Collections class, and all take the form of static methods whose first argument
is the collection on which the operation is to be performed.
The great majority of the algorithms provided by the Java platform operate on
List instances, but a few of them operate on arbitrary
Collection instances.  This section briefly describes the following algorithms:
sort algorithm reorders a List so that its
elements are in ascending order according to an ordering relationship.
Two forms of the operation are provided. The simple form takes a
List and sorts it according to its elements'
natural ordering. If you're unfamiliar with the concept
of natural ordering, read the
Object Ordering section.
The sort operation uses a slightly optimized merge sort
algorithm that is fast and stable:
n log(n)
time and runs substantially faster on nearly sorted lists.
Empirical tests showed it to be as fast as a highly optimized quicksort.
A quicksort is generally considered to be faster than a merge sort but isn't
stable and doesn't guarantee n log(n) performance.
trivial program
 prints out its arguments in lexicographic (alphabetical) order.
import java.util.*;
public class Sort {
    public static void main(String[] args) {
        List<String> list = Arrays.asList(args);
        Collections.sort(list);
        System.out.println(list);
    }
}
% java Sort i walk the line
[i, line, the, walk]
The second form of sort takes a
Comparator in addition to a List and sorts the elements with the
Comparator.  Suppose you want to print out the anagram
groups from our earlier example in reverse order of size — largest
anagram group first. The example that follows shows you how to achieve
this with the help of the second form of the sort method.
Recall that the anagram groups are stored as values in a Map,
in the form of List instances. The revised printing code iterates
through the Map's values view, putting every List
that passes the minimum-size test into a List of Lists.
Then the code sorts this List, using a Comparator
that expects List instances, and implements reverse size-ordering. Finally, the code iterates through the sorted List,
printing its elements (the anagram groups). The following code replaces
the printing code at the end of the main method in the
Anagrams example.
// Make a List of all anagram groups above size threshold.
List<List<String>> winners = new ArrayList<List<String>>();
for (List<String> l : m.values())
    if (l.size() >= minGroupSize)
        winners.add(l);
// Sort anagram groups according to size
Collections.sort(winners, new Comparator<List<String>>() {
    public int compare(List<String> o1, List<String> o2) {
        return o2.size() - o1.size();
    }});
// Print anagram groups.
for (List<String> l : winners)
    System.out.println(l.size() + ": " + l);
the program on the
same dictionary as in
The Map Interface section, with the same minimum anagram group size
(eight), produces the following output.
12: [apers, apres, asper, pares, parse, pears, prase,
       presa, rapes, reaps, spare, spear]
11: [alerts, alters, artels, estral, laster, ratels,
       salter, slater, staler, stelar, talers]
10: [least, setal, slate, stale, steal, stela, taels,
       tales, teals, tesla]
9: [estrin, inerts, insert, inters, niters, nitres,
       sinter, triens, trines]
9: [capers, crapes, escarp, pacers, parsec, recaps,
       scrape, secpar, spacer]
9: [palest, palets, pastel, petals, plates, pleats,
       septal, staple, tepals]
9: [anestri, antsier, nastier, ratines, retains, retinas,
       retsina, stainer, stearin]
8: [lapse, leaps, pales, peals, pleas, salep, sepal, spale]
8: [aspers, parses, passer, prases, repass, spares,
       sparse, spears]
8: [enters, nester, renest, rentes, resent, tenser,
       ternes, treens]
8: [arles, earls, lares, laser, lears, rales, reals, seral]
8: [earings, erasing, gainers, reagins, regains, reginas,
       searing, seringa]
8: [peris, piers, pries, prise, ripes, speir, spier, spire]
8: [ates, east, eats, etas, sate, seat, seta, teas]
8: [carets, cartes, caster, caters, crates, reacts,
       recast, traces]
shuffle algorithm does the opposite of what sort does, destroying any trace of order that may have been present in a List. That is, this algorithm reorders the List based on input from a source of randomness such that all possible permutations occur with equal likelihood, assuming a fair source of randomness. This algorithm is useful in implementing games of chance. For example, it could be used to shuffle a List of Card objects representing a deck. Also, it's useful for generating test cases.
This operation has two forms: one takes a List and uses a
default source of randomness, and the other requires the caller to
provide a
Random object to use as a source of randomness. The code for this algorithm
is used as an example in the
List section.
Collections class provides five algorithms for doing
routine data manipulation on List objects, all of which are pretty straightforward:
reverse — reverses the order of the elements in a List.
fill — overwrites every element in a List with the specified value.
This operation is useful for reinitializing a List.
copy — takes two arguments, a destination List
and a source List, and copies the elements of the source
into the destination, overwriting its contents.  The destination
List must be at least as long as the source. If it is longer,
the remaining elements in the destination List are unaffected.
swap — swaps the elements at the specified positions in a List.
addAll — adds all the specified elements to a Collection.
The elements to be added may be specified individually or as an array.
binarySearch algorithm searches for a specified element
in a sorted List. This algorithm has two forms. The first
takes a List and an element to search for (the "search key").
This form assumes that the List is sorted in ascending order
according to the natural ordering of its elements. The second form takes a
Comparator in addition to the List and the search key,
and assumes that the List is sorted into ascending order according
to the specified Comparator. The sort algorithm can
be used to sort the List prior to calling binarySearch.
The return value is the same for both forms. If the List
contains the search key, its index is returned. If not, the return
value is (-(insertion point) - 1), where the insertion point is the
point at which the value would be inserted into the List,
or the index of the first element greater than the value or
list.size() if all elements in the List are less
than the specified value. This admittedly ugly formula guarantees that
the return value will be >= 0 if and only if the search
key is found. It's basically a hack to combine a boolean (found)
and an integer (index) into a single int return value.
The following idiom, usable with both forms of the binarySearch
operation, looks for the specified search key and inserts it at the
appropriate position if it's not already present.
    int pos = Collections.binarySearch(list, key);
    if (pos < 0)
       l.add(-pos-1);
Collections:
frequency — counts the number of times the specified element occurs in the specified collection
disjoint — determines whether two Collections are disjoint; that is, whether they contain no elements in common
min and the max algorithms return, respectively,
the minimum and maximum element contained in a specified
Collection. Both of these operations come in two forms.
The simple form takes only a Collection and returns the
minimum (or maximum) element according to the elements' natural ordering.
The second form takes a Comparator in addition to the
Collection and returns the minimum (or maximum) element according
to the specified Comparator.