给定一个整数“ n”，生成康奈尔序列的前一个“ n”项。
Connell序列是由第一个奇数(即1作为其第一项)形成的序列。序列的后续项由前两个偶数(即2和4)组成，然后是后三个奇数(即5、7和9)，再由后四个偶数(即10、12、14)组成和16等…。序列继续。
公式：
a[n] = 2 * n - floor((1 + sqrt(8 * n - 7))/2) ; n > 1
例子：
Input : 6
Output : 1 2 4 5 7 9
Input : 12
Output : 1 2 4 5 7 9 10 12 14 16 17 19
在这里可能需要注意的是，用新行写的术语是，第一行的第一个术语，下一行的下两个术语，下一行的下三个术语，依此类推，给出了一个有趣的模式：
1：1
第2行：2 4
第3行：5 7 9
第4行：10 12 14 16
第5行：17 19 21 23 25
等等…
模式是特定行的每个最后一个数字等于该行号的平方。
例如
- 在第2行中，最后一个数字是4，等于其行数的平方，即2 ^ 2
- 在第5行中，最后一个数字为25，等于其行号的平方，即5 ^ 2
下面是一个简单的实现，我们通过交替添加奇数和偶数元素来生成结果。我们使用当前列表的大小来确定下一个要推送的元素数。
C++
// CPP code to generate first 'n' terms
// of Connell Sequence
#include
using namespace std;
// Function to generate a fixed number
// of even or odd terms. The size of r
// decides whether numbers to be generated
// even or odd.
vector gen(long long int n,
vector r)
{
long long int a = r[r.size() - 1];
a++;
for (int i = 1; i <= n; a += 2, i++)
r.push_back(a);
return r;
}
// Generating the first 'n' terms of
// Connell Sequence
vector conell(long long int n)
{
vector res;
long long int k = 1;
// A dummy 0 is inserted at the
// beginning for consistency
res.push_back(0);
while (1)
{
// Calling function gen() to generate
// 'k' number of terms
res = gen(k, res);
k++;
int j = res.size() - 1;
while (j != n && j + k > n)
k--;
// Checking if 'n' terms are
// already generated
if (j >= n)
break;
}
// Removing the previously inserted dummy 0
res.erase(res.begin());
return res;
}
// Driver Method
int main()
{
long long int n = 10;
cout << "The first " << n
<< " terms are" << endl;
vector res = conell(n);
for (int i = 0; i < res.size(); i++)
cout << res[i] << " ";
cout << endl;
return 0;
} Java
// Java code to generate
// first 'n' terms
// of Connell Sequence
import java.util.*;
class GFG
{
// Function to generate a
// fixed number of even or
// odd terms. The size of r
// decides whether numbers
// to be generated even or odd.
static Vector gen(long n, Vector r)
{
long a = r.get(r.size() - 1);
a++;
for (int i = 1; i <= n; a += 2, i++)
{
r.add(a);
}
return r;
}
// Generating the first
// 'n' terms of
// Connell Sequence
static Vector conell(long n)
{
Vector res = new Vector();
long k = 1;
// A dummy 0 is inserted
// at the beginning for
// consistency
res.add(0L);
while (true)
{
// Calling function
// gen() to generate
// 'k' number of terms
res = gen(k, res);
k++;
int j = res.size() - 1;
while (j != n && j + k > n)
{
k--;
}
// Checking if 'n'
// terms are already
// generated
if (j >= n)
{
break;
}
}
// Removing the previously
// inserted dummy 0
res.remove(0);
return res;
}
// Driver Code
public static void main(String[] args)
{
long n = 10;
System.out.println("The first "
+ n + " terms are");
Vector res = conell(n);
for (int i = 0; i < res.size(); i++)
{
System.out.print(res.get(i) + " ");
}
System.out.println();
}
}
// This code has been contributed
// by Rajput-Ji Python3
# Python3 code to generate first 'n' terms
# of Connell Sequence
# Function to generate a fixed number
# of even or odd terms. The size of r
# decides whether numbers to be generated
# even or odd.
def gen(n, r):
a = r[-1]
a += 1
for i in range(1, n + 1):
r.append(a)
a += 2
return r
# Generating the first 'n' terms of
# Connell Sequence
def conell(n):
res = []
k = 1
# A dummy 0 is inserted at the
# beginning for consistency
res.append(0)
while 1:
# Calling function gen() to generate
# 'k' number of terms
res = gen(k, res)
k += 1
j = len(res) - 1
while j != n and j + k > n:
k -= 1
# Checking if 'n' terms are
# already generated
if j >= n:
break
# Removing the previously inserted dummy 0
res.remove(res[0])
return res
# Driver Code
if __name__ == "__main__":
n = 10
print("The first %d terms are" % n)
res = conell(n)
for i in range(len(res)):
print(res[i], end = " ")
print()
# This code is contributed by
# sanjeev2552C#
// C# code to generate
// first 'n' terms
// of Connell Sequence
using System;
using System.Collections.Generic;
class GFG
{
// Function to generate a
// fixed number of even or
// odd terms. The size of r
// decides whether numbers
// to be generated even or odd.
static List gen(long n,
List r)
{
long a = r[r.Count - 1];
a++;
for (int i = 1; i <= n;
a += 2, i++)
r.Add(a);
return r;
}
// Generating the first
// 'n' terms of
// Connell Sequence
static List conell(long n)
{
List res = new List();
long k = 1;
// A dummy 0 is inserted
// at the beginning for
// consistency
res.Add(0);
while (true)
{
// Calling function
// gen() to generate
// 'k' number of terms
res = gen(k, res);
k++;
int j = res.Count - 1;
while (j != n &&
j + k > n)
k--;
// Checking if 'n'
// terms are already
// generated
if (j >= n)
break;
}
// Removing the previously
// inserted dummy 0
res.RemoveAt(0);
return res;
}
// Driver Code
static void Main()
{
long n = 10;
Console.WriteLine("The first " +
n + " terms are");
List res = conell(n);
for (int i = 0; i < res.Count; i++)
Console.Write(res[i] + " ");
Console.WriteLine();
}
}
// This code is contributed by
// Manish Shaw(manishshaw1) 输出：
The first 10 terms are
1 2 4 5 7 9 10 12 14 16