Un vector o lista de arreglos es un arreglo unidimensional de elementos. Los elementos de un vector disperso tienen en su mayoría valores cero. Es ineficiente usar una array unidimensional para almacenar un vector disperso. También es ineficiente agregar elementos cuyos valores son cero al formar sumas de vectores dispersos. Convertimos el vector unidimensional en un vector de pares (índice, valor).
Ejemplos
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)
Acercarse
Para almacenar el vector disperso de manera eficiente, solo almacenamos los valores distintos de cero del vector junto con el índice. El primer elemento del par será el índice del elemento vectorial disperso (que no es cero) y el segundo elemento será el elemento real.
Estamos utilizando TreeMap como vector para los pares de valores de índice. La ventaja de usar TreeMap es que el mapa se ordena según el orden natural de sus claves. Esto demuestra ser una forma eficiente de ordenar y almacenar los pares clave-valor.
Implementación
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)); } }
Producción
Publicación traducida automáticamente
Artículo escrito por yasserarafat y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA