Implement a Python function that finds the k largest items in a list. DO NOT USE ANY BUILD IN FUNCTIONS.

Implement find$\_$k$\_$largest$($nums$,$k$)$function that takes a list nums of integers and an integer k as parameters. The function should return a list containing the k largest items in descending order.

## TESTING find$\_$k$\_$largest function

## DO NOT EDIT THIS CELL.

def test$\_$find$\_$k$\_$largest$()$:

# Test Case $1$: Positive Integers

nums$1=[3,1,4,1,5,9,2,6,5,3,5]$

k$1=3$

expected$1=[9,6,5]$

assert find$\_$k$\_$largest$($nums$1,$ k$1)==$ expected$1,$ f$"$Test Case $1$ failed: Expected $\{$expected$1\},$ but got $\{$find$\_$k$\_$largest$($nums$1,$ k$1)\}"$

# Test Case $2$: Negative Integers

nums$2=[-3,-1,-4,-1,-5,-9,-2,-6,-5,-3,-5]$

k$2=4$

expected$2=[-1,-1,-2,-3]$

assert find$\_$k$\_$largest$($nums$2,$ k$2)==$ expected$2,$ f$"$Test Case $2$ failed: Expected $\{$expected$2\},$ but got $\{$find$\_$k$\_$largest$($nums$2,$ k$2)\}"$

# Test Case $3$: Mixed Integers

nums$3=[3,-1,4,-1,5,-9,2,-6,5,3,-5]$

k$3=5$

expected$3=[5,5,4,3,3]$

assert find$\_$k$\_$largest$($nums$3,$ k$3)==$ expected$3,$ f$"$Test Case $3$ failed: Expected $\{$expected$3\},$ but got $\{$find$\_$k$\_$largest$($nums$3,$ k$3)\}"$

# Test Case $4$: Duplicate Integers

nums$4=[3,1,4,1,5,9,2,6,5,3,5]$

k$4=4$

expected$4=[9,6,5,5]$

assert find$\_$k$\_$largest$($nums$4,$ k$4)==$ expected$4,$ f$"$Test Case $4$ failed: Expected $\{$expected$4\},$ but got $\{$find$\_$k$\_$largest$($nums$4,$ k$4)\}"$

# Test Case $5$: Empty List

nums$5=[]$

k$5=3$

expected$5=[]$

assert find$\_$k$\_$largest$($nums$5,$ k$5)==$ expected$5,$ f$"$Test Case $5$ failed: Expected $\{$expected$5\},$ but got $\{$find$\_$k$\_$largest$($nums$5,$ k$5)\}"$

# Test Case $6$: List with Fewer than k items

nums$6=[3,1,4,1]$

k$6=5$

expected$6=[4,3,1,1]$

assert find$\_$k$\_$largest$($nums$6,$ k$6)==$ expected$6,$ f$"$Test Case $6$ failed: Expected $\{$expected$6\},$ but got $\{$find$\_$k$\_$largest$($nums$6,$ k$6)\}"$