This is type of Subset sum problem
Here is my solution. I don’t know if it was known earlier or not. Imagine 3D plot of function of two variables i and j:
sum(i,j) = a[i]+a[j]
For every i
there is such j
that a[i]+a[j]
is closest to x
. All these (i,j)
pairs form closest-to-x line. We just need to walk along this line and look for a[i]+a[j] == x
:
int i = 0;
int j = lower_bound(a.begin(), a.end(), x) - a.begin();
while (j >= 0 && j < a.size() && i < a.size()) {
int sum = a[i]+a[j];
if (sum == x) {
cout << "found: " << i << " " << j << endl;
return;
}
if (sum > x) j--;
else i++;
if (i > j) break;
}
cout << " not found\n";
Complexity: O(n)