# Pair Sum

Posted: 8 Sep, 2020

Difficulty: Easy

#### You are given an integer array 'ARR' of size 'N' and an integer 'S'. Your task is to return the list of all pairs of elements such that each sum of elements of each pair equals 'S'.

#### Note:

```
Each pair should be sorted i.e the first value should be less than or equals to the second value.
Return the list of pairs sorted in non-decreasing order of their first value. In case if two pairs have the same first value, the pair with a smaller second value should come first.
```

##### Input Format:

```
The first line of input contains two space-separated integers 'N' and 'S', denoting the size of the input array and the value of 'S'.
The second and last line of input contains 'N' space-separated integers, denoting the elements of the input array: ARR[i] where 0 <= i < 'N'.
```

##### Output Format:

```
Print 'C' lines, each line contains one pair i.e two space-separated integers, where 'C' denotes the count of pairs having sum equals to given value 'S'.
```

##### Note:

```
You are not required to print the output, it has already been taken care of. Just implement the function.
```

##### Constraints:

```
1 <= N <= 10^3
-10^5 <= ARR[i] <= 10^5
-2 * 10^5 <= S <= 2 * 10^5
Time Limit: 1 sec
```

Approach 1

- Initialize a list to store our results.
- For each element in the array 'ARR[i]', check if ('ARR[i]' + ‘ARR[j]’), equals to given sum or not, where ‘i’ < ‘j’ < ‘N’.
- If the condition matches, add the pair('ARR[i]', ‘ARR[j]’) to the list. Sort the list of pairs as per the given output format and return this list.

Approach 2

- Initialize a list to store our results.
- For each element in the array ‘ARR[i]’, we will check whether there exists an element equals to ('S' - ‘ARR[i]’) already in the map.
- If it exists we will add the pair('ARR[i]', ‘S’ - ‘ARR[i]’ ) ‘COUNT’ number of times to the list, where ‘COUNT’ represents the frequency of ('S' - ‘ARR[i]’) in the map.
- Also, we will increment the frequency of the current element ('ARR[i]') in the map. Sort the list of pairs as per the given output format and return this list.

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