Given two integers N and M, where N straight lines are parallel to the X-axis and M straight lines are parallel to Y-axis, the task is to calculate the number of rectangles that can be formed by these lines.
Examples:
Input: N = 3, M = 6
Output: 45
Explanation:
There are total 45 rectangles possible with 3 lines parallel to x axis and 6 lines parallel to y axis.
Input: N = 2, M = 4
Output: 6
Explanation:
There are total 6 rectangles possible with 2 lines parallel to x axis and 4 lines parallel to y axis.
Approach:
To solve the problem mentioned above we need to observe that a rectangle is formed by 4 straight lines in which opposite sides are parallel and the angle between any two sides is 90. Hence, for every rectangle, two sides need to be parallel to X-axis and the other two sides need to be parallel to Y-axis.
- Number of ways to select two lines parallel to X axis = NC2and the Number of ways to select two lines parallel to Y axis = MC2.
- So the total number of rectangles = NC2 * MC2 = [ N * (N – 1) / 2 ] * [ M * (M – 1) / 2 ]
Below is implementation of above approach:
// C++ Program to count number of // rectangles formed by N lines // parallel to X axis M lines // parallel to Y axis #include <bits/stdc++.h> using namespace std;
// Function to calculate // number of rectangles int count_rectangles( int N, int M)
{ // Total number of ways to
// select two lines
// parallel to X axis
int p_x = (N * (N - 1)) / 2;
// Total number of ways
// to select two lines
// parallel to Y axis
int p_y = (M * (M - 1)) / 2;
// Total number of rectangles
return p_x * p_y;
} // Driver Program int main()
{ int N = 3;
int M = 6;
cout << count_rectangles(N, M);
} |
// Java Program to count number of // rectangles formed by N lines // parallel to X axis M lines // parallel to Y axis class GFG{
// Function to calculate // number of rectangles static int count_rectangles( int N, int M)
{ // Total number of ways to
// select two lines
// parallel to X axis
int p_x = (N * (N - 1 )) / 2 ;
// Total number of ways
// to select two lines
// parallel to Y axis
int p_y = (M * (M - 1 )) / 2 ;
// Total number of rectangles
return p_x * p_y;
} // Driver Program public static void main(String[] args)
{ int N = 3 ;
int M = 6 ;
System.out.print(count_rectangles(N, M));
} } // This code is contributed by sapnasingh4991 |
# Python3 program to count number of rectangles # formed by N lines parallel to X axis # and M lines parallel to Y axis def count_rectangles(N, M):
# Total number of ways to select
# two lines parallel to X axis
p_x = (N * (N - 1 )) / / 2
# Total number of ways to select
# two lines parallel to Y axis
p_y = (M * (M - 1 )) / / 2
# Total number of rectangles
return p_x * p_y
# Driver code N = 3
M = 6
print (count_rectangles(N, M))
# This code is contributed by himanshu77 |
// C# Program to count number of // rectangles formed by N lines // parallel to X axis M lines // parallel to Y axis using System;
class GFG{
// Function to calculate // number of rectangles static int count_rectangles( int N, int M)
{ // Total number of ways to
// select two lines
// parallel to X axis
int p_x = (N * (N - 1)) / 2;
// Total number of ways
// to select two lines
// parallel to Y axis
int p_y = (M * (M - 1)) / 2;
// Total number of rectangles
return p_x * p_y;
} // Driver Program public static void Main()
{ int N = 3;
int M = 6;
Console.Write(count_rectangles(N, M));
} } // This code is contributed by Code_mech |
<script> // JavaScript Program to count number of // rectangles formed by N lines // parallel to X axis M lines // parallel to Y axis // Function to calculate // number of rectangles function count_rectangles(N, M)
{ // Total number of ways to
// select two lines
// parallel to X axis
let p_x = (N * (N - 1)) / 2;
// Total number of ways
// to select two lines
// parallel to Y axis
let p_y = (M * (M - 1)) / 2;
// Total number of rectangles
return p_x * p_y;
} // Driver Code let N = 3;
let M = 6;
document.write(count_rectangles(N, M));
</script> |
45
Time Complexity: O(1), as constant operations are being performed.
Auxiliary Space: O(1), as constant space is being used.