Question

[12] 3. a) Draw the binary min-heap after inserting the following values, one after another. 21, 13, 12, 25, 4, 20, 16, 1, 11 You must show each step of building the heap and eventually the final tree. Please, put your final tree inside a box so that it can be easily understood among other intermediate trees. b) A 4-ary max heap is like a binary max heap, but instead of 2 children, nodes have 4 children. A 4-ary heap can be represented by an array as shown in Figure 1 (up to level 2). A[0] A[1] A[2] A[3] A[4] 10 IN 1121 114 TIS 1171 IN 130 2 Figure 1: 4-ary heap representation using an array Write down MAX_HEAPIFY (A, i) function for a 4-ary max-heap that restores the heap property for th node. 111

Answer 1

(a)

2 13 3 D 21 12 21 13 Heapify 13 12 21 113 2) 21 12 2) 13 4 25 5 4 12 4 12 Heapify 219 iz 13 13 2) 13 25 21 25 25 4 6 20 7 16 8 4 4 4 13 13 13 12 25 21 20 2) 25 21 20 16 20 U 9 ) 1 13 и 13 M 4 13 2 20 16 12 21 20 16 12 21 16 20 (25 '12 25 25 ) (11) final Heal 4 13 11 21 20 16 25 12

(b)MAXHEAPIFY(A , i)
{
    child1 = 4*i + 1;
    child2 = 4*i + 2;
    child3 = 4*i + 3;
    child4 = 4*i + 4;
    max = i;
    if (child1 < A.length && A[child1] > A[max])
        max = child1;
    if (child2 < A.length && A[child2] > A[max])
        max = child2;
    if (child3 < A.length && A[child3] > A[max])
        max = child3;
    if (child4 < A.length && A[child4] > A[max])
        max = child4;
    if (max != i)
    {
        swap(A[i], A[max]);
        MAXHEAPIFY(A , max)
    }
}