Split given isosceles triangle of height H into N equal parts

0 0 3 minutes read

Given an integer N and an isosceles triangle consisting of height H, the task is to find (N – 1) points on the triangle such that the line passing through these points and parallel to the base of the triangle, divide the total area into N equal parts.

Examples:

Input: N = 3, H = 2
Output: 1.15 1.63
Explanation: Make cuts at point 1.15 and 1.63 as shown below:

Input: N = 2, H = 1000
Output: 70710.67

Approach: The problem can be solved by observing the following properties:

Divide the triangle such that (x_i / h)² = i / N
=> x_i= h*?(i/n)
x_i = height of i^th cut from the top vertex of the triangle

Follow the steps below to solve the problem:

Iterate over the range [1, N – 1].
In every i^th iteration, print the value of x_i using the above formula.

Below is the implementation of the above approach:

C++

// C++ Code for above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to divide the isosceles triangle
// in equal parts by making N-1 cuts
// parallel to the base
void findPoint(int n, int h)
{
   
    // Iterate over the range [1, n - 1]
    for (int i = 1; i < n; i++)
        printf("%.2f ", sqrt(i / (n*1.0)) * h);
}
 
// Driver code
int main()
{
  // Given N
  int n = 3;
 
  // Given H
  int h = 2;
 
  // Function call
  findPoint(n, h);
 
  return 0;
}
 
// This code is contributed by mohit kumar 29

Java

// Java Code for above approach
import java.util.*;
class GFG
{
 
    // Function to divide the isosceles triangle
    // in equal parts by making N-1 cuts
    // parallel to the base
    static void findPoint(int n, int h)
    {
 
        // Iterate over the range [1, n - 1]
        for (int i = 1; i < n; i++)
            System.out.printf("%.2f ",
                    Math.sqrt(i / (n * 1.0)) * h);
    }
 
    // Driver code
    public static void main(String[] args)
    {
       
        // Given N
        int n = 3;
 
        // Given H
        int h = 2;
 
        // Function call
        findPoint(n, h);
    }
}
 
// This code is contributed by shikhasingrajput 

Python3

# Python Code for above approach
 
 
# Function to divide the isosceles triangle 
# in equal parts by making N-1 cuts 
# parallel to the base
def findPoint(n, h):
 
 
    # Iterate over the range [1, n - 1]
    for i in range(1, n):
        print("{0:.2f}".format(((i / n) ** 0.5) * h), end =' ')
 
 
# Driver Code
if __name__ == '__main__':
 
    # Given N
    n = 3
 
    # Given H
    h = 2
 
    # Function call
    findPoint(n, h)

C#

// C# Code for above approach
using System;
class GFG
{
 
  // Function to divide the isosceles triangle
  // in equal parts by making N-1 cuts
  // parallel to the base
  static void findPoint(int n, int h)
  {
 
    // Iterate over the range [1, n - 1]
    for (int i = 1; i < n; i++)
      Console.Write("{0:F2} ",
                    Math.Sqrt(i / (n * 1.0)) * h);
  }
 
  // Driver code
  public static void Main(String[] args)
  {
 
    // Given N
    int n = 3;
 
    // Given H
    int h = 2;
 
    // Function call
    findPoint(n, h);
  }
}
 
// This code is contributed by shikhasingrajput

Javascript

<script>
// Javascript program for the above approach
 
    // Function to divide the isosceles triangle
    // in equal parts by making N-1 cuts
    // parallel to the base
    function findPolet(n, h)
    {
  
        // Iterate over the range [1, n - 1]
        for (let i = 1; i < n; i++)
            document.write(
                    Math.sqrt(i / (n * 1.0)) * h + " ");
    }
     
// driver function
 
        // Given N
        let n = 3;
  
        // Given H
        let h = 2;
  
        // Function call
        findPolet(n, h);;
      
     // This code is contributed by souravghosh0416.
</script>    

Output:

1.15 1.63

Time Complexity: O(N)
Auxiliary Space: O(1)

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!