import java.util.Arrays;

class Uniqueness $\{$

$/**$ Returns true if there are no duplicate elements in the array. $*/$

public static boolean unique$1($int$[]$ data$)\{$

int n $=$ data.length;

for $($int j$=0$; j $<$ n$-1$; j$++)$

for $($int k$=$j$+1$; k $<$ n; k$++)$

if $($data$[$j$]==$ data$[$k$])$

return false; $//$ found duplicate pair

return true; $//$ if we reach this, elements are unique

$\}$

$/**$ Returns true if there are no duplicate elements in the array. $*/$

public static boolean unique$2($int$[]$ data$)\{$

int n $=$ data.length;

int$[]$ temp $=$ Arrays.copyOf$($data$,$ n$)$; $//$ make copy of data

Arrays.sort$($temp$)$; $//$ and sort the copy

for $($int j$=0$; j $<$ n$-1$; j$++)$

if $($temp$[$j$]==$ temp$[$j$+1])//$ check neighboring entries

return false; $//$ found duplicate pair

return true; $//$ if we reach this, elements are unique

$\}\}$

Question:

For each of the algorithms unique$1$ and unique$2($Uniqueness$.$java class in Lesson $4$ examples$)$ which solve the element uniqueness problem, perform an experimental analysis to determine the largest value of n such that the given algorithm runs in one $200$r $15$ sec$.$

Hint: Do a type of $$binary search$$ to determine the maximum effective value of n for each algorithm.