oral_quiz->#Fibonacci#

#include <stdio.h>
#include <exception>

//==================Method1:Recursive===============
long long Fibonacci_recursive(unsigned int n) {
	if(n <= 0) return 0;
	if(n == 1) return 1;
	return Fibonacci_recursive(n-1) + Fibonacci_recursive(n-2);
}

//==================Method2:Iterative===============
long long Fibonacci_iterative(unsigned int n) {
	int result[2] = {0, 1};
	if(n < 2) return result[n];

	long long fibnOne = 0, fibnTwo = 1;
	long long fibN = 0;
	for(unsigned int i=2; i<=n; ++i) {
		fibN = fibnOne + fibnTwo;
		fibnOne = fibnTwo;
		fibnTwo = fibN;
	}

	return fibN;
}

//==================Method3:Matrix===============
#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_matrix(unsigned int n)
{
    int result[2] = {0, 1};
    if(n < 2)
        return result[n];

    Matrix2By2 PowerNMinus2 = MatrixPower(n - 1);
    return PowerNMinus2.m_00;
}

// ====================测试代码====================
void Test(int n, int expected)
{
    if(Fibonacci_recursive(n) == expected)
        printf("Test for %d in recursive passed.\n", n);
    else
        printf("Test for %d in recursive failed.\n", n);

    if(Fibonacci_iterative(n) == expected)
        printf("Test for %d in iterative passed.\n", n);
    else
        printf("Test for %d in iterative failed.\n", n);

    if(Fibonacci_matrix(n) == expected)
        printf("Test for %d in matrix passed.\n", n);
    else
        printf("Test for %d in matrix failed.\n", n);
}

int main(int argc, char* argv[])
{
    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;
}