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How to calculate complexity of internal iterations

This is regarding identifying time complexity of a java program. If i've iterations like for or while etc, we can identify the complexity. But if i use java API to do some task, if it is internally iterating, i think we should include that as well. If so, how to do that.
Example :
String someString = null;
for(int i=0;i<someLength;i++){
someString.contains("something");// Here i think internal iteration will happen, likewise how to identify time complexity
}
Thanks,
Aditya

Internal operations in the Java APIs have their own time complexity based on their implementation. For example the contains method of the String variable runs with linear complexity, where the dependency is based on the length of your someString variable.
In short - you should check how inner operations work and take them into consideration when calculating complexity.
Particularly for your code the time complexity is something like O(N*K), where N is the number of iterations of your loop (someLength) and K is the length of your someString variable.

You are correct in that the internal iterations will add to your complexity. However, except in a fairly small number of cases, the complexity of API methods is not well documented. Many collection operations come with an upper bound requirement for all implementations, but even in such cases there is no guarantee that the actual code doesn't have lower complexity than required. For cases like String.contains() an educated guess is almost certain to be correct, but again there is no guarantee.
Your best bet for a consistent metric is to look at the source code for the particular API implementation you are using and attempt to figure out the complexity from that. Another good approach would be to run benchmarks on the methods you care about with a wide range of input sizes and types and simply estimate the complexity from the shape of the resulting graph. The latter approach will probably yield better results for cases where the code is too complex to analyze directly.

Implementing efficient data structure using Arrays only

As part of my programming course I was given an exercise to implement my own String collection. I was planning on using ArrayList collection or similar but one of the constraints is that we are not allowed to use any Java API to implement it, so only arrays are allowed. I could have implemented this using arrays however efficiency is very important as well as the amount of data that this code will be tested with. I was suggested to use hash tables or ordered tress as they are more efficient than arrays. After doing some research I decided to go with hash tables because they seemed easy to understand and implement but once I started writing code I realised it is not as straight forward as I thought.
So here are the problems I have come up with and would like some advice on what is the best approach to solve them again with efficiency in mind:
ACTUAL SIZE: If I understood it correctly hash tables are not ordered (indexed) so that means that there are going to be gaps in between items because hash function gives different indices. So how do I know when array is full and I need to resize it?
RESIZE: One of the difficulties that I need to create a dynamic data structure using arrays. So if I have an array String[100] once it gets full I will need to resize it by some factor I decided to increase it by 100 each time so once I would do that I would need to change positions of all existing values since their hash keys will be different as the key is calculated:
int position = "orange".hashCode() % currentArraySize;
So if I try to find a certain value its hash key will be different from what it was when array was smaller.
HASH FUNCTION: I was also wondering if built-in hashCode() method in String class is efficient and suitable for what I am trying to implement or is it better to create my own one.
DEALING WITH MULTIPLE OCCURRENCES: one of the requirements is to be able to add multiple words that are the same, because I need to be able to count how many times the word is stored in my collection. Since they are going to have the same hash code I was planning to add the next occurrence at the next index hoping that there will be a gap. I don't know if it is the best solution but here how I implemented it:
public int count(String word) {
int count = 0;
while (collection[(word.hashCode() % size) + count] != null && collection[(word.hashCode() % size) + count].equals(word))
count++;
return count;
}
Thank you in advance for you advice. Please ask anything needs to be clarified.
P.S. The length of words is not fixed and varies greatly.
UPDATE Thank you for your advice, I know I did do few stupid mistakes there I will try better. So I took all your suggestions and quickly came up with the following structure, it is not elegant but I hope it is what you roughly what you meant. I did have to make few judgements such as bucket size, for now I halve the size of elements, but is there a way to calculate or some general value? Another uncertainty was as to by what factor to increase my array, should I multiply by some n number or adding fixed number is also applicable? Also I was wondering about general efficiency because I am actually creating instances of classes, but String is a class to so I am guessing the difference in performance should not be too big?

ACTUAL SIZE: The built-in Java HashMap just resizes when the total number of elements exceeds the number of buckets multiplied by a number called the load factor, which is by default 0.75. It does not take into account how many buckets are actually full. You don't have to, either.
RESIZE: Yes, you'll have to rehash everything when the table is resized, which does include recomputing its hash.
So if I try to find a certain value it's hash key will be different from what it was when array was smaller.
Yup.
HASH FUNCTION: Yes, you should use the built in hashCode() function. It's good enough for basic purposes.
DEALING WITH MULTIPLE OCCURRENCES: This is complicated. One simple solution would just be to have the hash entry for a given string also keep count of how many occurrences of that string are present. That is, instead of keeping multiple copies of the same string in your hash table, keep an int along with each String counting its occurrences.

