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

r

p

r

T’

q

C(T’) = C(T) + 4q - 4r + 2r - 2q = C(T) - 2(r-q) > C(T)

Previous slide

Next slide

Back to first slide

View graphic version