In this project, you are required to implement a set of min$-$heap operations in ARM assembly

language. You will use KEIL simulator to develop and test your code.

First of all, you will implement the min$-$heap data structure $($which has the logical structure of a

nearly complete binary tree$)$ as an array of $32-$bit integers. The first element in the array A$[0]$ is the

size of the heap, i$.$e$.$ the number of elements in the heap $($i$.$e the integer $$size$)$ is in A$[0].$ The rest

of the elements in A $($A$[1]$ to A$[$size$])$ are the values in the nodes of the binary tree.

Fundamental property of a min$-$heap is that for every node i other than the root, A$[$parent$($i A$[$i$],$

that is$,$ the value of a node is at most the value of its parent. If a node is at the kth location in the

array, its children will be at the $(2$k$)$ and the$(2$k$+1)$ locations of the array. The following figures gives

three different min$-$heaps which have $6,4$ and $3$ nodes.

Figure $1$: Three sample min$-$heaps with a$)6$ nodes, b$)4$ nodes and c$)2$ nodes.

Procedures of the Project

I. build $($list$,$ heap$)$

This procedure constructs a min$-$heap data structure from a list of integers. The values of the

integers in the list are in no particular order, but they are located in successive memory locations,

from first to last. The address of the first integer is in the list argument $($given in R$0)$; and assume

that the list is terminated by a special value, $-$MAXINT, the negative integer with

the largest possible absolute value. The address of the place where the procedure should create

the data structure is in heap argument $($given in R$1).$

II$.$ find $($value$,$ heap$)$

This procedure finds a particular value $($given in R$0$ register$)$ in the min$-$heap, where the address of

the first item of the data structure is in heap argument $($given in R$1).$ The search result should be

stored in R$0$ register. If the item is found R$0=1,$ otherwise R$0=0.$ If the value is found in the heap,

R$1$ should contain its address. For this procedure, the original data structure $($heap$)$ should be

unmodified.

III. sort $($size$,$ heap$)$

This procedure sorts the elements using the heap structure. Procedure takes two arguments: size

of array $($given in R$0$ register$)$ and the address of the first item of the data structure is in heap

argument $($given in R$1).$ End of the operation the address of the first element of sorted list should

be in R$0$ register.Figure $1.$a

Figure $1.$b

Figure $1.$c

Figure $1$: Three sample min$-$heaps with a$)6$ nodes, b$)4$ nodes and c$)2$ nodes.