十六进制数

hexanacci数 是斐波那契数的概括，其中每个项是前六个项的总和。头几个十六进制数字如下-0、0、0、0、0、1、1、2、4、8、16、32、63、125、248、492、976、1936、3840 …。

十六进制数的第N项由下式给出：

T(n) = T(n-1) + T(n-2) + T(n-3) + T(n-4) + T(n-5) + T(n-6)

with T(0) = T(1) = T(2) = T(3) = T(4) = 0, T(5) = 1 
 

查找十六进制数的^第N^个项

给定数字N。任务是找到第N个十六进制数字。

例子：

Input: N = 8 
Output: 2

Input: N = 11 
Output: 16 
 

天真的方法：想法是跟随递归来找到数字并使用递归来求解。

下面是上述方法的实现：

C++

// C++ simple recursive program to print
// Nth Hexanacci numbers.
#include
#include
using namespace std;
 
// Function to print the Nth
// Hexanacci number
int printhexaRec(int n)
{
    if (n == 0 || n == 1 ||
        n == 2 || n == 3 ||
        n == 4 || n == 5)
        return 0;
         
    else if (n == 6)
        return 1;
         
    else
        return (printhexaRec(n - 1) +
                printhexaRec(n - 2) +
                printhexaRec(n - 3) +
                printhexaRec(n - 4) +
                printhexaRec(n - 5) +
                printhexaRec(n - 6));
}
             
int printhexa(int n)
{
    cout << printhexaRec(n) << endl;
}
             
// Driver code
int main()
{
    privatenthexa(n);
}
 
// This code is contributed by Ritik Bansal

Java

// Java simple recursive program to print
// Nth Hexanacci numbers.
import java.util.*;
class GFG{
 
// Function to print the Nth
// Hexanacci number
static int printhexaRec(int n)
{
    if (n == 0 || n == 1 ||
        n == 2 || n == 3 ||
        n == 4 || n == 5)
        return 0;
         
    else if (n == 6)
        return 1;
         
    else
        return (printhexaRec(n - 1) +
                printhexaRec(n - 2) +
                printhexaRec(n - 3) +
                printhexaRec(n - 4) +
                printhexaRec(n - 5) +
                printhexaRec(n - 6));
}
             
static void printhexa(int n)
{
    System.out.print(printhexaRec(n) + "\n");
}
             
// Driver code
public static void main(String[] args)
{
    int n = 11;
    printhexa(n);
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python simple recursive program to print
# Nth Hexanacci numbers.
   
# Function to print the Nth
# Hexanacci number
def printhexaRec(n) :
    if (n == 0 or n == 1 or\
        n == 2 or n == 3 or\
        n == 4 or n == 5):
        return 0
    elif (n == 6):
        return 1
    else :
        return (printhexaRec(n - 1) +
                printhexaRec(n - 2) +
                printhexaRec(n - 3)+
                printhexaRec(n - 4)+
                printhexaRec(n - 5)+
                printhexaRec(n - 6))
           
def printhexa(n) :
    print(printhexaRec(n))
           
   
# Driver code
n = 11
printhexa(n)

C#

// C# simple recursive program to print
// Nth Hexanacci numbers.
using System;
class GFG{
 
// Function to print the Nth
// Hexanacci number
static int printhexaRec(int n)
{
    if (n == 0 || n == 1 ||
        n == 2 || n == 3 ||
        n == 4 || n == 5)
        return 0;
         
    else if (n == 6)
        return 1;
         
    else
        return (printhexaRec(n - 1) +
                printhexaRec(n - 2) +
                printhexaRec(n - 3) +
                printhexaRec(n - 4) +
                printhexaRec(n - 5) +
                printhexaRec(n - 6));
}
             
static void printhexa(int n)
{
    Console.Write(printhexaRec(n) + "\n");
}
             
// Driver code
public static void Main()
{
    int n = 11;
    printhexa(n);
}
}
 
// This code is contributed by Code_Mech

Javascript

 
    // Javascript simple recursive program to print
    // Nth Hexanacci numbers.
     
    // Function to print the Nth
    // Hexanacci number
    function printhexaRec(n)
    {
        if (n == 0 || n == 1 ||
            n == 2 || n == 3 ||
            n == 4 || n == 5)
            return 0;
 
        else if (n == 6)
            return 1;
 
        else
            return (printhexaRec(n - 1) +
                    printhexaRec(n - 2) +
                    printhexaRec(n - 3) +
                    printhexaRec(n - 4) +
                    printhexaRec(n - 5) +
                    printhexaRec(n - 6));
    }
 
    function printhexa(n)
    {
        document.write(printhexaRec(n) + "</br>");
    }
     
    let n = 11;
    printhexa(n);
     

输出：

16

高效的方法：更好的解决方案是使用动态编程，其思想是跟踪的最后六个项以计算该系列的最后一个当前项。将系列的最后六个术语初始化为：

T(0) = T(1) = T(2) = T(3) = T(4) = 0, T(5) = 1

最后，计算直到系列的^第N^个项的项：

下面是上述方法的实现：

C++

// C++ implementation to print 
// Nth term of hexanacci numbers. 
#include 
using namespace std;
 
// Function to print the Nth
// term of the Hexanacci number
void printhexa(int n)
{
    if (n < 0)
        return;
         
    // Initialize first five
    // numbers to base cases
    int first = 0;
    int second = 0;
    int third = 0;
    int fourth = 0;
    int fifth = 0;
    int sixth = 1;
   
