Dado un número n, encuentra el término n-ésimo en la serie 3, 13, 42, 108, 235…
Ejemplos:
Input : 3 Output : 42 Input : 4 Output : 108
Restricciones:
1 <= T <= 100
1 <= N <= 100
Enfoque ingenuo:
la serie representa básicamente sumas de cubos de números naturales y número de términos multiplicados por 2. El primer término es la suma del número único. El segundo término es la suma de dos números, y así sucesivamente.
Ejemplos:
n = 2 2nd term equals to sum of 1st term and 8 i.e A2 = A1 + 23 + n*2 = 1 + 8 + 4 = 13 Similarly, A3 = A2 + 33 + n*2 = 9 + 27 + 6 = 42 and so on..
Una solución sencilla es sumar los primeros n números naturales al cubo y el número de términos multiplicado por 2.
C++
// C++ program to find n-th term of
// series 3, 13, 42, 108, 235…
#include <bits/stdc++.h>
using namespace std;
// Function to generate a fixed number
int magicOfSequence(int N)
{
int sum = 0;
for (int i = 1; i <= N; i++)
sum += (i*i*i + i*2);
return sum;
}
// Driver Method
int main()
{
int N = 4;
cout << magicOfSequence(N) << endl;
return 0;
}
Java
// Java Program to Finding n-th term
// of series 3, 13, 42, 108, 235 ...
class GFG {
// Function to generate
// a fixed number
public static int magicOfSequence(int N)
{
int sum = 0;
for (int i = 1; i <= N; i++)
sum += (i * i * i + i * 2);
return sum;
}
// Driver Method
public static void main(String args[])
{
int N = 4;
System.out.println(magicOfSequence(N));
}
}
// This code is contributed by Jaideep Pyne
Python3
# Python3 program to # find n-th term of # series 3, 13, 42, 108, 235… # Function to generate # a fixed number def magicOfSequence(N) : sum = 0 for i in range(1, N + 1) : sum += (i * i * i + i * 2) return sum; # Driver Code N = 4 print(magicOfSequence(N)) # This code is contributed by vij.
C#
// C# Program to Finding
// n-th term of series
// 3, 13, 42, 108, 235 ...
using System;
class GFG
{
// Function to generate
// a fixed number
public static int magicOfSequence(int N)
{
int sum = 0;
for (int i = 1; i <= N; i++)
sum += (i * i * i + i * 2);
return sum;
}
// Driver Code
static public void Main ()
{
int N = 4;
Console.WriteLine(magicOfSequence(N));
}
}
// This code is contributed
// by ajit
PHP
<?php
// PHP program to find n-th term of
// series 3, 13, 42, 108, 235…
// Function to generate a fixed number
function magicOfSequence($N)
{
$sum = 0;
for ($i = 1; $i <= $N; $i++)
$sum += ($i*$i*$i + $i*2);
return $sum;
}
// Driver Method
$N = 4;
echo magicOfSequence($N);
// This code is contributed by m_kit
?>
Javascript
<script>
// JavaScript program to find n-th term of
// series 3, 13, 42, 108, 235…
// Function to generate a fixed number
function magicOfSequence( N)
{
let sum = 0;
for (let i = 1; i <= N; i++)
sum += (i*i*i + i*2);
return sum;
}
// Driver Function
let N = 4;
document.write(magicOfSequence(N));
// This code contributed by Rajput-Ji
</script>
120
La complejidad temporal de esta solución es O(n).
Enfoque eficiente:
sabemos que la suma de los cubos de los primeros n números naturales es (n*(n+1)/2) 2 . También sabemos que si multiplicamos el i-ésimo término por 2 y lo sumamos todo, obtenemos la suma de n términos como 2*n.
Entonces nuestro resultado es (n*(n+1)/2) 2 + 2*n.
Ejemplo :
Para n = 4 la suma por la fórmula es
(4 * (4 + 1 ) / 2)) ^ 2 + 2*4
= (4 * 5 / 2) ^ 2 + 8
= (10) ^ 2 + 8
= 100 + 8
= 108
Para n = 6 , la suma por la fórmula es
(6 * (6 + 1 ) / 2)) ^ 2 + 2*6
= (6 * 7 / 2) ^ 2 + 12
= (21) ^ 2 + 12
= 441 + 12
= 453
C++
// A formula based C++ program to find sum
// of series with cubes of first n natural
// numbers
#include <iostream>
using namespace std;
int magicOfSequence(int N)
{
return (N * (N + 1) / 2) + 2 * N;
}
// Driver Function
int main()
{
int N = 6;
cout << magicOfSequence(N);
return 0;
}
Java
// A formula based Java program to find sum
// of series with cubes of first n natural
// numbers
class GFG {
static int magicOfSequence(int N)
{
return (N * (N + 1) / 2) + 2 * N;
}
// Driver Function
public static void main(String[] args)
{
int N = 6;
System.out.println(magicOfSequence(N));
}
}
// This code is contributed by Smitha.
Python 3
# A formula based Python program to find sum # of series with cubes of first n natural # numbers def magicOfSequence(N): return (N * (N + 1) / 2) + 2 * N # Driver Function N = 6 print(int(magicOfSequence(N))) # This code is contributed by Smitha.
C#
// A formula based C# program to find sum
// of series with cubes of first n natural
// numbers
using System;
class GFG {
static int magicOfSequence(int N)
{
return (N * (N + 1) / 2) + 2 * N;
}
// Driver Function
public static void Main()
{
int N = 6;
Console.Write(magicOfSequence(N));
}
}
// This code is contributed by Smitha.
PHP
<?php
// A formula based PHP program
// to find sum of series with
// cubes of first n natural numbers
function magicOfSequence($N)
{
return ($N * ($N + 1) / 2) + 2 * $N;
}
// Driver Code
$N = 6;
echo magicOfSequence($N) . "\n";
// This code is contributed by mits
?>
Javascript
<script>
// A formula based Java program to find sum
// of series with cubes of first n natural
// numbers
function magicOfSequence( N)
{
return (N * (N + 1) / 2) + 2 * N;
}
// Driver Function
let N = 6;
document.write(magicOfSequence(N));
// This code is contributed by 29AjayKumar
</script>
33
Complejidad de tiempo: O(1)
Complejidad espacial : O (1) ya que el espacio constante se usa para variables