Categories

# Determine whether or not there exist two elements in Set S whose sum is exactly x – correct solution?

Taken from Introduction to Algorithms Describe a Θ(n lg n)-time algorithm that, given a set S of n integers and another integer x, determines whether or not there exist two elements in S …

Taken from Introduction to Algorithms

Describe a Θ(n lg n)-time algorithm that, given a set S of n integers and another integer x, determines whether or not there exist two elements in S whose sum is exactly x.

This is my best solution implemented in Java so far:

```    public static boolean test(int[] a, int val) {
mergeSort(a);

for (int i = 0; i < a.length - 1; ++i) {
int diff = (val >= a[i]) ? val - a[i] : a[i] - val;

if (Arrays.binarySearch(a, i, a.length, diff) >= 0) {
return true;
}
}

return false;
}
```

Now my 1st question is: Is this a correct solution? From my understanding, mergeSort should perform the sort in O(n lg n), the loop should take O(n lg n) (n for the iteration multiplied by O(lg n) for the binary search, resulting in O(2n lg n), so it should be correct.

My 2nd question is: Are there any better solutions? Is sorting the array essential?

Your solution seems fine. Yes you need to sort because its a pre requisite for binary search. You can make a slight modification to your logic as follows:

```public static boolean test(int[] a, int val)
{
Arrays.sort(a);

int i = 0;            // index of first element.
int j = a.length - 1; // index of last element.

while(i<j)
{
// check if the sum of elements at index i and j equals val, if yes we are done.
if(a[i]+a[j] == val)
return true;
// else if sum if more than val, decrease the sum.
else if(a[i]+a[j] > val)
j--;
// else if sum is less than val, increase the sum.
else
i++;
}
// failed to find any such pair..return false.
return false;
}
```
Source: stackoverflow
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Privacy Policy, and Copyright Policy. Content is available under CC BY-SA 3.0 unless otherwise noted. The answers/resolutions are collected from stackoverflow, are licensed under cc by-sa 2.5 , cc by-sa 3.0 and cc by-sa 4.0 © No Copyrights, All Questions are retrived from public domain..