This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: except perhaps the last o Indeed, if a search passes a pillar at level l, it would have passed it at a higher level, so would not have returned to t at level l o Each pillar w/ max level >= l has max level exactly l w/ probability Pr(Max level = l | max level >= l) = ½ (1/2) l+1 /(1/2) l o Chance that j pillars in a row of max level >= l are at max level exactly =(1/2) j Define Y = # pillars in a row that reach level l but fail to reach level l+1 E(Y) = sum from j=0 to inf of j*(1/2) j == (1/2)/(1-(1/2)) 2 = 2 o Conclude: at level l, we pass an average of 2 pillars of height = l+1 before seeing a pillar of height >l+1, which causes us to stop and go down to the next level o Therefore, expected number of pillars inspected at level l is 2+1 = 3 o...
View Full Document
This note was uploaded on 12/05/2011 for the course ENGINEERIN 131 taught by Professor Cytron during the Spring '11 term at Washington University in St. Louis.
- Spring '11
- Computer Science