Pizza cut problem (Or Circle Division by Lines)
Given number of cuts, find the maximum number of possible pieces.
Examples:
Input : 2 Output : 4 Input : 3 Output : 7
This problem is nothing but The Lazy Caterer’s Problem and has below formula.
Maximum number of pieces = 1 + n*(n+1)/2
Refer this for proof.
C++
// C++ program to find maximum no of pieces // by given number of cuts #include<bits/stdc++.h> using namespace std; // Function for finding maximum pieces // with n cuts. int findMaximumPieces( int n) { return 1 + n*(n+1)/2; } // Driver code int main() { cout << findMaximumPieces(3); return 0; } |
Java
// Java program to find maximum no of // pieces by given number of cuts class GFG { // Function for finding maximum pieces // with n cuts. static int findMaximumPieces( int n) { return 1 + n * (n + 1 ) / 2 ; } // Driver Program to test above function public static void main(String arg[]) { System.out.print(findMaximumPieces( 3 )); } } // This code is contributed by Anant Agarwal. |
Python3
# Python3 program to find maximum # no. of pieces by given # number of cuts # Function for finding maximum # pieces with n cuts. def findMaximumPieces(n): return int ( 1 + n * (n + 1 ) / 2 ) # Driver code print (findMaximumPieces( 3 )) # This code is contributed 29AjayKumar |
C#
// C# program to find maximum no of // pieces by given number of cuts using System; class GFG { // Function for finding maximum pieces // with n cuts. static int findMaximumPieces( int n) { return 1 + n * (n + 1) / 2; } // Driver Program to test above function public static void Main() { Console.Write(findMaximumPieces(3)); } } // This code is contributed by nitin mittal. |
PHP
<?php // PHP program to find maximum // no. of pieces by given // number of cuts // Function for finding maximum // pieces with n cuts. function findMaximumPieces( $n ) { return 1 + $n * ( $n + 1) / 2; } // Driver code echo findMaximumPieces(3); // This code is contributed by nitin mittal. ?> |
Javascript
<script> // Javascript program to find maximum no of pieces // by given number of cuts // Function for finding maximum pieces // with n cuts. function findMaximumPieces(n) { return 1 + n * (n + 1) / 2; } // Driver Code document.write(findMaximumPieces(3)); </script> |
Output:
7
Time Complexity: O(1)
Auxiliary Space: O(1)