Considere un cubo 3D y n planos. Podemos hacer cortes en el cubo usando planos dados. Un Número de Torta para un n dado es el número máximo de regiones que pueden estar formadas por n planos.
Serie después de n cortes de plano (0 ≤ n) :
1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697…
Ejemplos:
Input : 1 Output : 2 Explanation : With 1 plane cut the cube is divided into 2 regions Input : 2 Output : 4 Explanation: With 2 plane cuts, we can divide the cube into 4 regions Input : 4 Output : 15 Input : 5 Output : 26
La fórmula del n-ésimo término del número de pastel:
Número de pastel n = n C 3 + n C 2 + n C 1 + n C 0
= (n 3 + 5*n + 6) / 6
A continuación se muestra la implementación del enfoque anterior:
C++
// CPP Program to find the
// nth Cake number
#include <iostream>
using namespace std;
// function for Cake number
int number_cake(int n)
{
// formula for find Cake number
// nth term
return (n * n * n + 5 * n + 6) / 6;
}
// Driver Code
int main()
{
// For 2nd cake Number
int n = 2;
cout << number_cake(n) << endl;
// For 8th cake Number
n = 8;
cout << number_cake(n) << endl;
// For 25th cake Number
n = 25;
cout << number_cake(n) << endl;
return 0;
}
C
// C Program to find the
// nth Cake number
#include <stdio.h>
// function for Cake number
int number_cake(int n)
{
// formula for find Cake number
// nth term
return (n * n * n + 5 * n + 6) / 6;
}
// Driver Code
int main()
{
// For 2nd cake Number
int n = 2;
printf("%d\n",number_cake(n));
// For 8th cake Number
n = 8;
printf("%d\n",number_cake(n));
// For 25th cake Number
n = 25;
printf("%d\n",number_cake(n));
return 0;
}
// This code is contributed by kothavvsaakash
Java
// Java Program to find the nth Cake number
import java.io.*;
class GFG {
// function for Cake number
static int number_cake(int n)
{
// formula for find Cake number
// nth term
return (n * n * n + 5 * n + 6) / 6;
}
// Driver Code
public static void main (String[] args)
{
// For 2nd cake Number
int n = 2;
System.out.println( number_cake(n));
// For 8th cake Number
n = 8;
System.out.println( number_cake(n));
// For 25th cake Number
n = 25;
System.out.println( number_cake(n));
}
}
// This code is contributed by anuj_67.
Python3
# Python program to find # nth Cake number # Function to calculate # Cake number def number_cake(n): # Formula to calculate nth # Cake number return (n * n * n + 5 * n + 6) // 6 # Driver Code n = 2 print(number_cake(n)) n = 8 print(number_cake(n)) n = 25 print(number_cake(n)) # This code is contributed by aj_36
C#
// C# Program to find the nth Cake number
using System;
class GFG {
// function for Cake number
static int number_cake(int n)
{
// formula for find Cake number
// nth term
return (n * n * n + 5 * n + 6) / 6;
}
// Driver Code
public static void Main ()
{
// For 2nd cake Number
int n = 2;
Console.WriteLine( number_cake(n));
// For 8th cake Number
n = 8;
Console.WriteLine( number_cake(n));
// For 25th cake Number
n = 25;
Console.WriteLine( number_cake(n));
}
}
// This code is contributed by anuj_67.
PHP
<?php
// PHP Program to find the
// nth Cake number
// function for Cake number
function number_cake( $n)
{
// formula for find Cake
// number nth term
return ($n * $n * $n +
5 * $n + 6) / 6;
}
// Driver Code
// For 2nd cake Number
$n = 2;
echo number_cake($n) ,"\n";
// For 8th cake Number
$n = 8;
echo number_cake($n)," \n";
// For 25th cake Number
$n = 25;
echo number_cake($n);
// This code is contributed by anuj_67.
?>
Javascript
<script>
// Javascript Program to find the nth Cake number
// function for Cake number
function number_cake(n)
{
// formula for find Cake number
// nth term
return parseInt((n * n * n + 5 * n + 6) / 6, 10);
}
// For 2nd cake Number
let n = 2;
document.write( number_cake(n) + "</br>");
// For 8th cake Number
n = 8;
document.write( number_cake(n) + "</br>");
// For 25th cake Number
n = 25;
document.write( number_cake(n));
</script>
Producción :
4 93 2626
Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)