Implementing Sparse Vector in Java

A vector or arraylist is a one-dimensional array of elements. The elements of a Sparse Vector have mostly zero values. It is inefficient to use a one-dimensional array to store a sparse vector. It is also inefficient to add elements whose values are zero in forming sums of sparse vectors. We convert the one-dimensional vector to a vector of (index, value) pairs.

Examples

Input: 
Enter size of Sparse Vectors : 
100
Enter number of entries for Vector A :
5
Enter 5 (int, double) pairs
2 20.0
5 12.2
19 23.1
4 66.0
11 100.0
Enter number of entries for vector B :
5
Enter 5 (int, double) pairs
9 21.0
10 44.5
6 13.22
71 30.0
63 99.0

Output:
Vector A = (2, 20.0) (4, 66.0) (5, 12.2) (11, 100.0) (19, 23.1)
Vector B = (6, 13.22) (9, 21.0) (10, 44.5) (63, 99.0) (71, 30.0)
A dot B = 0.0
A  +  B   = (2, 20.0) (4, 66.0) (5, 12.2) (6, 13.22) (9, 21.0) (10, 44.5) (11, 100.0) (19, 23.1) (63, 99.0) (71, 30.0)

Approach

To store the Sparse Vector efficiently we only store the non-zero values of the vector along with the index. The First element of pair will be the index of sparse vector element(which is non-zero) and the second element will be the actual element.

We are using TreeMap as the vector for the index-value pairs. The advantage of using TreeMap is, the map is sorted according to the natural ordering of its keys. This proves to be an efficient way of sorting and storing the key-value pairs. 

Implementation

Java

// importing generic packages
import java.util.Scanner;
import java.util.TreeMap;
import java.util.Map;

public class SparseVector {

    // TreeMap is used to maintain sorted order
    private TreeMap<Integer, Double> st;
    private int size;

    // Constructor
    public SparseVector(int size)
    {
        this.size = size;

        // assigning empty TreeMap
        st = new TreeMap<Integer, Double>();
    }

    // Function to insert a (index, value) pair
    public void put(int i, double value)
    {
        // checking if index(i) is out of bounds
        if (i < 0 || i >= size)
            throw new RuntimeException(
                "\nError : Out of Bounds\n");

        // if value is zero, don't add to that index &
        // remove any previously held value
        if (value == 0.0)
            st.remove(i);

        // if value is non-zero add index-value pair to
        // TreeMap
        else
            st.put(i, value);
    }

    // Function to get value for an index
    public double get(int i)
    {
        // checking if index(i) is out of bounds
        if (i < 0 || i >= size)
            throw new RuntimeException(
                "\nError : Out of Bounds\n");

        // if index is valid, return value at index
        if (st.containsKey(i))
            return st.get(i);

        // if index not found, it means the value is zero as
        // only non-zero entries are added to the Map
        else
            return 0.0;
    }

    // Function to get size of the vector
    public int size() { return size; }

    // Function to get dot product of two vectors
    public double dot(SparseVector b)
    {
        SparseVector a = this;

        // Dot product of Sparse Vectors whose lengths are
        // different is not possible
        if (a.size != b.size)
            throw new RuntimeException(
                "Error : Vector lengths are not same");

        double sum = 0.0;

        // Traversing each sorted vector and getting
        // product of consequent entries of the vectors
        if (a.st.size() <= b.st.size()) {
            for (Map.Entry<Integer, Double> entry :
                 a.st.entrySet())
                if (b.st.containsKey(entry.getKey()))
                    sum += a.get(entry.getKey())
                           * b.get(entry.getKey());
        }

        // Traversing each sorted vector and getting
        // product of consequent entries of the vectors
        else {
            for (Map.Entry<Integer, Double> entry :
                 b.st.entrySet())
                if (a.st.containsKey(entry.getKey()))
                    sum += a.get(entry.getKey())
                           * b.get(entry.getKey());
        }
        return sum;
    }

    // Function to get sum of two vectors
    public SparseVector plus(SparseVector b)
    {
        SparseVector a = this;

        // Addition of Sparse Vectors whose lengths are
        // different is not possible
        if (a.size != b.size)
            throw new RuntimeException(
                "Error : Vector lengths are not same");

        // creating new empty Sparse Vector object
        SparseVector c = new SparseVector(size);

        // Traversing and adding the two vectors a & b and
        // constructing resultant Sparse Vector c
        for (Map.Entry<Integer, Double> entry :
             a.st.entrySet())
            c.put(entry.getKey(), a.get(entry.getKey()));

        for (Map.Entry<Integer, Double> entry :
             b.st.entrySet())
            c.put(entry.getKey(),
                  b.get(entry.getKey())
                      + c.get(entry.getKey()));

        return c;
    }

    // Function toString() for printing vector
    public String toString()
    {
        String s = "";
        for (Map.Entry<Integer, Double> entry :
             st.entrySet())
            s += "(" + entry.getKey() + ", "
                 + st.get(entry.getKey()) + ") ";

        return s;
    }

    public static void main(String[] args)
    {
        Scanner scan = new Scanner(System.in);
        System.out.println(
            "Enter size of Sparse Vectors : ");

        // Size of the two Sparse Vector
        int n = scan.nextInt();

        // sparse vector a and b
        SparseVector A = new SparseVector(n);
        SparseVector B = new SparseVector(n);

        // store key, value pairs
        System.out.println(
            "Enter number of entries for Vector A :");
        int n1 = scan.nextInt();
        System.out.println("Enter " + n1
                           + " (int, double) pairs :");
        for (int i = 0; i < n1; i++)
            A.put(scan.nextInt(), scan.nextDouble());

        System.out.println(
            "Enter number of entries for vector B :");
        int n2 = scan.nextInt();
        System.out.println("Enter " + n2
                           + " (int, double) pairs :");
        for (int i = 0; i < n2; i++)
            B.put(scan.nextInt(), scan.nextDouble());

        System.out.println("\nVector A = " + A);
        System.out.println("Vector B = " + B);
        System.out.println("\nA dot B = " + A.dot(B));
        System.out.println("A  +  B   = " + A.plus(B));
    }
}

Output