For 1GB: Create a boolean array (1 bit per entry) of size 4 billion + 1, initialized to false. Read the whole file. For each integer, if it's in the range 0 - 4 billion, set the array value to true. Then find any array value which is false (since the array size is 4 billion + 1 and the input is size 4 billion there is guaranteed to be one which is false). For 80MB: Read the file in 80MB chunks and sort each chunk. Write each sorted chunk to a new file with an index (e.g. filename for i'th file = file_i). Then perform an n-way merge on the files, where n is the number of files. Then read the resulting merged file and find any 2 integers which are not consecutive and return any value in the gap. If all numbers are consecutive, return either of the endpoints (plus or minus 1).