AmortizedAnalysis

# Starting from the172 an counter a sequence of n0 ito

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Unformatted text preview: 9 22 23 25 26 31 Theorem. Starting from the17.2 An counter, a sequence of n0 Ito 16 by a sequence of 16 I NCREMENT zero 8-bit binary counter as its value goes from NCREMENT Figure operations. operations flips O(n k) bits. Pf. At most k bits Bits that ﬂip to achieve the next value are shaded. The running cost for ﬂipping bits is shown at the right. Notice that the total cost is always less than twice the total number of I NCREMENT operations. flipped per increment. ▪ 13 operations on an initially zero counter causes AŒ1 to ﬂip bn=2c times. Similarly, bit AŒ2 ﬂips only every fourth time, or bn=4c times in a sequence of n I NCREMENT i Aggregate method (brute force) Aggregate method. Sum up sequence of operations, weighted by their cost. Counter value 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 455 A[ 7 A[ ] 6] A[ 5 A[ ] 4 A[ ] 3 A[ ] 2] A[ 1 A[ ] 0] 17.1 Aggregate analysis 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 Total cost 0 1 3 4 7 8 10 11 15 16...
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