# Find three elements in an array that sum to a given value

Objec­tive:  Given an array of inte­ger write an algo­rithm to find 3 ele­ments that sum to a given num­ber k. In short a+b+c = k.

Exam­ple:

```int a [] = { 3,1,7,4,5,9,10} , k = 21;Output: Elements are 7 4 10 int a [] = { 3,1,7,4,5,9,10} , k = 55;Output: Did not find 3 elements whose sum is 55
```

Approach: Brute Force

Use 3 nested loops and find the 3 ele­ments which sum to k.

Time Com­plex­ity: O(n^3)

Code:

Approach: Sort­ing

• Sort the array.
• Use the other loop to fix the one ele­ment at a time
• Now prob­lem is reduced to “Find a pair of num­bers from an array whose sum equals k”

Time Com­plex­ity: O(n^2)

Code:

Approach: Use Hashing

• Use the other loop to fix the one ele­ment at a time.
• Now required_sum is (with two ele­ments) = k-fixed element.
• Cre­ate a Hash­Set, Iter­ate through rest of the array.
• For current_element, remain_value = required_sum – current_element.
• Check if remain_value in the Hash­Set, we have found our triplets else add current_element to the hashset.

Time Com­plex­ity: O(n^2)

Code:

Out­put:

```Found 3 elements whose sum is = 22
Elements are 3 10 9```