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Php Program to Find a triplet such that sum of two equals to third element

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Given an array of integers, you have to find three numbers such that the sum of two elements equals the third element.
Examples:

Input: {5, 32, 1, 7, 10, 50, 19, 21, 2}
Output: 21, 2, 19

Input: {5, 32, 1, 7, 10, 50, 19, 21, 0}
Output: no such triplet exist

Question source: Arcesium Interview Experience | Set 7 (On campus for Internship)

Simple approach: Run three loops and check if there exists a triplet such that sum of two elements equals the third element.
Time complexity: O(n^3)
Efficient approach: The idea is similar to Find a triplet that sum to a given value.

  • Sort the given array first.
  • Start fixing the greatest element of three from the back and traverse the array to find the other two numbers which sum up to the third element.
  • Take two pointers j(from front) and k(initially i-1) to find the smallest of the two number and from i-1 to find the largest of the two remaining numbers
  • If the addition of both the numbers is still less than A[i], then we need to increase the value of the summation of two numbers, thereby increasing the j pointer, so as to increase the value of A[j] + A[k].
  • If the addition of both the numbers is more than A[i], then we need to decrease the value of the summation of two numbers, thereby decrease the k pointer so as to decrease the overall value of A[j] + A[k].

Below image is a dry run of the above approach:

Below is the implementation of the above approach:

PHP

<?php
// PHP program to find three numbers
// such that sum of two makes the third
// element in array
 
// Utility function for finding
// triplet in array
function findTriplet($arr, $n)
{
    // Sort the array
    sort($arr);
 
    // For every element in arr check
    // if a pair exist(in array) whose
    // sum is equal to arr element
    for ($i = $n - 1; $i >= 0; $i--)
    {
        $j = 0;
        $k = $i - 1;
        while ($j < $k)
        {
            if ($arr[$i] == $arr[$j] + $arr[$k])
            {               
                // Pair found
                echo "numbers are ", $arr[$i], " ",
                                      $arr[$j], " ",
                                      $arr[$k];
                return;
            }
            else if ($arr[$i] > $arr[$j] +
                                $arr[$k])
                $j += 1;
            else
                $k -= 1;
        }
    }
 
    // No such triplet is found in array
    echo "No such triplet exists";
}
 
// Driver Code
$arr = array(5, 32, 1, 7, 10,
             50, 19, 21, 2 );
$n = count($arr);
findTriplet($arr, $n);
// This code is contributed by anuj_67.
?>

                    

Output:  

numbers are 21 2 19

Time complexity: O(N^2) 

Space Complexity: O(1) as no extra space has been used.

Please refer complete article on Find a triplet such that sum of two equals to third element for more details!



Last Updated : 20 Apr, 2023
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