己 acci 编号
己纳奇数 是斐波那契数的推广，其中每个项都是前面六个项的总和。前几个己二醇数字如下–0，0，0，0，0，1，1，2，4，8，16，32，63，125，248，492，976，1936，3840…..
己 acci 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)
用 T(0) = T(1) = T(2) = T(3) = T(4) = 0，T(5) = 1
找到己二醇的第 N 个项
给定一个数字 N 。任务是找到第 n 个己方账号。
示例:
输入:N = 8 T3】输出: 2
输入:N = 11 T3】输出: 16
天真法:思路是按照递归求数，用递归求解。
下面是上述方法的实现:
C++
// C++ simple recursive program to print
// Nth Hexanacci numbers.
#include<bits/stdc++.h>
#include<iostream>
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 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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
java 描述语言
<script>
// 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);
</script>
Output:
16
高效方法:一个更好的解决方案是使用 动态编程 的想法是跟踪的最后六个术语来计算系列的最后一个当前术语。将本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，计算该系列第 N 个项之前的术语:
下面是上述方法的实现:
C++
// C++ implementation to print
// Nth term of hexanacci numbers.
#include <bits/stdc++.h>
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 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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 描述语言
<script>
// 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.
</script>
Output:
16
时间复杂度: O(N)
辅助空间: O(1)
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