C program :Your program will print all$$Cube Sums$$with integers $0..$ N in order from smallest to largest. $($Notice there was a tie above, figure out how it was broken.$)$ You cannot generate all values and sort them. This would require making $($N$+1)^2$ values, which would use excessive space. Instead you will use a Heap to generate them in order.

The basic algorithm is described below.

Create a new Heap

For integers i$=0$ up to N do

Add $($i$^3+0^3,$ i$,0)$ to the Heap

End For

While Heap is not Empty do

Get the Minimum Sum

Print the Sum

If the sum's j value is less than N:

Put a new sum in the heap $($i$^3+($j$+1)^3,$ i$,$ j$+1)$

End If

End Do

Delete the Heap

You may make a one assumptions.

$*$ The user will always give you a positive integer as input

You must implement the following in your solution.

You must use the following Structure to store the$$Cube Sums.

$/**$

Stores a sum i$^3+$ j$^3=$ k

$*/$

typedef struct CubeSum CubeSum;

struct CubeSum$\{$

int sum;$/**<$ result of i$^3+$ j$^3*/$

int i;$/**<$ First integer in sum $*/$

int j;$/**<$ Second integer in sum $*/$

$\}$;

You must implement a Heap with$$at least$$the following methods. You may create additional methods, but you$$must$$use these.

$/**$

Create a new heap with starting size $10.$

@return the heap that was created.

$*/$

Heap $*$newHeap$()$;

$/**$

Delete the heap. Free all memory used.

@param myHeap is the heap to delete

$*/$

void deleteHeap$($Heap $*$myHeap$)$;

$/**$

Determine if the heap is empty.

@param myHeap is the heap to check

@return true if the heap is empty and false otherwise

$*/$

bool isEmpty$($Heap $*$myHeap$)$;

$/**$

Insert a new sum into the heap.

@param myHeap is the heap to insert into

@param sum is a pointer to the sum to insert

$*/$

void insert$($Heap $*$myHeap$,$ CubeSum$*$ sum$)$;

$/**$

Remove the minimum from the heap.

@param myHeap is the heap to remove from

$*/$

void removeMin$($Heap $*$myHeap$)$;

$/**$

Get the pointer to the smallest CubeSum.

@param myHeap is the heap to get the min of

@return a pointer to the smallest CubeSum

$*/$

CubeSum $*$getMin$($Heap $*$myHeap$)$;

Example $1$

Cube Sum Program.

Computes Cube Sums from $0...$ N

Enter max value of N:

$2$

$0^3+0^3=0$

$0^3+1^3=1$

$1^3+0^3=1$

$1^3+1^3=2$

$0^3+2^3=8$

$2^3+0^3=8$

$1^3+2^3=9$

$2^3+1^3=9$

$2^3+2^3=16$