算法题目---斐波那契数列

// ====================方法1：递归====================

long long Fibonacci_Solution1(unsigned int n)

{

    if(n <= 0)

        return 0;

    if(n == 1)

        return 1;

    return Fibonacci_Solution1(n - 1) + Fibonacci_Solution1(n - 2);

}

// ====================方法2：循环====================

long long Fibonacci_Solution2(unsigned n)

{

    int result[2] = {0, 1};

    if(n < 2)

        return result
;

    long long  fibNMinusOne = 1;

    long long  fibNMinusTwo = 0;

    long long  fibN = 0;

    for(unsigned int i = 2; i <= n; ++ i)

    {

        fibN = fibNMinusOne + fibNMinusTwo;

        fibNMinusTwo = fibNMinusOne;

        fibNMinusOne = fibN;

    }

     return fibN;

}

// ====================方法3：基于矩阵乘法====================

#include <cassert>

struct Matrix2By2

{

    Matrix2By2

    (

        long long m00 = 0,

        long long m01 = 0,

        long long m10 = 0,

        long long m11 = 0

    )

    :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 MatrixPower(unsigned int n)

{

    assert(n > 0);

    Matrix2By2 matrix;

    if(n == 1)

    {

        matrix = Matrix2By2(1, 1, 1, 0);

    }

    else if(n % 2 == 0)

    {

        matrix = MatrixPower(n / 2);

        matrix = MatrixMultiply(matrix, matrix);

    }

    else if(n % 2 == 1)

    {

        matrix = MatrixPower((n - 1) / 2);

        matrix = MatrixMultiply(matrix, matrix);

        matrix = MatrixMultiply(matrix, Matrix2By2(1, 1, 1, 0));

    }

    return matrix;

}

long long Fibonacci_Solution3(unsigned int n)

{

    int result[2] = {0, 1};

    if(n < 2)

        return result
;

    Matrix2By2 PowerNMinus2 = MatrixPower(n - 1);

    return PowerNMinus2.m_00;

}

// ====================测试代码====================

void Test(int n, int expected)

{

    if(Fibonacci_Solution1(n) == expected)

        printf("Test for %d in solution1 passed.\n", n);

    else

        printf("Test for %d in solution1 failed.\n", n);

    if(Fibonacci_Solution2(n) == expected)

        printf("Test for %d in solution2 passed.\n", n);

    else

        printf("Test for %d in solution2 failed.\n", n);

    if(Fibonacci_Solution3(n) == expected)

        printf("Test for %d in solution3 passed.\n", n);

    else

        printf("Test for %d in solution3 failed.\n", n);

}

int main( )

{

    Test(0, 0);

    Test(1, 1);

    Test(2, 1);

    Test(3, 2);

    Test(4, 3);

    Test(5, 5);

    Test(6, 8);

    Test(7, 13);

    Test(8, 21);

    Test(9, 34);

    Test(10, 55);

    Test(40, 102334155);

    return 0;

}