Mathematics for Computer Science
20.2. Random Walks on Graphs 853 Sergey and Larry defined their page ranks to be a stationary distribution. They did this by sol ...
Chapter 20 Random Walks854 Problems for Section 20.1 Practice Problems Problem 20.1. Suppose that a gambler is playing a game in ...
20.2. Random Walks on Graphs 855 Problem 20.3. A gambler is placing $1 bets on the “1st dozen” in roulette. This bet wins when a ...
Chapter 20 Random Walks856 x y 1 1 Figure 20.3 w z 1 0.9 0.1 Figure 20.4 1 a b c 1/2 1/2 1/2 d^1 1/2 Figure 20.5 (a)Findd.x/for ...
20.2. Random Walks on Graphs 857 Problem 20.6. Asinkin a digraph is a vertex with no edges leaving it. Circle whichever of the f ...
Chapter 20 Random Walks858 (b)Explain why a long random walk starting at nodexin Figure 20.6 will not converge to a stationary d ...
20.2. Random Walks on Graphs 859 The student comes out of the final exam located on a particular node of the graph, correspondin ...
Chapter 20 Random Walks860 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1 2 3 (f)Now we are ready for the real problem. In order to make ...
20.2. Random Walks on Graphs 861 A Google-graph is a random-walk graph such that every edge leaving any given vertex has the sam ...
Chapter 20 Random Walks862 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 1 1 0.5 0.5 1 Figure 20.9 Which ones have uniform stationar ...
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Introduction Arecurrencedescribes a sequence of numbers. Early terms are specified explic- itly, and later terms are expressed a ...
Part V Recurrences866 in the guess-and-verify and plug-and-chug methods is replaced by a “Huh” at the end of a cookbook procedur ...
21 Recurrences 21.1 The Towers of Hanoi There are several methods for solving recurrence equations. The simplest is to guessthe ...
Chapter 21 Recurrences868 21.1.1 The Upper Bound Trap When the solution to a recurrence is complicated, one might try to prove t ...
21.1. The Towers of Hanoi 869 to remember—indeed, a rule applicable to the whole of college life—ischug in moderation. TnD2Tn 1 ...
Chapter 21 Recurrences870 Step 3: WriteTnUsing Early Terms with Known Values The last step is to expressTnas a function of early ...
21.2. Merge Sort 871 10, 7, 23, 5, 2, 8, 6, 9. Since there is more than one number, the first half (10, 7, 23, 5) and the second ...
Chapter 21 Recurrences872 Therefore, the maximum number of comparisons needed to Merge Sortnitems is given by this recurrence: T ...
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