title: Maximum number of different numbers, Huffman Compression
body: <p>I want to compress many 32bit number using huffman compression.</p>
  
  <p>Each number may appear multiple times, and I know that every number will be replaced with some bit sequences:</p>
  
  <p>111
  010
  110
  1010
  1000
  etc...</p>
  
  <p>Now, the question: How many different numbers can be added to the huffman tree before the length of the binary sequence exceeds 32bits?</p>
  
  <p>The rule of generating sequences (for those who don't know) is that every time a new number is added you must assign it the smallest binary sequence possible that is not the prefix of another.</p>