Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 4.5, Problem 3E
Program Plan Intro

To show that the solution of the binary search recurrence relation T(n)=T(n/2)+θ(1) is θ(lgn) by using the master method.

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i have attached my 2 java questions . please answer them correctly,  add all comments etc . thank you.
Can you help me solve this problem using Master's Theorem:Solve the recurrence relation f(n) = 3af(n/a) + (n + a)2 with f(1) = 1 and a > 1 byfinding an expression for f(n) in big-Oh notation.
here is example 7.6## Example 7.6 Suppose the sample population is χ 2 (2), which is non-normal but with same variance 4. ▶ Repeat the simulation, but replacing the N(0, 4) samples with χ 2 (2) samples. ▶ Calculate the empirical confidence level.(Empirical confidence level) n <- 20 alpha <- 0.05 UCL <- replicate(1000, expr = { x <- rchisq(n,df=2) (n-1)*var(x)/qchisq(alpha,df=n-1) }) sum(UCL >4) mean(UCL > 4) ## t.test function n <- 20 x <- rnorm(n,mean=2) result <- t.test(x,mu=1) result$statistic result$parameter result$p.value result$conf.int result$estimate
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