Count pieces of circle after N cuts

Given an integer N, where 1 \leq N \leq 10^{18}. The task is to print the count of pieces of a circle with N cuts where each cut passes through the centre of given circle.

Examples:

Input : N = 2
Output : 4

Input : N = 100
Output : 200



Approach: This problem can be easily solved with observation only. Since each cut passes through the centre, each cut creates two new pieces.

Let us see how above Intuition works.

  • At first cut we have 2 different pieces of circle.
  • At second cut we have 2 new different pieces from previous 2 pieces of circle.
  • At third cut we have again 2 new different pieces from any of previous 2 pieces which are opposite to each other.

Circle with N cuts through center

In this way, we proceed with N cuts to get the count of total pieces after N cuts.

Below is the implementation of above approach:

C++

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// C++ program to find number of pieces
// of circle after N cuts
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find number of pieces
// of circle after N cuts
int countPieces(int N)
{
    return 2 * N;
}
  
// Driver program
int main()
{
    int N = 100;
  
    cout << countPieces(N);
  
    return 0;
}

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Java

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// Java program to find number of pieces
// of circle after N cuts
import java.util.*;
  
class solution
{
  
// Function to find number of pieces
// of circle after N cuts
static int countPieces(int N)
{
    return 2 * N;
}
  
// Driver program
public static void main(String args[])
{
    int N = 100;
  
    System.out.println(countPieces(N));
  
}
  
}

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Python3

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# Python program to find number 
# of pieces of circle after N cuts 
  
# Function to find number of 
# pieces of circle after N cuts 
def countPieces(N):
    return 2 *
  
# Driver Code 
N = 100
  
print(countPieces(N))
  
# This code is contributed by
# Sanjit_Prasad

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C#

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// C# program to find number of pieces
// of circle after N cuts
  
class solution
{
  
// Function to find number of pieces
// of circle after N cuts
static int countPieces(int N)
{
    return 2 * N;
}
  
// Driver program
static void Main()
{
    int N = 100;
  
    System.Console.WriteLine(countPieces(N));
  
}
  
}
// This code is contributed by mits

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PHP

Output:

200

Time Complexity: O(1)



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