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:
// Javascript 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
arr.sort((a, b) => a - b);
// For every element in arr check
// if a pair exist(in array) whose
// sum is equal to arr element
for (let i = n - 1; i >= 0; i--) {
let j = 0;
let k = i - 1;
// Iterate forward and backward to
// find the other two elements
while (j < k) {
// If the two elements sum is
// equal to the third element
if (arr[i] == arr[j] + arr[k]) {
// Pair found
console.log("numbers are " + arr[i] +
" " + arr[j] + " " + arr[k]);
return;
}
// If the element is greater than
// sum of both the elements, then try
// adding a smaller number to reach the
// equality
else if (arr[i] > arr[j] + arr[k])
j += 1;
// If the element is smaller, then
// try with a smaller number
// to reach equality, so decrease K
else
k -= 1;
}
}
// No such triplet is found in array
console.log("No such triplet exists");
}
// Driver code
let arr = [5, 32, 1, 7, 10, 50, 19, 21, 2];
let n = arr.length;
findTriplet(arr, n);
// This code is contributed by Mayank Tyagi
Output
numbers are 21 2 19
Complexity Analysis:
- Time complexity: O(N^2)
- Space Complexity: O(1) as no extra space has been used.
