接下來將介紹一個菲波那切數列、階乘、求和的遞歸、迭代、動態規劃實現和只能用遞歸實現的漢諾塔;
頭文件;
# ifndef _RECURSION_
# define _RECURSION_
# include <iostream>
using namespace std;
//菲波那切數列遞歸、迭代和動態規劃實現;
int FibonacciRecursion(int val);
int FibonacciIteration(int val);
int FibonacciDP(int val);
//階乘遞歸、迭代和動態規劃實現;
int FactorialRecursion(int val);
int FactorialIteration(int val);
int FactorialDP(int val);
# endif
實現文件;
# include "Recursion.h"
//菲波那切數列遞歸、迭代和動態規劃實現;
//時間複雜度是O(2^n);
int FibonacciRecursion(int val)
{
if (1 == val || 2 == val)
{
return 1;
}
else
{
return (FibonacciRecursion(val - 1) + FibonacciRecursion(val - 2));
}
}
//空間複雜度是O(1);時間複雜度是O(n);
int FibonacciIteration(int val)
{
if (1 == val || 2 == val)
{
return 1;
}
else
{
int f1 = 1;
int f2 = 1;
int f3 = 0;
for (int i = 3; i <= val; i++)
{
f3 = f1 + f2;
f1 = f2;
f2 = f3;
}
return f3;
}
}
//空間複雜度是O(n);時間複雜度是O(n);
int FibonacciDP(int val)
{
int i = 0;
int * f = (int *)malloc(sizeof(int) * (val + 1));
f[1] = 1;
f[2] = 1;
for (i = 3; i <= val; i++)
{
f[i] = f[i - 1] + f[i - 2];
}
val = f[val];
free(f);
return val;
}
//階乘遞歸、迭代和動態規劃實現;
//時間複雜度是O(2^n);
int FactorialRecursion(int val)
{
if (1 == val)
{
return val;
}
else
{
return (val * FactorialRecursion(val - 1));
}
}
//空間複雜度是O(1);時間複雜度是O(n);
int FactorialIteration(int val)
{
int f = 1;
for (int i = 1; i <= val; i++)
{
f = f * i;
}
return f;
}
//空間複雜度是O(n);時間複雜度是O(n);
int FactorialDP(int val)
{
int i = 0;
int * f = (int *)malloc(sizeof(int) * (val + 1));
f[1] = 1;
for (i = 2; i <= val; i++)
{
f[i] = i * f[i - 1];
}
val = f[val];
free(f);
return val;
}
Main函數;
# include "Recursion.h"
int main(int argc, char ** argv)
{
int i = 0;
int j = 0;
cout << endl << "--------------------------Fibonacci--------------------------" << endl;
for (i = 1; i < 20; i++)
{
cout << FibonacciIteration(i) << " ";
}
cout << endl << FactorialRecursion(10) << endl;
cout << endl << "--------------------------Factorial--------------------------" << endl;
cout << FactorialDP(5) << endl;
cout << endl << endl;
system("pause");
return 0;
}