# QUESTION $1$

def element$\_$uniqueness$($L$)$:

$\text{'}\text{'}\text{'}($list$)->$bool

Returns True if all the elements in the list are distinct,

in other words, if there is no element in the list that appears more than once.

Precondition: L is not empty

$>>>$ element$\_$uniqueness$([2,2,2,2,8])$

False

$>>>$ element$\_$uniqueness$([1,-20,-1])$

True

$>>>$ element$\_$uniqueness$([3,2,4,0,3])$

False

$>>>$ element$\_$uniqueness$([10])$

True

$>>>$ element$\_$uniqueness$([10,10])$

False

$>>>$ element$\_$uniqueness$([10,-1])$

True

$\text{'}\text{'}\text{'}$

L$.$sort$()$

last $=$ None

for x in L:

if last is not None and x $==$ last:

return False

last $=$ x

return True

# QUESTION $2$

def one$\_$unique$\_$at$\_$least$($L$)$:

$\text{'}\text{'}\text{'}($list$)->$bool

Returns True if there exist at least one element in L that is unique,

in other words, that appears exactlly once in the list

Precondition: L is not empty

$>>>$ one$\_$unique$\_$at$\_$least$([2,2,2,2,8])$

True

$>>>$ one$\_$unique$\_$at$\_$least$([2,1,2])$

True

$>>>$ one$\_$unique$\_$at$\_$least$([1,-20,-1])$

True

$>>>$ one$\_$unique$\_$at$\_$least$([3,2,2,3,3])$

False

$>>>$ one$\_$unique$\_$at$\_$least$([10])$

True

$>>>$ one$\_$unique$\_$at$\_$least$([10,10])$

False

$>>>$ one$\_$unique$\_$at$\_$least$([10,-1])$

True

$\text{'}\text{'}\text{'}$

sorted$\_$list $=$ sorted$($L$)$

for i in range$($len$($sorted$\_$list$))$:

if $($i $==0$ or sorted$\_$list$[$i$]!=$ sorted$\_$list$[$i $-1])$ and $($i $==$ len$($sorted$\_$list$)-1$ or sorted$\_$list$[$i$]!=$ sorted$\_$list$[$i $+1])$:

return True

return False

# QUESTION $3$

def all$\_$unique$($L$)$:

$\text{'}\text{'}\text{'}($list$,$int$)->$list

Return a list of elements of L that appear exactlly once in L$.$

Precondition: L is not empty

$>>>$ all$\_$unique$([2,2,2,2,8])$

$[8]$

$>>>$ all$\_$unique$([1,-20,-1])$

$[-20,-1,,1]$

$>>>$ all$\_$unique$([3,2,2,3,3])$

$[]$

$>>>$ all$\_$unique$([10])$

$[10]$

$>>>$ all$\_$unique$([10,10])$

$[]$

$>>>$ all$\_$unique$([10,-1])$

$[-1,10]$

$\text{'}\text{'}\text{'}$

sorted$\_$list $=$ sorted$($L$)$

unique$\_$elements $=[]$

i $=0$

while i $<$ len$($sorted$\_$list$)$:

if $($i $==0$ or sorted$\_$list$[$i$]!=$ sorted$\_$list$[$i $-1])$ and $($i $==$ len$($sorted$\_$list$)-1$ or sorted$\_$list$[$i$]!=$ sorted$\_$list$[$i $+1])$:

unique$\_$elements.append$($sorted$\_$list$[$i$])$

while i $+1<$ len$($sorted$\_$list$)$ and sorted$\_$list$[$i$]==$ sorted$\_$list$[$i $+1]$:

i $+=1$

i $+=1$

return unique$\_$elements

# QUESTION $1$ again

def element$\_$uniqueness$\_$v$2($L$)$:

# make now a $2$nd solution to element$\_$uniqueness

# by making a call to all$\_$unique

# QUESTION $2$ again

def one$\_$unique$\_$at$\_$least$\_$v$2($L$)$:

# make now a $2$nd solution to one$\_$unique$\_$at$\_$least$\_$v$2$

# by making a call to all$\_$unique

# QUESTION $4$

def count$\_$unique$($L$)$:

$\text{'}\text{'}\text{'}($list$,$int$)->$int

Return the number of unique elements of L$,$

i$.$e$.$ the number of elements that appear exactlly once in L

Precondition: L is not empty

$>>>$ count$\_$unique$([2,2,2,2,8])$

$1$

$>>>$ count$\_$unique$([1,-20,-1])$

$3$

$>>>$ count$\_$unique$([3,2,2,3,3])$

$0$

$>>>$ count$\_$unique$([10])$

$1$

$>>>$ count$\_$unique$([10,10])$

$0$

$>>>$ count$\_$unique$([10,-1])$

$2$

$\text{'}\text{'}\text{'}$

# QUESTION $5$

def duplicates$($L$)$:

$\text{'}\text{'}\text{'}($list$)->$int

Returns True if the given list L has duplicates, in other,

if it has at least one element that appears two or more times.

Precondition: L is not empty

$>>>$ duplicates$([2,2,2,2,8])$

True

$>>>$ duplicates$([1,-20,-1])$

False

$>>>$ duplicates$([3,2,2,3,3])$

True

$>>>$ duplicates$([10])$

False

$>>>$ duplicates$([10,10])$

True

$>>>$ duplicates$([10,-1])$

False

$\text{'}\text{'}\text{'}$

# QUESTION $6$

def majority$($L$)$:

$\text{'}\text{'}\text{'}($list$)->$

An element of a list is called "majority" if MORE THAN half of the elements of the list are equal to it$.$

This function returns the majority element of L if such an element exsits, otherwise it returns None

$>>>$ majority$([2,1,2])$

$2$

$>>>$ majority$([10,5,1,5,5])$S

$5$

$>>>$ majority$([5,5,1,1])$

$>>>$ majority$([3])$

$3$

$>>>$ majority$([8,8,2,8])$

$8$

$\text{'}\text{'}\text{'}$