question

@Test fun twoSum () public int [] twoSum ( int [] nums , int target )

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 <= 10 4 • -10 9<= nums[i] <= 10 9 • -10 9<= target <= 10 9 • Only one valid answer exists. class Solution Time complexity – O(n 2) Space complexity – O(1) Approach 2: Using HashMap to store difference with index class Solution Time complexity – O(n) Space complexity – O(n)