Using C$++!!5\mathrm{.}7$ LAB: Finding the k$-$max values

In the cases where we are presented a large set of data, it is typical to sort the data to make searches easier.

We know that a good sort, like Heap sort, can accomplish this in $O(nlogn)$ time. Sometimes, however, we

might be interested in only the largest value in the data set. We know we can find this in $O(n)$ time. If we

needed to find the two$(2)$ largest values, we might repeat the process, which would take $O(2n)$ time or the

same $O(n)$ overall. It follows that to find the k$-$largest values, it would take about $O(kn)$ time. While that is still

$O(n)$ it is possible to do a bit better. Specifically, we can use a heap to find the k largest values without the

need to sort the entire data set.

The program should read in a seed value, the number of values to generate, and the number of the

largest values to return, all as integers. Then, allocate the necessary space and then randomly generate

all the values requested.

Complete a function, $)$ to return the $k-$largest values in the array. You will need to use one or

more helper functions to maintain the heap property. Use a max$-$heap and return a list with the $k-$

maximum numbers in Descending order.

Ex: When the input is:

$123,10,4$

the output is:

Result:

$950960938286819083736322$

#include $=0=0=0(0,1000000)0-1,000,000i=0ii++[i]=\frac{\frac{?}{?}}{?}[i]i=0$iIn the cases where $we$ are presented a large set $of$ data, $itis$ typical $to$ sort the data $to$ make searches easier. $We$ know that a good sort, like Heap sort, can accomplish this $inO(nlogn)$ time. Sometimes, however, $we$ might $be$ interested $in$ only the largest value $in$ the data set. $We$ know $we$ can find this $inO(n)$ time. $Ifwe$ needed $to$ find the two$(2)$ largest values, $we$ might repeat the process, which would take $O(2n)$ time $or$ the same $O(n)$ overall. $It$ follows that $to$ find the $k-$largest values, $it$ would take about $O(kn)$ time. While that $is$ still $O(n)itis$ possible $todo$ a bit better. Specifically, $we$ can use a heap $to$ find the $k$ largest values without the need $to$ sort the entire data set.

The program should read $in$ a seed value, the number $of$ values $to$ generate, and the number $of$ the largest values $to$ return, all $as$ integers. Then, allocate the necessary space and then randomly generate all the values requested.

Complete a function, $K_{M}ax()to$ return the $k-$largest values $in$ the array. You will need $to$ use one $or$ more helper functions $to$ maintain the heap property. Use a max$-$heap and return a list with the $k-$maximum numbers $in$ Descending order.

$Ex$: When the input $is$:

$123104$

the output $is$:

Result:

$950960938286819083736322$