[Java] 蓝桥杯BASIC-17 基础练习 矩阵乘法

问题描述

给定一个N阶矩阵A，输出A的M次幂（M是非负整数）

例如：

A =

1 2

3 4

A的2次幂

7 10

15 22

输入格式

第一行是一个正整数N、M（1<=N<=30, 0<=M<=5），表示矩阵A的阶数和要求的幂数

接下来N行，每行N个绝对值不超过10的非负整数，描述矩阵A的值

输出格式

输出共N行，每行N个整数，表示A的M次幂所对应的矩阵。相邻的数之间用一个空格隔开

样例输入

2 2

1 2

3 4

样例输出

7 10

15 22

package base17;
 
import java.util.Scanner;
 
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        in.close();
        long[][] a = new long[40][40];
        long[][] b = new long[40][40];
        long[][] t = new long[40][40];
        //输入
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                a[i][j] = in.nextLong();
                t[i][j] = a[i][j];
            }
        }
        //0次幂  输出单位矩阵
        if (m == 0) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i == j) {
                        System.out.print(1 + " ");
                    } else {
                        System.out.print(0 + " ");
                    }
                }
                System.out.println();
            }
            return;
        }
        //m次幂
        while (--m > 0) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    int k = n;
                    while (k > 0) {
                        b[i][j] += t[i][k - 1] * a[k - 1][j];
                        k--;
                    }
                }
            }
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    t[i][j] = b[i][j];
                    b[i][j] = 0;
                }
            }
        }
 
 
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                System.out.print(t[i][j] + " ");
            }
            System.out.println();
        }
    }
}