A Brief Introduction To NavigableSet And NavigableMap
The NavigableSet/NavigableMap interfaces are just add-ons for the SortedSet/SortedMap interfaces. They provide new methods that help you easily list, extract, and modify a SortedSet/SortedMap. This allows you to use a dedicated large number of NavigableSet/NavigableMap methods just for navigation without supplying any "helper" methods. Figure 3 shows the position of the NavigableSet/NavigableMap interfaces in the java.util package.

NavigableSet
The NavigableSet interface provides methods for accessing elements of a SortedSet. Table 1 below splits these methods by their nature:
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Iteration methods
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Polls methods
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LHCF methods
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Subset methods
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iterator
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pollFirst
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lower
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headSet
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descendingIterator
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pollLast
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higher
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subSet
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ceiling
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tailSet
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floor
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Table 1. The NavigableSet interface provides methods for accessing elements of a SortedSet.
Let's go over the items covered in the table:
Polls methods are used to extract elements from a SortedSet.
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E pollFirst() removes and returns the first element from the current SortedSet.
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E pollLast() removes and returns the last element from the current SortedSet.
Notice that unlike the first and last methods from the SortedSet interface, the pollFirst and pollLast methods removes and returns the first, respectively last element from the SortedSet and not just returns them.
Listing 4 is an example of using the pollFirst and pollLast methods. Figure 4 shows a graphical view of the application in Listing 4.

LHCF methods consist of the lower (L), higher (H), ceiling (C) and floor (F) methods:
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E lower(E e) returns the greater element "<" than the given element (null if there is no such element).
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E higher(E e) returns the lesser element ">" than the given element (null if there is no such element)
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E ceiling(E e) returns the least element ">=" to the given element (null if there is no such element)
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E floor(E e) returns the greatest element "<=" to the given element (null if there is no such element).
Listing 5 is an example of using the above methods (the tested element was "Hydro"). Figure 5 shows a graphical view of the application in Listing 5.

Subset methods are used to extract a subset from a SortedSet.
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NavigableSet<E> headSet(E toElement,boolean inclusive) returns a subset-view of the current set whose elements are less than (or equal to, if inclusive is true) toElement. Another headSet method is SortedSet<E> headSet(E toElement). This is equivalent to headSet(toElement, false).
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NavigableSet<E> subSet(E fromElement,boolean fromInclusive,E toElement, boolean toInclusive) returns a subset-view of the current set whose elements range is [fromElement, toElement). By modifying the fromInclusive, toInclusive arguments you can obtain the following ranges: [fromElement, toElement], (fromElement, toElement), (fromElement, toElement]. Another subSet method is: SortedSet<E> subSet(E fromElement,E toElement). This is equivalent to subSet(fromElement, true, toElement, false).
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NavigableSet<E> tailSet(E fromElement,boolean inclusive) returns a subset-view of this set whose elements are greater than (or equal to, if inclusive is true) fromElement. Another tailSet method is SortedSet<E> tailSet(E fromElement). This is equivalent to tailSet(fromElement, true).
Note: In all cases, the returned subset is backed by the current set, so changes in the returned subset are reflected in this set, and vice-versa.
Listing 6 shows what using these methods looks like. Figure 6 shows a graphical view of the application in Listing 6.

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