So how do I know when array is full and I need to resize it?
You keep track of the size and HashMap does. When the size used > capacity * load factor you grow the underlying array, either as a whole or in part.
int position = "orange".hashCode() % currentArraySize;
Some things to consider.
The % of a negative value is a negative value.
Math.abs can return a negative value.
Using & with a bit mask is faster however you need a size which is a power of 2.
I was also wondering if built-in hashCode() method in String class is efficient and suitable for what I am trying to implement or is it better to create my own one.
The built in hashCode is cached, so it is fast. However it is not a great hashCode and has poor randomness for lower bit, and higher bit for short strings. You might want to implement your own hashing strategy, possibly a 64-bit one.
DEALING WITH MULTIPLE OCCURRENCES:
This is usually done with a counter for each key. This way you can have say 32767 duplicates (if you use short) or 2 billion (if you use int) duplicates of the same key/element.

Fast string retrieval based on metric distance in Java

Given an arbitrary string s, I would like a method to quickly retrieve all strings S ⊆ M from a large set of strings M (where |M| > 1 million), where all strings of S have minimal edit distance < t (some minimum threshold) from s.
At worst, S may be empty if no strings in M match this criteria, and at best, S = {s} (an exact match). For any case in between, I completely expect that S may be quite large.
In general, I expect to have the maximum edit distance threshold fixed (e.g., 2), and need to perform this operation very many times over arbitrary strings s, thus the need for an efficient method, as naively iterating and testing all strings would be too expensive.
While I have used edit distance as an example metric, I would like to use other metrics as well, such as the Jaccard index.
Can anyone make a suggestion about an existing Java implementation which can achieve this, or point me to the right algorithms and data structures for solving this problem?
UPDATE #1
I have since learned that Metric trees are precisely the kind of structure I am after, which exploits the distance metric to organise subsets of strings in M based on their distance from each other with the metric. Both Vantage-Point, BK and other similar metric tree data structures and algorithms seem ideal for this kind of problem. Now, to find easy-to-use implementations in Java...
UPDATE #2
Using a combination of this bk-tree and this Levenshtein distance implementation, I'm successfully able to retrieve subsets against arbitrary strings from a set (M) of one million strings with retrieval times of around 10ms.

BK trees are designed for such a case. It works with metric distance, such as Levenshtein or Jaccard index.

Although I never tried it myself, it might be worth looking at a Levenshtein Automaton. I once bookmarked this article, which looks rather elaborate and provides several code snippets:
Damn Cool Algorithms: Levenshtein Automata
As already mentioned by H W you will not be able to avoid checking each word in your dictionary. However, the automaton will speed up calculating the distance. Combine this with an efficient data structure for your dictionary (e.g. a Trie, as mentioned in the Wikipedia article), and you might be able to accelerate you current approach.

What is the best algorithm for matching two string containing less than 10 words in latin script

I'm comparing song titles, using Latin script (although not always), my aim is an algorithm that gives a high score if the two song titles seem to be the same same title and a very low score if they have nothing in common.
Now I already had to code (Java) to write this using Lucene and a RAMDirectory - however using Lucene simply to compare two strings is too heavyweight and consequently too slow. I've now moved to using https://github.com/nickmancol/simmetrics which has many nice algorithms for comparing two strings:
https://github.com/nickmancol/simmetrics/tree/master/src/main/java/uk/ac/shef/wit/simmetrics/similaritymetrics
BlockDistance
ChapmanLengthDeviation
ChapmanMatchingSoundex
ChapmanMeanLength
ChapmanOrderedNameCompoundSimilarity
CosineSimilarity
DiceSimilarity
EuclideanDistance
InterfaceStringMetric
JaccardSimilarity
Jaro
JaroWinkler
Levenshtein
MatchingCoefficient
MongeElkan
NeedlemanWunch
OverlapCoefficient
QGramsDistance
SmithWaterman
SmithWatermanGotoh
SmithWatermanGotohWindowedAffine
Soundex
but I'm not well versed in these algorithms and what would be a good choice ?
I think Lucene uses CosineSimilarity in some form, so that is my starting point but I think there might be something better.
Specifically, the algorithm should work on short strings and should understand the concept of words, i.e spaces should be treated specially. Good matching of Latin script is most important, but good matching of other scripts such as Korean and Chinese is relevant as well but I expect would need different algorithm because of the way they treat spaces.

They're all good. They work on different properties of strings and have different matching properties. What works best for you depends on what you need.
I'm using the JaccardSimilarity to match names. I chose the JaccardSimilarity because it was reasonably fast and for short strings excelled in matching names with common typo's while quickly degrading the score for anything else. Gives extra weight to spaces. It is also insensitive to word order. I needed this behavior because the impact of a false positive was much much higher then that off a false negative, spaces could be typos but not often and word order was not that important.
Note that this was done in combination with a simplifier that removes non-diacritics and a mapper that maps the remaining characters to the a-z range. This is passed through a normalizes that standardizes all word separator symbols to a single space. Finally the names are parsed to pick out initials, pre- inner- and suffixes. This because names have a structure and format to them that is rather resistant to just string comparison.
To make your choice you need to make a list of what criteria you want and then look for an algorithm that satisfied those criteria. You can also make a reasonably large test set and run all algorithms on that test set too see what the trade offs are with respect to time, number of positives, false positives, false negatives and negatives, the classes of errors your system should handle, ect, ect.
If you are still unsure of your choice, you can also setup your system to switch the exact comparison algorithms at run time. This allows you to do an A-B test and see which algorithm works best in practice.
TLDR; which algorithm you want depends on what you need, if you don't know what you need make sure you can change it later on and run tests on the fly.

