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Head of Career Skills Development & Coaching

*Based on past data of successful IK students

Given an array and a target number, find the indices of the two values from the array that sum up to the given target number.

```
{
"numbers": [5, 3, 10, 45, 1],
"target": 6
}
```

Output:

```
[0, 4]
```

Sum of the elements at index 0 and 4 is 6.

```
{
"numbers": [4, 1, 5, 0, -1],
"target": 10
}
```

Output:

```
[-1, -1]
```

- The function returns an array of size two where the two elements specify the input array indices whose values sum up to the given target number.
- In case when no answer exists, return an array of size two with both values equal to -1, i.e.,
`[-1, -1]`

. - In case when multiple answers exist, you may return any of them.
- The order of the returned indices does not matter.
- A single index cannot be used twice.

Constraints:

- 2 <= array size <= 10
^{5} - -10
^{5}<= array elements <= 10^{5} - -10
^{5}<= target number <= 10^{5} - Array can contain duplicate elements.

We provided two solutions.

Throughout this editorial, we will refer to the input array as `numbers`

, its size as `numbers_size`

and the target integer as `target`

.

A brute force is to run two nested loops and check the sum of every pair of elements present in the array. If any pair sums up to the `target`

, we will return the indices of that pair of elements.

Otherwise, we will return `[-1, -1]`

.

O((numbers_size)^{2}).

Total number of possible pairs: `(numbers_size * (numbers_size - 1)) / 2`

.

O(1).

O(numbers_size).

Space used for input: O(numbers_size).

Auxiliary space used: O(1).

Space used for output: O(1).

So, total space complexity: O(numbers_size).

```
/*
* Asymptotic complexity in terms of the size of \`numbers\` = \`n\`:
* Time: O(n^2).
* Auxiliary space: O(1).
* Total space: O(n).
*/
static ArrayList<Integer> two_sum(ArrayList<Integer> numbers, Integer target) {
// A list to store the pair of indices that adds to target.
ArrayList<Integer> result = new ArrayList<Integer>();
for (int i = 0; i < numbers.size(); i++) {
// For every element in numbers we find it complementary pair that sum to
// target.
for (int j = i + 1; j < numbers.size(); j++) {
if (numbers.get(i) + numbers.get(j) == target) {
result.add(i);
result.add(j);
return result;
}
}
}
// If no such pair of indices exist, add -1, -1 to list.
result.add(-1);
result.add(-1);
return result;
}
```

While iterating through the array, let say we are at a number `current`

. Being at this number, we need to check whether `target - current`

has occurred at a smaller index in the array or not.

To check the occurrence of `target - current`

, one way is to run another loop on the array to linearly search for that element. But as discussed above, this won’t be very efficient.

We can check whether `target - current`

has previously occurred in the array or not in O(1) time using hashing. We will maintain a hashmap which stores the index of an element present in the array and will keep building this hashmap as we iterate through the array. Now, being at any number `current`

, we will use this hashmap to check whether `target - current`

has previously occurred in the array or not. If it has occurred, we will store the current index and the index of `target - current`

in an array of size two and return it.

In case we didn’t find any such pair after the complete traversal of the array, we will return `[-1, -1]`

.

O(numbers_size).

We iterate through each element in the `numbers`

array exactly once and are doing a constant amount of work in each iteration.

O(numbers_size).

At most, we will be storing all the elements in the hashmap.

O(numbers_size).

Space used for input: O(numbers_size).

Auxiliary space used: O(numbers_size).

Space used for output: O(1).

So, total space complexity: O(numbers_size).

```
/*
* Asymptotic complexity in terms of the size of \`numbers\` = \`n\`:
* Time: O(n).
* Auxiliary space: O(n).
* Total space: O(n).
*/
static ArrayList<Integer> two_sum(ArrayList<Integer> numbers, Integer target) {
// A list to store the pair of indices that adds to target.
ArrayList<Integer> result = new ArrayList<Integer>();
// This Map stores the array element as Key and its index as Value.
HashMap<Integer, Integer> array_index = new HashMap<Integer, Integer>();
for (int i = 0; i < numbers.size(); i++) {
int current = numbers.get(i);
int required = target - current; // complementary target pair
if (array_index.containsKey(required)) {
result.add(array_index.get(required)); // store index of required in result
result.add(i);
return result;
}
// Add every element to map after checking for required.
// This ensures that element does not match itself (indices to be unique).
array_index.put(current, i);
}
// If no such pair of indices exist, add -1, -1 to list.
result.add(-1);
result.add(-1);
return result;
}
```

We hope that these solutions to the 2 Sum in an Array problem have helped you level up your coding skills. You can expect problems like these at top tech companies like Amazon and Google.

If you are preparing for a tech interview at FAANG or any other Tier-1 tech company, register for Interview Kickstart’s FREE webinar to understand the best way to prepare.

Interview Kickstart offers interview preparation courses taught by FAANG+ tech leads and seasoned hiring managers. Our programs include a comprehensive curriculum, unmatched teaching methods, and career coaching to help you nail your next tech interview.

We offer 18 interview preparation courses, each tailored to a specific engineering domain or role, including the most in-demand and highest-paying domains and roles, such as:

- Back-end Engineering Interview Course
- Front-end Engineering Interview Course
- Full Stack Developer Interview Course

To learn more, register for the FREE webinar.

Note: Input and Output will already be taken care of.

