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public class HashST { private int N; // number of key-value pairs in the table private int M; // size of linear-probing table private Key[] keys; // the keys private Value[] vals; // the values public HashST() { this(16); } public HashST(int M) { this.M = M; keys = (Key[]) new Object[M]; vals = (Value[]) new Object[M]; } private void resize(int cap) { HashST t; t = new HashST(cap); for (int i = 0; i = M / 2) { resize(2 * M);} // double M (see text) int i; //uses empty spaces (marked by null) to terminate clusters of keys. If for (i = hash(key); keys[i] != null; i = (i + 1) % M) { if (keys[i].equals(key)) { vals[i] = val; return; } } keys[i] = key; vals[i] = val; N++; } public Value get(Key key) { for (int i = hash(key); keys[i] != null; i = (i + 1) % M) { if (keys[i].equals(key)) { return vals[i]; } } return null; } public void delete(Key key) { if (get(key) == null) {return;} int i = hash(key); while (!key.equals(keys[i])) { i = (i + 1) % M; } keys[i] = null; vals[i] = null; i = (i + 1) % M; while (keys[i] != null) { Key keyToRedo = keys[i]; Value valToRedo = vals[i]; keys[i] = null; vals[i] = null; N--; put(keyToRedo, valToRedo); i = (i + 1) % M; } N--; if (N > 0 && N == M / 8) resize(M / 2); } } 

public class SparseVector { // Implement Sparse Vector Class as an Hash Table // This provides constant time search and insertion private HashST st; // 1- constructor // 2- size // 3- put // 4- get public double dot(double[] that) { double sum = 0.0; // 5- USE: Object[] keys = st.keys(); // USE: get((int)keys[i]); return sum; } public static void show(double[] that){ for (int i = 0; i   Data Structures and Algorithms Hash Table Implementation of Sparse Vectors You are given the code for a linear probing hash table in HashST.java. Use this code to represent a sparse vector, where keys of HashST correspond to index of a sparse vector. The code for SparseVector is also given to you, but its constructor, size, put, get methods are missing. Also fill the missing parts of the dot-product method. 1. In the main method, create a sparse matrix as an array of SparseVector's. This sparse vector will have the same values as this matrix, 8 4 0 0 0 0 0 A-0 0 0 0 0 0 0 2. Write an array of type double r0.1 0.1 0.1 0.1 0. 0.25 0.25 3. Calulate and show the result of