Given a number of unit squares (1 x 1). How many different rectangles can be formed with them?
For example let us consider 4 units. We can form 5 different rectangles like the following. Two rectangles are considered same if they are oriented in a different way but same dimensions.
Basically we have to arrange 1 to N-1 units to form rectangles of different dimensions.
This boils down to finding the sum of the number of pairs factors of 1 to N numbers.
Here is the C++ program to do that.
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| #include <iostream> | |
| #include <cmath> | |
| using namespace std; | |
| int main() { | |
| int n; | |
| cin >> n; | |
| int i,j; | |
| int r = 0; | |
| for( i = 1; i <= n; i++ ) | |
| { | |
| for( j = 1; j <= sqrt(i*1.0); j++ ) | |
| { | |
| if( i % j == 0 ) | |
| r++; | |
| } | |
| } | |
| cout << r << endl; | |
| return 0; | |
| } |
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