Hashing Function/Code

Question

so I'm just learning (or trying to) a bit about hashing. I'm attempting to make a hashing function, however I'm confused where I save the data to. I'm trying to calculate the number of collisions and print that out. I have made 3 different files, one with 10,000 words, 20,000 words and 30,000 words. Each word is just 10 random numbers/letters.

long hash(char* s]){
    long h;
    for(int i = 0; i < 10; i++){
      h = h + (int)s[i];
    }
     //A lot of examples then mod h by the table size
     //I'm a bit confused what this table is... Is it an array of
     //10,000 (or however many words)?

    //h % TABLE_SIZE
    return h
  }

  int main (int argc, char* argv[]){
    fstream input(argv[1]);
    char* nextWord;
    while(!input.eof()){
      input >> nextWord;
      hash(nextWord);
    }
  }

So that's what I currently have, but I can't figure out what the table is exactly, as I said in the comments above... Is it a predefined array in my main with the number of words in it? For example, if I have a file of 10 words, do I make an array a of size 10 in my main? Then if/when I return h, lets say the order goes: 3, 7, 2, 3

The 4th word is a collision, correct? When that happens, I add 1 to collision and then add 1 to then check if slot 4 is also full?

Thanks for the help!

Answer 1

The point of hashing is to have a constant time access to every element you store. I'll try to explain on simple example bellow.

First, you need to know how much data you'd have to store. If for example you want to store numbers and you know, that you won't store numbers greater than 10. Simpliest solution is to create an array with 10 elements. That array is your "table", where you store your numbers. So how do I achieve that amazing constant time access? Hashing function! It's point is to return you an index to your array. Let's create a simple one: If you'd like to store 7, you just save it to array on position 7. Every time, you'd like to look, for element 7, you just pass it to your hasning funcion and bzaah! You got an position to your element in constant time! But what if you'd like to store more elements with value 7? Your simple hashing function is returning 7 for every element and now its position i already occupied! How to solve that? Well, there is not many solution, the simpliest are:

1: Chaining - you simply save element on first free position. This has significant draw back. Imagine, you want to delete some element ... (this is the method, you describing in question)

2: Linked list - if you create an array of pointers on some linked lists, you can easilly add your new element at the end of linked list, that is on position 7!

Both of this simple solutions has its drawbacks and cons. I guess you can see them. As @rwols has said, you don't have to use array. You can also use a tree or be a real C++ master and use unordered_map and unordered_set with custom hash function, which is quite cool. Also there is structure named trie, which is usefull, when you'd like to create some sort of dictionary (where is really hard to know, how many words you will need to store)

To sum it up. You has to know, how many things, you wan't to store and then, create ideal hashing function, that covers up array of apropriate size and in perfect world, it has to have uniform index distribution, with no colisions. (Achiving this is pretty hard and in the real world, I guess, this is impossible, so the less colisions, the better.)

Your hash function, is pretty bad. It will have lot of colisions (like strings "ab" and "ba") and also, you need to mod m it with m being the size of you array (aka. table), so you can save it to some array and you can profit of it. The modus is a way of simplyfiing the has function, because has function has to "fit" in table, that you specified in beginning, because you can't save element on position 11, 12, ... if you have array of 10.

How should good hashing function look like? Well, there is better sources than me. Some example (Alert! It's in Java)

To your example: You simply can't save 10k or even more words into table of size 10. That'll create a lot of collisions and you loose the main benefit of hashing function - constant access to elements you saved.

And how would your code look? Something like this:

int main (int argc, char* argv[]){
    fstream input(argv[1]);
    char* nextWord;

    TypeOfElement table[size_of_table];
    while(!input.eof()){
      input >> nextWord;
      table[hash(nextWord)] = // desired element which you want to save
    }
  }

But I guess, your goal isn't to save something somewhere, but to count number of colisions. Also note that code above doesn't solve colisions. If you'd like to count colisions, create array table of ints and initialize it to zero. Than, just increment the value, which is stored on index, which is returned by your hash funcion, like this:

table[hash(nextWord)]++;

I hope I helped. Please specify, what else you want to know.

Answer 2

If a hash table is required then as others have stated std::unordered_map will work in most cases. Now if you need something more powerful because of a large entry base, then I would suggest looking into tries. Tries combine the concepts of (Vector-Array) insertion, (Hashing) & Linked Lists. The run time is close to O(M) where M is the amount of characters in a string if you are hashing a string. It helps to remove the chance of collisions. And the more you add to a trie structure the less work has to be done as certain nodes are opened and created. The one draw back is that tries require more memory. Here is a diagram

Now your trie may vary on the size of the array due to what you are storing, but the overall concept and construction of one is the same. If you was doing a word - definition look up then you may want an array of 26 or a few more for each possible hashing character.

Answer 3

I am not sure that I understand what you do not understand. The explanations below might help you.

A hash table is a kind of associative array. It is used to map keys to values in a similar manner an array is used to map indexes (keys) to values. For instance, an array of three numbers, { 11, -22, 33 }, associates index 0 to 11, index 1 to -22 and index 2 to 33.

Now, let us assume that we would like to associate 1 to 11, 2 to -22 and 3 to 33. The solution is simple: we keep the same array, only we transform the key by subtracting one from it, thus obtaining the original index

This is fine until we realize that this is just a particular case. What if the keys are not so “predictable”? A solution would be to put the associations in a list of {key, value} pairs and when someone is asking for a key, just search the list: { 123, 11}, {3, -22}, {0, 33} If the value associated to 3 is asked, we simply search the keys in list for a match and find -22. That’s fine, but if the list is large we’re in trouble. We could speed the search if we sort the array by keys and use binary search, but still the search may take some time if the list is large.

The search speed may be further enhanced if we break the list in sub-lists (or buckets) made of related pairs. This is what a hash function does: puts together pairs by related keys (an ideal hash function would associate one key to one value).

A hash table is a two columns table (an array):

• The first column is the hash key (the index computed by a hash function). The size of the hash table is given by the maximum value of the hash function. If, for instance, the last step in computing the hash function is modulo 10, the size of the table will be 10; the pairs list will be broken into 10 sub-lists.
• The second column is a list (bucket) of key/values pairs (the sub-list I was taking about).

Answer 4

Hash function should not be responsible for storing data. Normally you would have a container that uses hash function internally.

From what you wrote I understood that you want to create hashtable. One way you could do that (probably not the most efficient one, but should give you an idea):

#include <fstream>
#include <vector>
#include <string>
#include <map>
#include <memory>

using namespace std;

namespace example {
long hash(char* s){
  long h;
  for(int i = 0; i < 10; i++){
    h = h + (int)s[i];
  }

  return h;
}
}

int main (int argc, char* argv[]){
  fstream input(argv[1]);
  char* nextWord;
  std::map<long, std::unique_ptr<std::vector<std::string>>> hashtable;
  while(!input.eof()){
    input >> nextWord;
    long newHash = example::hash(nextWord);
    auto it = hashtable.find(newHash);

    // Collision detected?
    if (it == hashtable.end()) {
      hashtable.insert(std::make_pair(newHash, std::unique_ptr<std::vector<std::string>>(new std::vector<std::string> { nextWord } )));
    }
    else {
      it->second->push_back(nextWord);
    }
  }
}

I used some C++ 11 features to write an example faster.

Answer 5

To count a number of words which have same hash, we should know hashes of all previous words. When you count a hash of some word, you should write it down, for example in some array. So you need an array with size equal to the number of words.
Then you should compare the new hash with all previous ones. Method of counting depends on what you need - number of pair of collisions or number off same elements.