    // Declare a current variable
    int curr = 0;
   
    if (n < 6)
        cout << first << endl;
    else if (n == 6)
        cout << sixth << endl;
    else
    {
         
        // Loop to add previous five numbers
        // for each number starting from 5
        // and then assign first, second,
        // third, fourth fifth to second,
        // third, fourth, fifth
        // and curr to sixth respectively
        for(int i = 6; i < n; i++) 
        {
            curr = first + second + third +
                   fourth + fifth + sixth;
                    
            first = second;
            second = third;
            third = fourth;
            fourth = fifth;
            fifth = sixth;
            sixth = curr;
        }
    }
    cout << curr << endl;
}
 
// Driver Code
int main()
{
    int n = 11;
       
    printhexa(n);
 
    return 0;
}
 
// This code is contributed by divyeshrabadiya07

Java

// Java implementation to print
// Nth term of hexanacci numbers.
class GFG {
     
// Function to print the Nth
// term of the Hexanacci number
static void printhexa(int n)
{
    if (n < 0)
        return;
 
    // Initialize first five
    // numbers to base cases
    int first = 0;
    int second = 0;
    int third = 0;
    int fourth = 0;
    int fifth = 0;
    int sixth = 1;
 
    // Declare a current variable
    int curr = 0;
 
    if (n < 6)
        System.out.println(first);
    else if (n == 6)
        System.out.println(sixth);
 
    else
    {
 
        // Loop to add previous five numbers
        // for each number starting from 5
        // and then assign first, second,
        // third, fourth fifth to second,
        // third, fourth, fifth
        // and curr to sixth respectively
        for(int i = 6; i < n; i++)
        {
            curr = first + second + third +
                   fourth + fifth + sixth;
            first = second;
            second = third;
            third = fourth;
            fourth = fifth;
            fifth = sixth;
            sixth = curr;
        }
    }
    System.out.println(curr);
}
 
// Driver code
public static void main(String[] args)
{
    int n = 11;
     
    printhexa(n);
}
}
 
// This code is contributed by Amit Katiyar

Python3

# Python3 implementation to print
# Nth term of hexanacci numbers.
   
# Function to print the Nth
# term of the Hexanacci number  
def printhexa(n) :
    if (n < 0): 
        return 
   
    # Initialize first five 
    # numbers to base cases 
    first = 0 
    second = 0 
    third = 0 
    fourth = 0
    fifth = 0
    sixth = 1
   
    # declare a current variable 
    curr = 0 
   
    if (n <6): 
        print(first)
    elif (n == 6): 
        print(sixth) 
   
    else:
   
        # Loop to add previous five numbers 
        # for each number starting from 5 
        # and then assign first, second, 
        # third, fourth fifth to second,
        # third, fourth, fifth 
        # and curr to sixth respectively 
        for i in range(6, n):
            curr = first + second + third +\
                   fourth + fifth + sixth
            first = second 
            second = third 
            third = fourth 
            fourth = fifth
            fifth = sixth
            sixth = curr 
           
    print(curr)  
   
# Driver code
n = 11
printhexa(n)

C＃

// C# implementation to print
// Nth term of hexanacci numbers.
using System;
 
class GFG{
     
// Function to print the Nth
// term of the Hexanacci number
static void printhexa(int n)
{
    if (n < 0)
        return;
 
    // Initialize first five
    // numbers to base cases
    int first = 0;
    int second = 0;
    int third = 0;
    int fourth = 0;
    int fifth = 0;
    int sixth = 1;
 
    // Declare a current variable
    int curr = 0;
 
    if (n < 6)
        Console.WriteLine(first);
    else if (n == 6)
        Console.WriteLine(sixth);
 
    else
    {
 
        // Loop to add previous five numbers
        // for each number starting from 5
        // and then assign first, second,
        // third, fourth fifth to second,
        // third, fourth, fifth
        // and curr to sixth respectively
        for(int i = 6; i < n; i++)
        {
            curr = first + second + third +
                   fourth + fifth + sixth;
            first = second;
            second = third;
            third = fourth;
            fourth = fifth;
            fifth = sixth;
            sixth = curr;
        }
    }
    Console.WriteLine(curr);
}
 
// Driver code
public static void Main(String[] args)
{
    int n = 11;
     
    printhexa(n);
}
}
 
// This code is contributed by Amit Katiyar

Java脚本

    // Javascript implementation to print 
    // Nth term of hexanacci numbers.
     
    // Function to print the Nth
    // term of the Hexanacci number
    function printhexa(n)
    {
        if (n < 0)
            return;
 
        // Initialize first five
        // numbers to base cases
        let first = 0;
        let second = 0;
        let third = 0;
        let fourth = 0;
        let fifth = 0;
        let sixth = 1;
 
        // Declare a current variable
        let curr = 0;
 
        if (n < 6)
            document.write(first);
        else if (n == 6)
            document.write(sixth);
        else
        {
 
            // Loop to add previous five numbers
            // for each number starting from 5
            // and then assign first, second,
            // third, fourth fifth to second,
            // third, fourth, fifth
            // and curr to sixth respectively
            for(let i = 6; i < n; i++) 
            {
                curr = first + second + third +
                       fourth + fifth + sixth;
 
                first = second;
                second = third;
                third = fourth;
                fourth = fifth;
                fifth = sixth;
                sixth = curr;
            }
        }
        document.write(curr);
    }
    let n = 11;
    printhexa(n);
     
    // This code is contributed by divyesh072019.

输出：

16

时间复杂度： O(N)

辅助空间： O(1)