Given an array and a target number, find the indices of the two values from the array that sum up to the given target number.

```
{
"numbers": [5, 3, 10, 45, 1],
"target": 6
}
```

Output:

```
[0, 4]
```

Sum of the elements at index 0 and 4 is 6.

```
{
"numbers": [4, 1, 5, 0, -1],
"target": 10
}
```

Output:

```
[-1, -1]
```

- The function returns an array of size two where the two elements specify the input array indices whose values sum up to the given target number.
- In case when no answer exists, return an array of size two with both values equal to -1, i.e.,
`[-1, -1]`

. - In case when multiple answers exist, you may return any of them.
- The order of the returned indices does not matter.
- A single index cannot be used twice.

Constraints:

- 2 <= array size <= 10
^{5} - -10
^{5}<= array elements <= 10^{5} - -10
^{5}<= target number <= 10^{5} - Array can contain duplicate elements.

We provided two solutions.

Throughout this editorial, we will refer to the input array as `numbers`

, its size as `numbers_size`

and the target integer as `target`

.

A brute force is to run two nested loops and check the sum of every pair of elements present in the array. If any pair sums up to the `target`

, we will return the indices of that pair of elements.

Otherwise, we will return `[-1, -1]`

.

O((numbers_size)^{2}).

Total number of possible pairs: `(numbers_size * (numbers_size - 1)) / 2`

.

O(1).

O(numbers_size).

Space used for input: O(numbers_size).

Auxiliary space used: O(1).

Space used for output: O(1).

So, total space complexity: O(numbers_size).

```
/*
* Asymptotic complexity in terms of the size of \`numbers\` = \`n\`:
* Time: O(n^2).
* Auxiliary space: O(1).
* Total space: O(n).
*/
static ArrayList<Integer> two_sum(ArrayList<Integer> numbers, Integer target) {
// A list to store the pair of indices that adds to target.
ArrayList<Integer> result = new ArrayList<Integer>();
for (int i = 0; i < numbers.size(); i++) {
// For every element in numbers we find it complementary pair that sum to
// target.
for (int j = i + 1; j < numbers.size(); j++) {
if (numbers.get(i) + numbers.get(j) == target) {
result.add(i);
result.add(j);
return result;
}
}
}
// If no such pair of indices exist, add -1, -1 to list.
result.add(-1);
result.add(-1);
return result;
}
```

While iterating through the array, let say we are at a number `current`

. Being at this number, we need to check whether `target - current`

has occurred at a smaller index in the array or not.

To check the occurrence of `target - current`

, one way is to run another loop on the array to linearly search for that element. But as discussed above, this won’t be very efficient.

We can check whether `target - current`

has previously occurred in the array or not in O(1) time using hashing. We will maintain a hashmap which stores the index of an element present in the array and will keep building this hashmap as we iterate through the array. Now, being at any number `current`

, we will use this hashmap to check whether `target - current`

has previously occurred in the array or not. If it has occurred, we will store the current index and the index of `target - current`

in an array of size two and return it.

In case we didn’t find any such pair after the complete traversal of the array, we will return `[-1, -1]`

.

O(numbers_size).

We iterate through each element in the `numbers`

array exactly once and are doing a constant amount of work in each iteration.

O(numbers_size).

At most, we will be storing all the elements in the hashmap.

O(numbers_size).

Space used for input: O(numbers_size).

Auxiliary space used: O(numbers_size).

Space used for output: O(1).

So, total space complexity: O(numbers_size).

```
/*
* Asymptotic complexity in terms of the size of \`numbers\` = \`n\`:
* Time: O(n).
* Auxiliary space: O(n).
* Total space: O(n).
*/
static ArrayList<Integer> two_sum(ArrayList<Integer> numbers, Integer target) {
// A list to store the pair of indices that adds to target.
ArrayList<Integer> result = new ArrayList<Integer>();
// This Map stores the array element as Key and its index as Value.
HashMap<Integer, Integer> array_index = new HashMap<Integer, Integer>();
for (int i = 0; i < numbers.size(); i++) {
int current = numbers.get(i);
int required = target - current; // complementary target pair
if (array_index.containsKey(required)) {
result.add(array_index.get(required)); // store index of required in result
result.add(i);
return result;
}
// Add every element to map after checking for required.
// This ensures that element does not match itself (indices to be unique).
array_index.put(current, i);
}
// If no such pair of indices exist, add -1, -1 to list.
result.add(-1);
result.add(-1);
return result;
}
```

We hope that these solutions to the 2 Sum in an Array problem have helped you level up your coding skills. You can expect problems like these at top tech companies like Amazon and Google.

If you are preparing for a tech interview at FAANG or any other Tier-1 tech company, register for Interview Kickstart’s FREE webinar to understand the best way to prepare.

Interview Kickstart offers interview preparation courses taught by FAANG+ tech leads and seasoned hiring managers. Our programs include a comprehensive curriculum, unmatched teaching methods, and career coaching to help you nail your next tech interview.

We offer 18 interview preparation courses, each tailored to a specific engineering domain or role, including the most in-demand and highest-paying domains and roles, such as:

- Back-end Engineering Interview Course
- Front-end Engineering Interview Course
- Full Stack Developer Interview Course

To learn more, register for the FREE webinar.

**Attend our free webinar to amp up your career and get the salary you deserve.**

Hosted By

Ryan Valles

Founder, Interview Kickstart