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Find three elements in an array that sum to a given value
Objective: Given an array of integers 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 one element at a time
 Now the 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 one element at a time.
 Now required_sum is (with two elements) = kfixed element.
 Create a HashSet, and Iterate through the 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
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