You are likely need to solve a string-to-string correction problem. Levenshtein distance algorithm is implemented in many languages. Before running it I'd remove all spaces from string, because they don't contain any sensitive information, but may influence two strings difference. For string search prefix trees are also useful, you can have a look in this direction as well. For example here or here. Was already discussed on SO. If spaces are so much significant in your case, just assign a greater weight to them.

Each algorithm is going to focus on a similar, but slightly different aspect of the two strings. Honestly, it depends entirely on what you are trying to accomplish. You say that the algorithm needs to understand words, but should it also understand interactions between those words? If not, you can just break up each string according to spaces, and compare each word in the first string to each word in the second. If they share a word, the commonality factor of the two strings would need to increase.
In this way, you could create your own algorithm that focused only on what you were concerned with. If you want to test another algorithm that someone else made, you can find examples online and run your data through to see how accurate the estimated commonality is with each.
I think http://jtmt.sourceforge.net/ would be a good place to start.

Interesting. Have you thought about a radix sort?
http://en.wikipedia.org/wiki/Radix_sort
The concept behind the radix sort is that it is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys by the individual digits. If you convert your string into an array of characters, which will be a number no greater than 3 digits, then your k=3(maximum number of digits) and you n = number of string to compare. This will sort the first digits of all your strings. Then you will have another factor s=the length of the longest string. your worst case scenario for sorting would be 3*n*s and the best case would be (3 + n) * s. Check out some radix sort examples for strings here:
http://algs4.cs.princeton.edu/51radix/LSD.java.html
http://users.cis.fiu.edu/~weiss/dsaajava3/code/RadixSort.java

Did you take a look at the levenshtein distance ?
int org.apache.commons.lang.StringUtils.getLevenshteinDistance(String s, String t)
Find the Levenshtein distance between two Strings.
This is the number of changes needed to change one String into
another, where each change is a single character modification
(deletion, insertion or substitution).
The previous implementation of the Levenshtein distance algorithm was
from http://www.merriampark.com/ld.htm
Chas Emerick has written an implementation in Java, which avoids an
OutOfMemoryError which can occur when my Java implementation is used
with very large strings. This implementation of the Levenshtein
distance algorithm is from http://www.merriampark.com/ldjava.htm
Anyway, I'm curious to know what do you choose in this case !

Efficient Intersection and Union of Lists of Strings

I need to efficiently find the ratio of (intersection size / union size) for pairs of Lists of strings. The lists are small (mostly about 3 to 10 items), but I have a huge number of them (~300K) and have to do this on every pair, so I need this actual computation to be as efficient as possible. The strings themselves are short unicode strings -- averaging around 5-10 unicode characters.
The accepted answer here Efficiently compute Intersection of two Sets in Java? looked extremely helpful but (likely because my sets are small (?)) I haven't gotten much improvement by using the approach suggested in the accepted answer.
Here's what I have so far:
protected double uuEdgeWeight(UVertex u1, UVertex u2) {
Set<String> u1Tokens = new HashSet<String>(u1.getTokenlist());
List<String> u2Tokens = u2.getTokenlist();
int intersection = 0;
int union = u1Tokens.size();
for (String s:u2Tokens) {
if (u1Tokens.contains(s)) {
intersection++;
} else {
union++;
}
}
return ((double) intersection / union);
My question is, is there anything I can do to improve this, given that I'm working with Strings which may be more time consuming to check equality than other data types.
I think because I'm comparing multiple u2's against the same u1, I could get some improvement by doing the cloning of u2 into a HashSet outside of the loop (which isn't shown -- meaning I'd pass in the HashSet instead of the object from which I could pull the list and then clone into a set)
Anything else I can do to squeak out even a small improvement here?
Thanks in advance!
Update
I've updated the numeric specifics of my problem above. Also, due to the nature of the data, most (90%?) of the intersections are going to be empty. My initial attempt at this used the clone the set and then retainAll the items in the other set approach to find the intersection, and then shortcuts out before doing the clone and addAll to find the union. That was about as efficient as the code posted above, presumably because of the trade of between it being a slower algorithm overall versus being able to shortcut out a lot of the time. So, I'm thinking about ways to take advantage of the infrequency of overlapping sets, and would appreciate any suggestions in that regard.
Thanks in advance!

You would get a large improvement by moving the HashSet outside of the loop.
If the HashSet really has only got a few entries in it then you are probably actually just as fast to use an Array - since traversing an array is much simpler/faster. I'm not sure where the threshold would lie but I'd measure both - and be sure that you do the measurements correctly. (i.e. warm up loops before timed loops, etc).
One thing to try might be using a sorted array for the things to compare against. Scan until you go past current and you can immediately abort the search. That will improve processor branch prediction and reduce the number of comparisons a bit.

If you want to optimize for this function (not sure if it actually works in your context) you could assign each unique String an Int value, when the String is added to the UVertex set that Int as a bit in a BitSet.
This function should then become a set.or(otherset) and a set.and(otherset). Depending on the number of unique Strings that could be efficient.