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 (xi / h)2 = i / N
=> xi = h*?(i/n)
xi = height of ith 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 ith iteration, print the value of xi 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 basevoid 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 codeint 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 approachimport 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 basedef 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 Codeif __name__ == '__main__': # Given N n = 3 # Given H h = 2 # Function call findPoint(n, h) |
C#
// C# Code for above approachusing 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)
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