Given an integer N, the task is to find the number of ways to split N into ordered triplets which can together form a triangle.
Examples:
Input: N = 15
Output: Total number of triangles possible are 28Input: N = 9
Output: Total number of triangles possible is 10
Approach: The following observation needs to be made in order to solve the problem:
If N is split into 3 integers a, b and c, then the following conditions need to be satisfied for a, b and c to form a triangle:
- a + b > c
- a + c > b
- b + c > a
Therefore, iterate over the range [1, N] using nested loops to generate triplets, and for each triplet check if it forms a triangle or not.
Below is the implementation of the above approach:
C++
// C++ Program to implement// the above approach#include <bits/stdc++.h>using namespace std;// Function to return the// required number of waysint Numberofways(int n){ int count = 0; for (int a = 1; a < n; a++) { for (int b = 1; b < n; b++) { int c = n - (a + b); // Check if a, b and c can // form a triangle if (a + b > c && a + c > b && b + c > a) { count++; } } } // Return number of ways return count;}// Driver Codeint main(){ int n = 15; cout << Numberofways(n) << endl; return 0;} |
Java
// Java Program to implement// the above approachimport java.io.*;class GFG { // Function to return the // required number of ways static int Numberofways(int n) { int count = 0; for (int a = 1; a < n; a++) { for (int b = 0; b < n; b++) { int c = n - (a + b); // Check if a, b, c can // form a triangle if (a + b > c && a + c > b && b + c > a) { count++; } } } return count; } // Driver Code public static void main(String[] args) { int n = 15; System.out.println(Numberofways(n)); }} |
Python3
# Python Program to implement# the above approach# Function to return the# required number of waysdef Numberofways(n): count = 0 for a in range(1, n): for b in range(1, n): c = n - (a + b) # Check if a, b, c can form a triangle if(a < b + c and b < a + c and c < a + b): count += 1 return count# Driver coden = 15print(Numberofways(n)) |
C#
// C# Program to implement// the above approachusing System;class GFG { // Function to return the // required number of ways static int Numberofways(int n) { int count = 0; for (int a = 1; a < n; a++) { for (int b = 1; b < n; b++) { int c = n - (a + b); // Check if a, b, c can form // a triangle or not if (a + b > c && a + c > b && b + c > a) { count++; } } } // Return number of ways return count; } // Driver Code static public void Main() { int n = 15; Console.WriteLine(Numberofways(n)); }} |
Javascript
<script>// Javascript Program to implement// the above approach// Function to return the// required number of waysfunction Numberofways(n){ var count = 0; for (var a = 1; a < n; a++) { for (var b = 1; b < n; b++) { var c = n - (a + b); // Check if a, b and c can // form a triangle if (a + b > c && a + c > b && b + c > a) { count++; } } } // Return number of ways return count;}// Driver Codevar n = 15;document.write( Numberofways(n));// This code is contributed by noob2000.</script> |
Output:
28
Time Complexity: O(N2)
Auxiliary Space: O(N)
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 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
