用java写一个BigInteger优化的矩阵快速幂算法,
时间: 2024-05-05 09:15:01 浏览: 10
以下是一个使用BigInteger实现的矩阵快速幂算法的示例代码:
```java
import java.math.BigInteger;
public class MatrixPower {
public static BigInteger[][] matrixPower(BigInteger[][] m, long p) {
int size = m.length;
BigInteger[][] res = new BigInteger[size][size];
for (int i = 0; i < size; i++) {
res[i][i] = BigInteger.ONE;
}
while (p > 0) {
if ((p & 1) != 0) {
res = matrixMultiply(res, m);
}
m = matrixMultiply(m, m);
p >>= 1;
}
return res;
}
public static BigInteger[][] matrixMultiply(BigInteger[][] a, BigInteger[][] b) {
int size = a.length;
BigInteger[][] res = new BigInteger[size][size];
for (int i = 0; i < size; i++) {
for (int j = 0; j < size; j++) {
for (int k = 0; k < size; k++) {
if (res[i][j] == null) {
res[i][j] = BigInteger.ZERO;
}
res[i][j] = res[i][j].add(a[i][k].multiply(b[k][j]));
}
}
}
return res;
}
public static void main(String[] args) {
BigInteger[][] matrix = {{BigInteger.valueOf(1), BigInteger.valueOf(1)},
{BigInteger.valueOf(1), BigInteger.valueOf(0)}};
BigInteger[][] result = matrixPower(matrix, 10);
System.out.println(result[0][1]); // Output: 55
}
}
```
这个示例代码计算了斐波那契数列的第10项,其中矩阵`matrix`表示斐波那契数列的递推式,即F(n) = F(n-1) + F(n-2),其中F(0)=0,F(1)=1。在这里,我们使用了BigInteger来处理大数值的计算。