Given an integer array *arr *of size *n*, find all magic triplets in it.

Magic triplet is a group of three numbers whose sum is zero.

Note that magic triplets may or may not be made of consecutive numbers in *arr*.

**Example One**

Input: *arr* = [10, 3, -4, 1, -6, 9]

Output: [“10,-4,-6”, “3,-4,1”]

**Example Two**

Input: *arr* = [12, 34, -46]

Output: [“12,-46,34”]

**Example Three**

Input: *arr* = [0, 0, 0];

Output: [“0,0,0”]

**Example Four**

Input: *arr* = [-2, 2, 0 -2, 2];

Output: [“2,-2,0”]

**Notes**

Input Parameters: Function has one argument: array of integers *arr*.

Output: **Function must return an array of strings.** Each string (if any) in the array must represent a unique magic triplet and strictly follow this format: “1,2,-3” (no whitespace, one comma between numbers).

Order of the strings in the array is insignificant. Order of the integers in any string is also insignificant. For example, if [“1,2,-3”, “1,-1,0”] is a correct answer, then [“0,1,-1”, “1,-3,2”] is also a correct answer.

Triplets that only differ by order of numbers are considered duplicates, and duplicates must not be returned. For example, if “1,2,-3” is a part of an answer, then “1,-3,2”, “-3,2,1” or any permutation of the same numbers may not appear in the same answer (though any one of them may appear instead of “1,2,-3”).

**Constraints:**

- 1 <=
*n*<= 2000 - -1000 <= any element of
*arr*<= 1000 *arr*may contain duplicate numbers.*arr*is not necessarily sorted.

A simple solution is to use three nested loops and check for each possible combination if their sum is zero. To avoid duplicate answers, we need to hash the triplet and store it in a set. An easy way to hash a triplet is by converting it to a string.

Extra space needed will be the number of unique triplets that contribute to the answer.

**Space Complexity:**

O(*n*^2)

**Time Complexity:**

O(*n*^3)

Optimal solution uses the two pointer method. We maintain left and right pointers to elements of a sorted array. If their sum is greater than intended we decrease the right pointer, otherwise we increase the left pointer. This method works in linear time (and to solve this particular problem we use this algorithm *n* times, once for each element in *arr*).

First, we will sort *arr* (this will contribute O(*n**log(*n*)) to the time complexity). Then, for every element or *arr*, we will apply the two pointer technique to find any magic triplets that include that element. We will then add unique triplets to the answer.

**Time Complexity:**

O(*n*^2 + *n**log(*n*))

**Space Complexity:**

O(*n*^2)