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 arrayfunction 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!
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