Derive the Huffman tree using Huffmans algorithm for the alphabet A = {a, b, c, d}, when the frequencies are given by f(a) = 1000, f(b) = 3000, f(c) = 2000, and f(d) = 5000. The minimum priority queue Q has initially the state 1) and after each iteration of Huffmans algorithm the states 2), 3), and 4).

1) Q =

2) Q =

3) Q =

4) Q =