Algorithm 1 Minimum Heapify

1:procedure MinHeapify( $A, i$ )

2: $l =$ Left( $i$ )

3: $r =$ Right( $i$ )

4:if $l\le A.\text{heap-size}$ and $A[l] < A[i]$ then

5: $smallest = l$

6:else

7: $smallest = i$

8:end if

9:if $r\le A.\text{heap-size}$ and $A[r] < A[i]$ then

10: $smallest = r$

11:end if

12:if $smallest \ne i$ then

13:exchange $A[i]$ with $A[smallest]$

14:MaxHeapify( $A, smallest$ )

15:end if

16:end procedure