{面试题9: 斐波那契数列}

From 剑指Offer 何海涛 著

#include <iostream>
using namespace std;

long long fibonacciRecursively(unsigned int n) {
    if(n <= 1) {
        return n;
    }
    return fibonacciRecursively(n-1) + fibonacciRecursively(n-2);
}

long long fibonacciIteratively(unsigned int n) {
    long long res = 0ll;
    long long one = 0ll;
    long long two = 1ll;
    if(n == 0) {
        return one;
    }
    if(n == 1) {
        return two;
    }
    for(unsigned int i=2; i<=n; i++) {
        res = one + two;
        one = two;
        two = res;
    }
    return res;
}

struct Matrix2By2 {
    Matrix2By2(long long m00 = 0ll, long long m01 = 0ll, long long m10  = 0ll, long long m11 = 0ll) : m_00(m00), m_01(m01), m_10(m10), m_11(m11) {

    }
    long long m_00 ;
    long long m_01 ;
    long long m_10 ;
    long long m_11 ;
};

Matrix2By2 MatrixMultiply(const Matrix2By2& matrix1, const Matrix2By2& matrix2) {
    return Matrix2By2(
        matrix1.m_00 * matrix2.m_00 + matrix1.m_01 * matrix2.m_10,
        matrix1.m_00 * matrix2.m_01 + matrix1.m_01 * matrix2.m_11,
        matrix1.m_10 * matrix2.m_00 + matrix1.m_11 * matrix2.m_10,
        matrix1.m_10 * matrix2.m_01 + matrix1.m_11 * matrix2.m_11
        );
}

Matrix2By2 MatrixPowerCore(unsigned int n) {
    Matrix2By2 matrix;
    if(n == 1) {
        return Matrix2By2(1, 1, 1, 0);
    }
    matrix = MatrixPowerCore(n/2);
    matrix = MatrixMultiply(matrix, matrix);
    if(n % 2 != 0) {
        matrix = MatrixMultiply(matrix, Matrix2By2(1, 1, 1, 0));
    }
    return matrix;
}
Matrix2By2 MatrixPower(unsigned int n) {
    if(n == 0) {
        return Matrix2By2();
    }
    if(n == 1) {
        return Matrix2By2(1, 1, 1, 0);
    }return MatrixPowerCore(n-1);
}

测试集:

void test(unsigned int n, long long expected) {
    std::cout << std::boolalpha << (fibonacciRecursively(n) == expected) << std::endl;
    std::cout << std::boolalpha << (fibonacciIteratively(n) == expected) << std::endl;
    std::cout << std::boolalpha << (MatrixPower(n-1).m_00 == expected) << std::endl;
}

int main(int argc, char* argv[]) {
    test(0, 0ll);
    test(1, 1ll);
    test(2, 1ll);
    test(3, 2ll);
    test(4, 3ll);
    test(5, 5ll);
    test(6, 8ll);
    test(7, 13ll);
    test(8, 21ll);
    test(9, 34ll);
    test(10, 55ll);
    test(40, 102334155ll);

    return 0;
}