In-Place Calculation of Minimum-Redundancy Codes

The optimal prefix-free code problem is to determine, for a given array p = [p~li 9 {1.. . n}] of n weights, an integer array l -[l~ I i 9 {1.. . n}] of n codeword lengths such that ~ 1 2-~' ~ 1 and ~i~=1 pil~ is minimized. Huff-man's famous greedy algorithm solves this problem in O(n log n) time, if p is unsorted; and can be implemented to execute in O(n) time, if the input array p is sorted. Here we consider the space requirements of the greedy method. We show that if p is sorted then it is possible to calculate the array I in-place, with li overwriting Pi, in O(n) time and using O(1) additional space. The new implementation leads directly to an O(nlogn)-time and n + O(1) words of extra space implementation for the case when p is not sorted. The proposed method is simple to implement and executes quickly.