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++
// CPP Program to find the// nth Cake number#include <iostream>using namespace std;// function for Cake numberint number_cake(int n){ // formula for find Cake number // nth term return (n * n * n + 5 * n + 6) / 6;}// Driver Codeint 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 numberint number_cake(int n){ // formula for find Cake number // nth term return (n * n * n + 5 * n + 6) / 6;}// Driver Codeint 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 numberimport 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 numberdef number_cake(n): # Formula to calculate nth # Cake number return (n * n * n + 5 * n + 6) // 6# Driver Coden = 2print(number_cake(n))n = 8print(number_cake(n))n = 25print(number_cake(n)) # This code is contributed by aj_36 |
C#
// C# Program to find the nth Cake numberusing 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 numberfunction 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> |
Output :
4 93 2626
Time Complexity: O(1)
Auxiliary Space: O(1)
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