Lab 14, Task 3
--------------
1.  At the end of the previous task, we had the following heap:

			   +----+
			   | 12 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  8 |                  |  6 |
	       +----+                  +----+
	      /      \                /      \
	+----+        +----+    +----+        +----+
	|  3 |        |  7 |    |  4 |        |  5 |
	+----+        +----+    +----+        +----+

    The corresponding array looks like this:

       {12, 8, 6, 3, 7, 4, 5}


2.  Remove 12.
    Place 5 at the root and sift down.

			   +----+
			   |  5 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  8 |                  |  6 |
	       +----+                  +----+
	      /      \                /
	+----+        +----+    +----+
	|  3 |        |  7 |    |  4 |
	+----+        +----+    +----+

    The 8 moves up.

			   +----+
			   |  8 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  5 |                  |  6 |
	       +----+                  +----+
	      /      \                /
	+----+        +----+    +----+
	|  3 |        |  7 |    |  4 |
	+----+        +----+    +----+

    The 7 moves up, and the 5 goes where the 7 used to be.

			   +----+
			   |  8 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  7 |                  |  6 |
	       +----+                  +----+
	      /      \                /
	+----+        +----+    +----+
	|  3 |        |  5 |    |  4 |
	+----+        +----+    +----+

    The removed item (the 12) is put in the last position of the array, 
    which now looks like this:

       {8, 7, 6, 3, 5, 4, 12}


2.  Remove 8. 
    Place 4 at the root and sift down.

			   +----+
			   |  4 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  7 |                  |  6 |
	       +----+                  +----+
	      /      \
	+----+        +----+
	|  3 |        |  5 |
	+----+        +----+

    The 7 moves up.

			   +----+
			   |  7 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  4 |                  |  6 |
	       +----+                  +----+
	      /      \
	+----+        +----+
	|  3 |        |  5 |
	+----+        +----+

    The 5 moves up, and the 4 goes where the 5 used to be.

			   +----+
			   |  7 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  5 |                  |  6 |
	       +----+                  +----+
	      /      \
	+----+        +----+
	|  3 |        |  4 |
	+----+        +----+

    The removed item (the 8) is put in the second-to-last position of
    the array, which now looks like this:

       {7, 5, 6, 3, 4, 8, 12}


3.  Remove 7.
    Place 4 at the root and sift.

			   +----+
			   |  4 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  5 |                  |  6 |
	       +----+                  +----+
	      /
	+----+
	|  3 |
	+----+

    The 6 moves up, and the 4 goes where the 6 used to be:

			   +----+
			   |  6 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  5 |                  |  4 |
	       +----+                  +----+
	      /
	+----+
	|  3 |
	+----+

    The removed item (the 7) is put in the third-to-last position of
    the array, which now looks like this:

       {6, 5, 4, 3, 7, 8, 12}


4.  Remove 6.
    Place 3 at the root and sift.

			   +----+
			   |  3 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  5 |                  |  4 |
	       +----+                  +----+

    The 5 moves up, and the 3 goes where the 5 used to be.

			   +----+
			   |  5 |
			   +----+
		      ____/      \____
		     /                \
	       +----+                  +----+
	       |  3 |                  |  4 |
	       +----+                  +----+


    The removed item (the 6) is put in the fourth-to-last position of
    the array, which now looks like this:

       {5, 3, 4, 6, 7, 8, 12}


5.  Remove 5.
    Place 4 at the root and sift, but it doesn't move.

			   +----+
			   |  4 |
			   +----+
		      ____/
		     /
	       +----+
	       |  3 |
	       +----+

    The removed item (the 5) is put in the fifth-to-last position of
    the array, which now looks like this:

       {4, 3, 5, 6, 7, 8, 12}


6.  Remove 4. 
    Place 3 at the root, and we're done, because there is only one 
    item left in the heap. 

    The removed item (the 4) is put in position 1 of the array, which
    is now fully sorted:

       {3, 4, 5, 6, 7, 8, 12}