Optimality Principle 2

• The second lowest probability is a sibling of the the smallest in some optimal Huffman tree.

  • If not, we can move it there not raising the cost.

p

q

T

p smallest

q 2nd smallest

q < r

k < h

r

p

r

T’

q

C(T’) = C(T) + hq - hr + kr - kq = C(T) - (h-k)(r-q) < C(T)

h

k

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