打印 N 个数字，这样它们的和就是一个完美的立方体

原文:https://www . geeksforgeeks . org/print-n-numbers-这样-他们的总和就是一个完美的立方体/

给定一个数字 N ，任务是找到 N 个数字，这样它们的和就是一个完美立方体。

示例:

输入: N = 3 输出: 1 7 19 解释: 数之和= 1 + 7 + 19 = 27， 是 3 = > 3 3 = 27 的完美立方

输入: N = 4 输出: 1 7 19 37 数之和= 1 + 7 + 19 + 37 = 64， 是 4 = > 4 3 = 64 的完美立方

方法: 在考虑 中心六边形数字 后，该数字表示:

第一个 N 个中心六边形数的和是 N 的完美立方

所以从中心六边形数开始，级数的前 N 项将给出 N 个数，这样它们的和就是一个完美的立方体。

例如:

For N = 1,
    Centered Hexagonal Series = 1
    and 13 = 1
    Hence, {1} is the required N number

For N = 2,
    Centered Hexagonal Series = 1, 7
    and 23 = 1 + 7 = 8
    Hence, {1, 7} are the required N number

For N = 3,
    Centered Hexagonal Series = 1, 7, 19
    and 33 = 1 + 7 + 19 = 27
    Hence, {1, 7, 19} are the required N number
.
.
and so on.

因此，可以说打印中心六边形数字的前 N 项将给出所需的 N 个数字。 同样，中心六边形数字的第 n 项是: 3 * N * (N - 1) + 1

算法:

  • 用一个循环变量(比如说 i )从 1 到 N 迭代一个循环，对于每个迭代–
    1. 使用公式 3i(i-1) + 1 求出中心六边形数的第 N 个项。
    2. 在数组中追加第 i 个项。

下面是上述方法的实现:

C++

// C++ implementation to find the N
// numbers such that their
// sum is a perfect cube

#include <bits/stdc++.h>
using namespace std;

// Function to find the N
// numbers such that their
// sum is a perfect cube
void findNumbers(int n)
{
    int i = 1;
    // Loop to find the Ith term
    // of the Centered Hexagonal number
    while (i <= n) {
        cout << (3 * i * (i - 1) + 1)
             << " ";
        i++;
    }
}

// Driver Code
int main()
{
    int n = 4;

    // Function Call
    findNumbers(n);
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java implementation to find the N
// numbers such that their
// sum is a perfect cube
class GFG
{

    // Function to find the N
    // numbers such that their
    // sum is a perfect cube
    static void findNumbers(int n)
    {
        int i = 1;

        // Loop to find the Ith term
        // of the Centered Hexagonal number
        while (i <= n)
        {
            System.out.print((3 * i * (i - 1) + 1) + " ");
            i++;
        }
    }

    // Driver Code
    public static void main (String[] args)
    {
        int n = 4;

        // Function Call
        findNumbers(n);
    }
}

// This code is contributed by AnkitRai01

C

// C# implementation to find the N
// numbers such that their
// sum is a perfect cube
using System;

public class GFG
{

    // Function to find the N
    // numbers such that their
    // sum is a perfect cube
    static void findNumbers(int n)
    {
        int i = 1;

        // Loop to find the Ith term
        // of the Centered Hexagonal number
        while (i <= n)
        {
            Console.Write((3 * i * (i - 1) + 1) + " ");
            i++;
        }
    }

    // Driver Code
    public static void Main()
    {
        int n = 4;

        // Function Call
        findNumbers(n);
    }
}

// This code is contributed by AnkitRai01

Python 3

# Python3 implementation to find the N
# numbers such that their
# sum is a perfect cube

# Function to find the N
# numbers such that their
# sum is a perfect cube
def findNumbers(n):
    i = 1

    # Loop to find the Ith term
    # of the Centered Hexagonal number
    while (i <= n):
        print((3 * i * (i - 1) + 1), end=" ")
        i += 1

# Driver Code
n = 4

# Function Call
findNumbers(n)

# This code is contributed by mohit kumar 29

java 描述语言

<script>

// Javascript implementation to find
// the N numbers such that their sum
// is a perfect cube

// Function to find the N
// numbers such that their
// sum is a perfect cube
function findNumbers(n)
{
    let i = 1;

    // Loop to find the Ith term
    // of the Centered Hexagonal number
    while (i <= n)
    {
        document.write((3 * i * (i - 1) +
                       1) + " ");
        i++;
    }
}

// Driver Code
let n = 4;

// Function Call
findNumbers(n);

// This code is contributed by Surbhi Tyagi.

</script>

Output: 

1 7 19 37

性能分析:

  • 时间复杂度:和上面的方法一样，我们正在寻找所有的 N Centered 六边形数，所以需要 O(N) 。
  • 辅助空间:和上面的方法一样，没有使用额外的空间，所以使用的辅助空间将是 O(1)

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