Overflow issues
If the largest two integers added together exceed the maximum integer value, you will not come up with the correct answer. For example, 2000000000 + 2000000000 becomes some negative value and you would miss that as the answer. To do this correctly you should do the addition using long and store the max value in a long as well:
long currentMax = (long) array[i] + (long) array[j];
Even if you used the better algorithm of finding the two largest values in the array, you would still need to return a long in order to return the correct sum.
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