Php Program to Find a triplet such that sum of two equals to third element
Last Updated :
20 Apr, 2023
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
function findTriplet( $arr , $n )
{
sort( $arr );
for ( $i = $n - 1; $i >= 0; $i --)
{
$j = 0;
$k = $i - 1;
while ( $j < $k )
{
if ( $arr [ $i ] == $arr [ $j ] + $arr [ $k ])
{
echo "numbers are " , $arr [ $i ], " " ,
$arr [ $j ], " " ,
$arr [ $k ];
return ;
}
else if ( $arr [ $i ] > $arr [ $j ] +
$arr [ $k ])
$j += 1;
else
$k -= 1;
}
}
echo "No such triplet exists" ;
}
$arr = array (5, 32, 1, 7, 10,
50, 19, 21, 2 );
$n = count ( $arr );
findTriplet( $arr , $n );
?>
|
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!
Share your thoughts in the comments
Please Login to comment...