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Fibonacci.cpp
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/*******************************************************************
Copyright(c) 2016, Harry He
All rights reserved.
Distributed under the BSD license.
(See accompanying file LICENSE.txt at
https://github.com/zhedahht/CodingInterviewChinese2/blob/master/LICENSE.txt)
*******************************************************************/
//==================================================================
// 《剑指Offer——名企面试官精讲典型编程题》代码
// 作者：何海涛
//==================================================================
// 面试题10：斐波那契数列
// 题目：写一个函数，输入n，求斐波那契（Fibonacci）数列的第n项。
#include <cstdio>
// ====================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[n];
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[n];
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(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;
}