Count pieces of circle after N cuts
Given an integer N, where . 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.
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.
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:
Time Complexity: O(1)