## Problem Statement

Given an array of distinct integers, find the pair of integers whose sum is equal to the target number, if any.

**Arguments**

- numbersArray - Array of distinct integers
- targetSum - Target sum number

## Solution

#### Approach 1

- Run 2
*for*loops, one nested inside the other. - Check if the sum of the iterating elements equal the target sum.

```
const twoNumerSum = (numbersArray, targetSum) => {
for (let i = 0; i < numbersArray.length; i++) {
const firstNumber = numbersArray[i];
for (let j = 0; j < numbersArray.length; j++) {
const secondNumber = numbersArray[j];
if (firstNumber + secondNumber === targetSum) {
return [firstNumber, secondNumber];
}
}
}
return [];
};
```

**Time complexity** *O(n^2)*

**Space complexity** *O(1)*

#### Approach 2

- Initiate an empty object & iterate through the input array using a
*for*loop. - Because we already know the target sum, we can instead search for the unique number, whose summation with the iterating number will be equal to the target sum.

```
const twoNumerSum = (numbersArray, targetSum) => {
const numbersMap = {};
for (const number of numbersArray) {
const match = targetSum - number;
if (numbersMap[match]) {
return [match, number];
} else {
numbersMap[number] = 'true';
}
}
return [];
};
```

**Time complexity** *O(n)*

**Space complexity** *O(n)*

#### Approach 3

- Input array can be sorted in O(nlogn) using quick sort. Let's do that first.
- Begin summation from the extreme indices and close in. If the sum is less than the target sum, move one index further from the left side, else, the right side.

```
const twoNumerSum = (numbersArray, targetSum) => {
numbersArray.sort();
let left = 0, right = numbersArray.length - 1;
while (left < right) {
const currentSum = numbersArray[left] + numbersArray[right];
if (currentSum === targetSum) {
return [numbersArray[left], numbersArray[right]];
} else if (currentSum < targetSum) {
left += 1;
} else {
right -= 1;
}
}
return [];
};
```

**Time complexity** *O(nlogn)*

**Space complexity** *O(1)*

## Link to Code

in node.js. Feel free to raise a PR in any other language.

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