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Maximum given sized rectangles that can be cut out of a sheet of paper in C
We are given the dimensions of the sheet of paper, it’s Length L, and Breadth B. Also, we are given the dimensions of a small rectangle, it’s length l, and breadth b. The goal is to find the maximum number of smaller rectangles that can be cut out of a sheet of paper.
We will do following steps −
Firstly, we will take horizontal alignment, lengths L and l of sheet and rectangle respectively. Start aligning the L by l and B by b and count the rectangles.
Then also do the same in vertical alignments. Count again. Return the maximum value of count.
Let us understand with an example.
Input
Sheet L=18, B=6 Rectangle l=4, b=3
Output
Maximum rectangles: 8
Explanation
Horizontal 18/4=4 6/3=2 2*4=8 rectangles possible Vertical 18/3=6 6/4=1 6*1=6 rectangles possible Maximum rectangles here is 8
Input
Sheet L=10, B=6 Rectangle l=4, b=2
Output
Maximum rectangles: 6
Explanation
Horizontal 10/4=2 6/2=3 2*3=6 rectangles possible Vertical 10/2=5 6/4=1 5*1=5 rectangles possible Maximum rectangles here is 6
Approach used in the below program is as follows
The variables Length and Breadth are used to store dimensions of sheet.
The variables len and bre are used to store dimensions of rectangle.
Function maxRectangles (int L, int B, int l, int b) takes dimensions of sheet and rectangle and returns the maximum number of rectangles possible.
Variables numh and numv are used to store the number of rectangles that can be cut horizontally and vertically.
For horizontally, divide cols=L/l and rows=B/b, rectangles possible, numh=cols*rows.
For vertically, divide cols=L/b and rows=B/l, rectangles possible, numv=cols*rows.
Return maximum value as result obtained in above two steps numh or numv.
Example
#include <stdio.h>
int maxRectangles (int L, int B, int l, int b){
int numh = 0, numv = 0;
// Cut rectangles horizontally if possible
if (l <= L && b <= B){
// One rectangle is a single cell
int cols = B / b;
int rows = L / l;
// Total rectangles = total cells
numh = rows * cols;
}
// Cut rectangles vertically if possible
if (l <= B && b <= L){
int cols = L / b;
int rows = B / l;
numv = rows * cols;
}
// Return the maximum possible rectangles
return numh>numv?numh:numv;
}
// Driver code
int main (){
int Length = 18;
int Breadth =6;
int len = 4, bre = 3;
printf("Maximum rectangles: %d",maxRectangles(Length,Breadth,len,bre));
return 0;
}Output
If we run the above code it will generate the following output −
Maximum given sized rectangles that can be cut out of a sheet of paper: 8
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