/******************************************************************************
 *  Compilation:  javac MarkovSquaring.java
 *  Execution:    java MarkovSquaring trials
 *  Dependencies: StdArrayIO.java Matrix.java
 *
 *  This program reads a transition matrix from standard input and
 *  computes the probabilities that a random surfer goes from page i
 *  to page j in 2^trials steps.
 *
 *  % java Transition < tinyGraph.txt | java MarkovSquaring 5
 *  5 5
 *    0.27303   0.26573   0.14619   0.24723   0.06783
 *    0.27303   0.26573   0.14619   0.24723   0.06783
 *    0.27303   0.26573   0.14619   0.24723   0.06783
 *    0.27303   0.26573   0.14619   0.24723   0.06783
 *    0.27303   0.26573   0.14619   0.24723   0.06783
 *
 ******************************************************************************/

public class MarkovSquaring {

    public static void main(String[] args) {

        // number of iterations of power method
        int trials = Integer.parseInt(args[0]);

        // Transition matrix: p[i][j] = prob. that surfer moves from page i to
        double[][] p = StdArrayIO.readDouble2D();

        // compute p^(2^trials)
        for (int t = 0; t < trials; t++) {
            p = Matrix.multiply(p, p);
        }

        StdArrayIO.print(p);
    }
}