Sorting 100 unique numbers by using 40bytes of memory

Question

I've been asked a good programming problem:

In the input I've got 100 unique numbers from 0-255(1 byte). I can only read one number at a time and only once. I've got 40 bytes of memory which I can use. The goal is to sort all numbers and print them in the output. I know for sure that the uniqueness of the numbers is very important.

Any ideas?

Answer 1

32 bytes give you 256 bits, just enough to maintain a bit map of which of the 256 possible byte values are seen in the input. One additional byte is used to store the input value. Read each value, mark it in the bitmap, then discard. Once you've read all 100 input values, simply write out the value associated with the bits you set in the bit map.

Then ask what you are supposed to do with the other 7 bytes :)

Answer 2

Since your numbers are unique and they are only 1-byte long, they have to be within 0 to 255. Treat your 40 bytes of storage as a long bit vector. As you read each number, set the appropriate bit in this 320-bit bit-vector. When you're done reading the input, turn around and scan through this bit-vector, printing the number corresponding to each set bit.

In response to @JavaNewb, here is some more detail. First, since a byte contains 8 bits, it can assume only one of 256 possible values, namely, 0 through 255. Armed with this little factoid, you look at the 40-byte storage array you have. This array turns out to have 40 bytes * 8 bits/byte = 320 bits. Since the problem states that each of the 100 1-byte numbers are unique, you know that you will see a particular number (which can range from 0 through 255) at most once. Each time you see a number, you set the corresponding bit in the 40-byte array. For instance, if you encounter the number 50, you set bit number 2 in byte number 6. A number N corresponds to bit N%8 in byte N/8. You are guaranteed to never encounter a set bit in this array since that would imply the existence of duplicates in the 100 numbers. After you've read in all the numbers, you look at the 40-byte array. Each bit that is set in this array corresponds to one of the 100 numbers you read in. By traversing this 40-byte array from the 0th bit in the 0th byte all the way to the 7th bit in the 31st byte, you will by:

1. Capturing all the numbers that were read in
2. Observing them in a sorted order

All you have to do now is print the numbers corresponding to the set bits as you traverse the 40-byte array.