给定两个整数N和M ,其中N条直线平行于X轴, M条直线平行于Y轴,任务是计算可以由这些直线形成的矩形的数量。
例子:
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.
方法:
为了解决上述问题,我们需要观察到一个矩形是由4条直线形成的,其中相对的边是平行的,并且任意两个边之间的角度都是90度。因此,对于每个矩形,必须使两个边平行于X-轴和其他两侧必须与Y轴平行。
- 选择两条平行于X轴的线的方式数目= N C 2 并且选择两条平行于Y轴的线的方式数= M C 2 。
- 因此,矩形的总数= N C 2 * M C 2 = [N *(N – 1)/ 2] * [M *(M – 1)/ 2]
下面是上述方法的实现:
C++
// C++ Program to count number of
// rectangles formed by N lines
// parallel to X axis M lines
// parallel to Y axis
#include
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
// 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
# 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#
// 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
Javascript
输出:
45
时间复杂度: O(1)