H10:07••.o Define the cumulative sumsSi= a1 + a2+...+ ai andSo = 0.Pick a random integer r uniformlybetween 0 and Sn – 1.-o Find the unique index i between 1and n such that S;-1 (€)10:06••.1. Discrete distribution. Write aprogram DiscreteDistribution.javathat takes an integer command-lineargument m, followed by asequence of positive integercommand-line argumentsa1, a2,..random indices (separated bywhitespace), choosing each index iwith probability proportional to a¡.An, and prints m9 •• •-/Desktop/arrays> java DiscreteDistribution 25 1 1 1 1115 2 4 4 5 5 4 3 4 3 1 5 2 4 2 6 1 3 6 2 3 2 4 1 4~ /Desktop/arrays> java DiscreteDistribution 25 10 10 10 10 10 503 6 6 16 6 2 4 6 6 3 6 6 6 6 4 5 6 2 2 66 2 6 2-/Desktop/arrays> java DiscreteDistribution 25 80 201 2 1 2 1 1 2 1 1 1 1 1 1 11 2 2 2 1 111111~/Desktop/arrays> java DiscreteDistribution 100 301 176 125 97 79 67 58 51 466 2 4 3 2 3 3 1 7 1 1 3 47 1 4 2 2 1 1 3 1 8 6 21 3 6 185 1 3 6 1 1 2 3 8 7 4 6 4 3 1 5 3 3 7 31 3 177 2 2 3 6 5 4 1 1 1 7 2 3 5 2 2 1 4 1 2 12 1 2 2 3 2 8 4 3 2 1 8 3 5 3 3 8 1 2 3 3 1 2 3 1To generate a random index i withprobability proportional to a;:o Define the cumulative sumsS; =a1 + a2 +...+ a; and0.SoPick a random integer r uniformlybetween 0 and Sn – 1.o Find the unique index i between 1and n such that S;-1 < r < S¿.-Geometrically, this subdivides theinterval [0, Sn) into n subintervals[S;-1, S;), with the length ofsubinterval i proportional to aj. Forexample, if the discrete distributionis defined hy.

public class DiscreteDistribution { public static void main(String[] args) { // read in…

Discrete distribution. Write a program DiscreteDistribution.java that takes an integer command-line argument m, followed by a sequence of positive integer command-line arguments A1, a2, . .., An, and prints m random indices (separated by whitespace), choosing each index i with probability proportional to a¡.

Discrete distribution. Write a program DiscreteDistribution.java that takes an integer command-line argument m, followed by a sequence of positive integer command-line arguments A1, a2, . .., An, and prints m random indices (separated by whitespace), choosing each index i with probability proportional to a¡.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter13: Overloading And Templates

Section: Chapter Questions

Problem 20PE

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Do you reach many, do you reach one? def knight_jump(knight, start, end): An ordinary chess knight on a two-dimensional board of squares can make an “L-move” into up toneight possible neighbours. However, we can generalize the entire chessboard into k dimensions from just the puny two. A natural extension of the knight's move to keep moves symmetric with respect to these dimensions is to define the possible moves as some k-tuple of strictly decreasing nonnegative integer offsets. Each one of these k offsets must be used for exactly one dimension of your choice during the move, either as a positive or a negative version. For example, the three-dimensional (4,3,1)-knight makes its way by first moving four steps along any one of the three dimensions, then three steps along any other dimension, and then one step along the remaining dimension, whichever dimensions that was. These steps are considered to be performed together as a single jump that does not visit or is blocked by any of the…
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