Algorithm to find the smallest snippet from searching a document?

Question

I\'ve been going through Skiena\'s excellent \"The Algorithm Design Manual\" and got hung up on one of the exercises.

The question is: \"Given a search string of three w

Answer 1

Sample implementation in java (tested only with the implementation in the example, there might be bugs). The implementation is based on the replies above.

import java.util.Arrays;


public class SmallestSnippet {
    WordIndex[] words; //merged array of word occurences

    public enum Word {W1, W2, W3};

    public SmallestSnippet(Integer[] word1, Integer[] word2, Integer[] word3) {
        this.words = new WordIndex[word1.length + word2.length + word3.length];
        merge(word1, word2, word3);
        System.out.println(Arrays.toString(words));
    }

    private void merge(Integer[] word1, Integer[] word2, Integer[] word3) {
        int i1 = 0;
        int i2 = 0;
        int i3 = 0;
        int wordIdx = 0;
        while(i1 < word1.length || i2 < word2.length || i3 < word3.length) {
            WordIndex wordIndex = null;
            Word word = getMin(word1, i1, word2, i2, word3, i3);
            if (word == Word.W1) {
                wordIndex = new WordIndex(word, word1[i1++]);
            }
            else if (word == Word.W2) {
                wordIndex = new WordIndex(word, word2[i2++]);
            }
            else {
                wordIndex = new WordIndex(word, word3[i3++]);
            }
            words[wordIdx++] = wordIndex;
        }       
    }

    //determine which word has the smallest index
    private Word getMin(Integer[] word1, int i1, Integer[] word2, int i2, Integer[] word3,
            int i3) {
        Word toReturn = Word.W1;
        if (i1 == word1.length || (i2 < word2.length && word2[i2] < word1[i1])) {
            toReturn  = Word.W2;
        }
        if (toReturn == Word.W1 && i3 < word3.length && word3[i3] < word1[i1])
        {
            toReturn = Word.W3;
        }
        else if (toReturn == Word.W2){
            if (i2 == word2.length || (i3 < word3.length && word3[i3] < word2[i2])) {
                toReturn = Word.W3;
            }
        }
        return toReturn;
    }

    private Snippet calculate() {
        int start = 0;
        int end = 0;
        int max = words.length;
        Snippet minimum = new Snippet(words[0].getIndex(), words[max-1].getIndex());
        while (start < max)
        {
            end = start;
            boolean foundAll = false;
            boolean found[] = new boolean[Word.values().length];
            while (end < max && !foundAll) {
                found[words[end].getWord().ordinal()] = true;
                boolean complete = true;
                for (int i=0 ; i < found.length && complete; i++) {
                    complete = found[i];
                }
                if (complete)
                {
                    foundAll = true;
                }
                else {
                    if (words[end].getIndex()-words[start].getIndex() == minimum.getLength())
                    {
                        // we won't find a minimum no need to search further
                        break;
                    }
                    end++;
                }
            }
            if (foundAll && words[end].getIndex()-words[start].getIndex() < minimum.getLength()) {
                minimum.setEnd(words[end].getIndex());
                minimum.setStart(words[start].getIndex());
            }
            start++;
        }
        return minimum;

    }


    /**
     * @param args
     */
    public static void main(String[] args) {
        Integer[] word1 = {1,4,5};
        Integer[] word2 = {3,9,10};
        Integer[] word3 = {2,6,15};
        SmallestSnippet smallestSnippet = new SmallestSnippet(word1, word2, word3);
        Snippet snippet = smallestSnippet.calculate();
        System.out.println(snippet);

    }
}

Helper classes:

public class Snippet {

    private int start;

    private int end;

//getters, setters etc

    public int getLength()
    {
        return Math.abs(end - start);
    }
}



public class WordIndex
{
    private SmallestSnippet.Word word;
    private int index;
    public WordIndex(SmallestSnippet.Word word, int index) {

        this.word = word;
        this.index = index;
    }
}