Consider a 3D cube and n planes. We can make cuts in the cube using given planes. A Cake Number for a given n is the maximum number of regions that can be formed by n planes.
Series after n plane cuts (0 ≤ n) :
1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697…
Examples:
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
The formula of nth Term of Cake number:
n-th Cake Number = nC3 + nC2 + nC1 + nC0
= (n3 + 5*n + 6) / 6
Below is the implementation of above approach :
C++
#include <iostream>
using namespace std;
int number_cake( int n)
{
return (n * n * n + 5 * n + 6) / 6;
}
int main()
{
int n = 2;
cout << number_cake(n) << endl;
n = 8;
cout << number_cake(n) << endl;
n = 25;
cout << number_cake(n) << endl;
return 0;
}
|
C
#include <stdio.h>
int number_cake( int n)
{
return (n * n * n + 5 * n + 6) / 6;
}
int main()
{
int n = 2;
printf ( "%d\n" ,number_cake(n));
n = 8;
printf ( "%d\n" ,number_cake(n));
n = 25;
printf ( "%d\n" ,number_cake(n));
return 0;
}
|
Java
import java.io.*;
class GFG {
static int number_cake( int n)
{
return (n * n * n + 5 * n + 6 ) / 6 ;
}
public static void main (String[] args)
{
int n = 2 ;
System.out.println( number_cake(n));
n = 8 ;
System.out.println( number_cake(n));
n = 25 ;
System.out.println( number_cake(n));
}
}
|
Python3
def number_cake(n):
return (n * n * n + 5 * n + 6 ) / / 6
n = 2
print (number_cake(n))
n = 8
print (number_cake(n))
n = 25
print (number_cake(n))
|
C#
using System;
class GFG {
static int number_cake( int n)
{
return (n * n * n + 5 * n + 6) / 6;
}
public static void Main ()
{
int n = 2;
Console.WriteLine( number_cake(n));
n = 8;
Console.WriteLine( number_cake(n));
n = 25;
Console.WriteLine( number_cake(n));
}
}
|
PHP
<?php
function number_cake( $n )
{
return ( $n * $n * $n +
5 * $n + 6) / 6;
}
$n = 2;
echo number_cake( $n ) , "\n" ;
$n = 8;
echo number_cake( $n ), " \n" ;
$n = 25;
echo number_cake( $n );
?>
|
Javascript
<script>
function number_cake(n)
{
return parseInt((n * n * n + 5 * n + 6) / 6, 10);
}
let n = 2;
document.write( number_cake(n) + "</br>" );
n = 8;
document.write( number_cake(n) + "</br>" );
n = 25;
document.write( number_cake(n));
</script>
|
Output :
4
93
2626
Time Complexity: O(1)
Auxiliary Space: O(1)
Last Updated :
06 Jun, 2022
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