康奈尔序列
给定一个整数“n”，生成连接序列的前“n”项。 康奈尔序列是以第一个奇数即 1 为第一项形成的序列。序列的后续项由前两个偶数组成，即 2 和 4，接下来是三个奇数，即 5、7 和 9，接下来是四个偶数，即 10、12、14 和 16，依此类推。序列继续。 配方:
a[n] = 2 * n - floor((1 + sqrt(8 * n - 7))/2) ; n > 1
例:
Input : 6
Output : 1 2 4 5 7 9
Input : 12
Output : 1 2 4 5 7 9 10 12 14 16 17 19
这里需要注意的是，将新行中的术语写成，第一行中的第一个术语，下一行中的下两个术语，下一行中的下三个术语等等，给出了一个有趣的模式: 第 1 行: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…… 该模式是特定行的每最后一个数字等于该行号的平方。 例如
- 在第 2 行，最后一个数字是 4，等于其行号的平方，即 2^2
- 第 5 行最后一个数字是 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个元素来生成结果。我们使用当前列表的大小来决定下一个要推送的元素数量。
C++
// CPP code to generate first 'n' terms
// of Connell Sequence
#include <bits/stdc++.h>
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<long long int> gen(long long int n,
vector<long long int> 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<long long int> conell(long long int n)
{
vector<long long int> 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<long long int> res = conell(n);
for (int i = 0; i < res.size(); i++)
cout << res[i] << " ";
cout << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// 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<Long> gen(long n, Vector<Long> 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<Long> conell(long n)
{
Vector<Long> res = new Vector<Long>();
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<Long> 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
Python 3
# 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
# sanjeev2552
C
// 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<long> gen(long n,
List<long> 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<long> conell(long n)
{
List<long> res = new List<long>();
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<long> 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)
java 描述语言
<script>
// Javascript 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.
function gen(n, r)
{
var a = r[r.length - 1];
a++;
for (var i = 1; i <= n; a += 2, i++)
r.push(a);
return r;
}
// Generating the first 'n' terms of
// Connell Sequence
function conell(n)
{
var res = [];
var k = 1;
// A dummy 0 is inserted at the
// beginning for consistency
res.push(0);
while (1)
{
// Calling function gen() to generate
// 'k' number of terms
res = gen(k, res);
k++;
var j = res.length - 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.shift();
return res;
}
// Driver Method
var n = 10;
document.write( "The first " + n
+ " terms are" + "<br>");
var res = conell(n);
for (var i = 0; i < res.length; i++)
document.write( res[i] + " ");
// This code is contributed by rrrtnx.
</script>
输出:
The first 10 terms are
1 2 4 5 7 9 10 12 14 16
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