> (define empty-tree-of-strings(leftist-tree string<=? ))
> (define non-empty-tree-of-strings(leftist-tree string<=? '("once""upon""a""time")))
> empty-tree-of-strings

#<leftist-tree [empty]>
> non-empty-tree-of-strings

#<leftist-tree [count=4; min="a"]>

procedure
( leftist-tree? x)→boolean?
x:any/c

Returns #t if x is a leftist tree, #f otherwise.

Examples:

> (leftist-tree? (leftist-tree <= ))

#t
> (leftist-tree? "I can haz treaz?")

#f

procedure
( leftist-tree-empty? t)→leftist-tree?
t:leftist-tree?

Returns #t if t is empty, #f otherwise.

Examples:

> (define t(leftist-tree string<=? ))
> (leftist-tree-empty? t)

#t
> (leftist-tree-empty? (leftist-tree-add t"κατέβην χθὲς εἰς Πειραιᾶ μετὰ Γλαύκωνος τοῦ Ἀρίστωνος..."))

#f

procedure
( leftist-tree-count t)→exact-nonnegative-integer?
t:leftist-tree?

Returns the number of elements in t.

Examples:

> (define t(leftist-tree string<=? ))
> (leftist-tree-count t)

0
> (leftist-tree-count (leftist-tree-add-all t(enum->liststring/e10)))

10

procedure
( leftist-tree-add tx)→leftist-tree?
t:leftist-tree?
x:any/c

Functionally extends t by adding x and returns the extended tree.

Examples:

> (define empty(leftist-tree string<=? ))
> (define non-empty(leftist-tree-add empty"Hello world!"))

procedure
( leftist-tree-add-all txs)→leftist-tree?
t:leftist-tree?
xs:sequence?

Functionally extends t by adding all elements of the sequence xs and returns the extended tree.

Examples:

> (define empty(leftist-tree string<=? ))
> (define words'("some pig!""terrific""radiant""humble"))
> (leftist-tree-add-all emptywords)

#<leftist-tree [count=4; min="humble"]>

procedure
( leftist-tree-min t)→any/c
t:leftist-tree?

Returns the least element in t according to the tree’s ordering. If the tree is empty, an exception is raised.

Examples:

> (define empty(leftist-tree string<=? ))
> (define words'("some pig!""terrific""radiant""humble"))
> (leftist-tree-min (leftist-tree-add-all emptywords))

"humble"

procedure
( leftist-tree-remove-min t)→leftist-tree?
t:leftist-tree?

Functionally removes the least element in t and returns the fresh tree.

Examples:

> (define empty(leftist-tree string<=? ))
> (define words'("some pig!""terrific""radiant""humble"))
> (define full(leftist-tree-add-all emptywords))
> (leftist-tree-count full)

4
> (leftist-tree-count (leftist-tree-remove-min full))

3

procedure
( leftist-tree->list t)→(listof any/c )
t:leftist-tree?

Returns an ordered list of the elements of t.

Examples:

> (define empty(leftist-tree string<=? ))
> (define words'("some pig!""terrific""radiant""humble"))
> (define full(leftist-tree-add-all emptywords))
> (leftist-tree->list full)

'("humble" "radiant" "some pig!" "terrific")

procedure
( in-leftist-tree t)→sequence?
t:leftist-tree?

Returns a sequence that generates the elements of t in order.

Examples:

> (define empty(leftist-tree string<=? ))
> (define words'("some pig!""terrific""radiant""humble"))
> (define full(leftist-tree-add-all emptywords))

> (for ([word(in-leftist-tree full)])
(displayln word))

humble

radiant

some pig!

terrific

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