02-greedy

Heap 71 72 thefinalhuffmancodingtree character code a

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Unformatted text preview: gth and differ only in the last bit. Rephrased: the greedy choice property (of picking the two lowest-frequency nodes) will yield an optimal tree On board --> 76 Step 2 • Lemma 16.3: Let C be a given alphabet with frequency c.freq defined for each character c C. Let x and y be two characters in C with minimum frequency. Let C’ be the alphabet C with the characters x and y removed and a new character z added, so that C’ = C-{x,y}{z}. Define f for C’ as for C, except that x.freq = x.freq + y.freq. Let T’ be any tree representing an optimal prefix code for the alphabet C’. Then the tree T, obtained from T’ by replacing the leaf node for z with an internal node having x and y as children, represnts an optimal prefix code for the alphabet C. Rephrased: constructing prefix codes has the optimal sub-structure property 77 Dijkstra’s Shortest Path 78 Weighted Shortest Path no negative weight edges. Dijkstra’s algorithm: uses similar ideas as the unweighted case. Greedy algorithms: do what seems to be best at every decision point. s 79 S “known” v V-S “unknown” Dijkstra’s algori...
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This note was uploaded on 02/25/2014 for the course CS 4102 taught by Professor Horton during the Spring '10 term at UVA.

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