Pages

Sunday 4 November 2012

UVA - 10689 - Yet another Number Sequence

//Using matrix multiplication and divide and Conquer concepts
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int cases = Integer.parseInt(br.readLine());
        StringBuffer sb = new StringBuffer("");
        for (int i = 0; i < cases; i++) {
            String[] str = br.readLine().split(" ");
            int[][] seq = new int[2][1];
            seq[1][0] = Integer.parseInt(str[0]);
            seq[0][0] = Integer.parseInt(str[1]);
            int[][] intial = {{1, 1}, {1, 0}};
            int n = Integer.parseInt(str[2]);
            int rem = (int) Math.pow(10, Integer.parseInt(str[3]));
            int[][] powMat = matPow(intial, n, rem);
            int[][] result = matrixMultiply(powMat, seq, rem);
            sb.append(result[1][0]).append("\n");
        }
        System.out.print(sb);
    }

    public static int[][] matrixMultiply(int[][] x, int[][] y, int mod) {
        int[][] temp = new int[x.length][y[0].length];
        for (int i = 0; i < temp.length; i++) {
            for (int j = 0; j < temp[0].length; j++) {
                for (int k = 0; k < x.length; temp[i][j] %= mod, k++) {
                    temp[i][j] += x[i][k] * y[k][j];
                }
            }
        }
        return temp;
    }

    public static int[][] matPow(int[][] matrix, int exponent, int mod) {
        int[][] result = new int[matrix.length][matrix.length];
        int[][] tempMatrix = new int[matrix.length][];
        for (int i = 0; i < result.length; i++) {
            result[i][i] = 1;
            tempMatrix[i] = matrix[i].clone();
        }
        while (exponent > 0) {
            if ((exponent & 1) == 1) {
                result = matrixMultiply(result, tempMatrix, mod);
            }
            tempMatrix = matrixMultiply(tempMatrix, tempMatrix, mod);
            exponent /= 2;
        }
        return result;

    }
}

No comments:

Post a Comment