Merge pull request #501 from DDullahan/master

Added MatrixFastPower.java

DataStructures/Matrix/MatrixFastPower.java

@@ -0,0 +1,191 @@
+/**
+ *
+ * Java implementation of Matrix fast power
+ * It can calculate the high power of constant Matrix with O( log(K) )
+ * where K is the power of the Matrix
+ *
+ * In order to do that, Matrix must be square Matrix ( columns equals rows)
+ *
+ * Notice : large power of Matrix may cause overflow
+ *
+ *
+ * other Matrix basic operator is based on  @author Kyler Smith, 2017
+ *
+ * @author DDullahan, 2018
+ *
+ */
+
+class MatrixFastPower {
+
+    /**
+     * Matrix Fast Power
+     *
+     * @param matrix : square Matrix
+     * @param k : power of Matrix
+     * @return product
+     */
+    public static Matrix FastPower(Matrix matrix, int k) throws RuntimeException {
+
+        if(matrix.getColumns() != matrix.getRows())
+            throw new RuntimeException("Matrix is not square Matrix.");
+
+        int[][] newData = new int[matrix.getColumns()][matrix.getRows()];
+
+        for(int i = 0; i < matrix.getColumns(); i++)
+            newData[i][i] = 1;
+
+        Matrix newMatrix = new Matrix(newData),
+        coMatrix = new Matrix(matrix.data);
+
+        while(k != 0) {
+
+            if((k & 1) != 0)
+                newMatrix = newMatrix.multiply(coMatrix);
+
+            k >>= 1;
+            coMatrix = coMatrix.multiply(coMatrix);
+
+        }
+
+        return newMatrix;
+    }
+
+    public static void main(String[] argv) {
+
+        int[][] data = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
+        Matrix matrix = new Matrix(data);
+
+        System.out.println("original matrix : ");
+        System.out.println(matrix.toString());
+
+        matrix = MatrixFastPower.FastPower(matrix, 5);
+
+        System.out.println("after power : ");
+        System.out.println(matrix.toString());
+
+        matrix = MatrixFastPower.FastPower(matrix, 1000000);
+
+        System.out.println("notice, large power may cause overflow : ");
+        System.out.print(matrix.toString());
+        System.out.println("you can use mod to fix that :-) ");
+
+    }
+}
+class Matrix {
+    public int[][] data;
+
+    /**
+     * Constructor for the matrix takes in a 2D array
+     *
+     * @param pData
+     */
+    public Matrix(int[][] pData) {
+
+        /** Make a deep copy of the data */
+        if(pData.length != 0) {
+            int[][] newData = new int[pData.length][pData[0].length];
+
+            for(int i = 0; i < pData.length; i++)
+                for(int j = 0; j < pData[0].length; j++)
+                    newData[i][j] = pData[i][j];
+
+            this.data = newData;
+        } else {
+            this.data = null;
+        }
+    }
+
+    /**
+     * Returns the element specified by the given location
+     *
+     * @param x : x cooridinate
+     * @param y : y cooridinate
+     * @return int : value at location
+     */
+    public int getElement(int x, int y) {
+        return data[x][y];
+    }
+
+    /**
+     * Returns the number of rows in the Matrix
+     *
+     * @return rows
+     */
+    public int getRows() {
+        if(this.data == null)
+            return 0;
+
+        return data.length;
+    }
+
+    /**
+     * Returns the number of rows in the Matrix
+     *
+     * @return columns
+     */
+    public int getColumns() {
+        if(this.data == null)
+            return 0;
+
+        return data[0].length;
+    }
+
+    /**
+     * Multiplies this matrix with another matrix.
+     *
+     * @param other : Matrix to be multiplied with
+     * @return product
+     */
+    public Matrix multiply(Matrix other) throws RuntimeException {
+
+        int[][] newData = new int[this.data.length][other.getColumns()];
+
+        if(this.getColumns() != other.getRows())
+            throw new RuntimeException("The two matrices cannot be multiplied.");
+
+        int sum;
+
+        for (int i = 0; i < this.getRows(); ++i)
+            for(int j = 0; j < other.getColumns(); ++j) {
+                sum = 0;
+
+                for(int k = 0; k < this.getColumns(); ++k) {
+                    sum += this.data[i][k] * other.getElement(k, j);
+                }
+
+                newData[i][j] = sum;
+            }
+
+        return new Matrix(newData);
+    }
+
+    /**
+    * Returns the Matrix as a String in the following format
+    *
+    * [ a b c ] ...
+    * [ x y z ] ...
+    * [ i j k ] ...
+    *    ...
+    *
+    * @return Matrix as String
+    * TODO: Work formatting for different digit sizes
+    */
+    public String toString() {
+        String str = "";
+
+        for(int i = 0; i < this.data.length; i++) {
+            str += "[ ";
+
+            for(int j = 0; j < this.data[0].length; j++) {
+                str += data[i][j];
+                str += " ";
+            }
+
+            str += "]";
+            str += "\n";
+        }
+
+        return str;
+    }
+
+}