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Maximum number of pieces in N cuts in C++
Given the task is to calculate the maximum number of square or rectangle pieces of equal size that can be obtained by cutting a given square piece in total N number of cuts horizontally or vertically.
Let’s now understand what we have to do using an example −
Input − N=8
Output − 25
Explanation − When N=8, the number of vertical cuts = 4 and the number of horizontal cuts = 4.
Total pieces = 25
| 1 | 2 | 3 | 4 | 5 |
| 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 |
| 16 | 17 | 18 | 19 | 20 |
| 21 | 22 | 23 | 24 | 25 |
Input − 7
Output − 20
| 1 | 2 | 3 | 4 | 5 |
| 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 |
| 16 | 17 | 18 | 19 | 20 |
Approach used in the below program as follows
If N is the number of cuts and we have to maximize the resultant pieces then equal number of horizontal and vertical cuts have to be made.
If N is even then there will be equal horizontal and vertical cuts else if N is odd, then the horizontal cuts will be 1 more than the vertical cuts or vice versa.
Therefore, the number of horizontal = N/2 and vertical cuts = N-H.
In function MaxPieces() initialize a variable H =N/2 of type int to store the number of Horizontal cuts.
Initialize another variable V=N-H of type int to store the number of vertical cuts.
Final number of pieces = (Horizonal Rows)*(Vertical rows) = (H+1)*(V+1)
Example
#include <bits/stdc++.h>
using namespace std;
int MaxPieces(int N){
//H is the number of horizontal cuts
int H = N / 2;
//V is the number of vertical cuts
int V = N-H;
// maximum number of pieces = (H+1)*(V+1)
return ((H + 1) * (V + 1));
}
//Main function
int main(){
//Number of cuts
int N = 7;
cout << "Max pieces = "<<MaxPieces(N);
return 0;
}Output
If we run the above code we will get the following output −
20
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