Algorithm 1 Mergable Heap Implemented with Sorted List

1:procedure MakeHeap()

2:Let $L$ be an empty singly linked list, i.e. $L.head$ is $NIL$

3:return $L$

4:end procedure

6:procedure Insert( $L, x$ )

7:if $L.head == NIL$ or $x.key \le L.head.key$ then

8: $x.next = L.head$

9: $L.head = x$

10:else

11: $prev = L.head$

12: $cur = L.head.next$

13:while $cur \ne NIL$ and $x.key > cur.key$ do

14: $prev = cur$

15: $cur = cur.next$

16:end while

17: $prev.next = x$

18: $x.next = cur$

19:end if

20:end procedure

21:

22:procedure Minimum( $L$ )

23:return $L.head$

24:end procedure

25:

26:procedure ExtractMin( $L$ )

27:if $L.head == NIL$ then

28:return $NIL$

29:end if

30: $x = L.head$

31: $L.head = x.next$

32:return $x$

33:end procedure

34:

35:procedure Union( $L_1, L_2$ )

36:if $L_1.head == NIL$ then

37:return $L_2$

38:else if $L_2.head == NIL$ then

39:return $L_1$

40:else

41: $p_1 = L_1.head$

42: $p_2 = L_2.head$

43:Let $L$ be an empty singly linked list, i.e. $L.head$ is $NIL$ .

44:if $p_1.key < p_2.key$ then

45: $L.head = p_1$

46: $p_1 = p_1.next$

47:else

48: $L.head = p_2$

49: $p_2 = p_2.next$

50:end if

51: $tail = L.head$

52:while $p_1 \ne NIL$ and $p_2 \ne NIL$ do

53:if $p_1.key < p_2.key$ then

54: $tail.next = p_1$

55: $tail = p_1$

56: $p_1 = p_1.next$

57:else

58: $tail.next = p_2$

59: $tail = p_2$

60: $p_2 = p_2.next$

61:end if

62:end while

63:if $p_1 \ne NIL$ then

64: $tail.next = p_1$

65:else if $p_2 \ne NIL$ then

66: $tail.next = p_2$

67:end if

68:return $L$

69:end if

70:end procedure