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Minimum and maximum possible length of the third side of a triangle

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  • Difficulty Level : Basic
  • Last Updated : 07 Jun, 2022
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Given two sides of a triangle s1 and s2, the task is to find the minimum and maximum possible length of the third side of the given triangle. Print -1 if it is not possible to make a triangle with the given side lengths. Note that the length of all the sides must be integers.
Examples: 
 

Input: s1 = 3, s2 = 6 
Output: 
Max = 8 
Min = 4
Input: s1 = 5, s2 = 8 
Output: 
Max = 12 
Min = 4 
 

 

Approach: Let s1, s2 and s3 be the sides of the given triangle where s1 and s2 are given. As we know that in a triangle, the sum of two sides must always be greater than the third side. So, the following equations must be satisfied: 
 

  1. s1 + s2 > s3
  2. s1 + s3 > s2
  3. s2 + s3 > s1

Solving for s3, we get s3 < s1 + s2, s3 > s2 – s1 and s3 > s1 – s2
It is clear now that the length of the third side must lie in the range (max(s1, s2) – min(s1, s2), s1 + s2) 
So, the minimum possible value will be max(s1, s2) – min(s1, s2) + 1 and the maximum possible value will be s1 + s2 – 1.
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <iostream>
using namespace std;
 
// Function to find the minimum and the
// maximum possible length of the third
// side of the given triangle
void find_length(int s1, int s2)
{
 
    // Not a valid triangle
    if (s1 <= 0 || s2 <= 0) {
        cout << -1;
        return;
    }
    int max_length = s1 + s2 - 1;
    int min_length = max(s1, s2) - min(s1, s2) + 1;
 
    // Not a valid triangle
    if (min_length > max_length) {
        cout << -1;
        return;
    }
 
    cout << "Max = " << max_length << endl;
    cout << "Min = " << min_length;
}
 
// Driver code
int main()
{
    int s1 = 8, s2 = 5;
    find_length(s1, s2);
 
    return 0;
}

Java




// Java implementation of the approach
import java.io.*;
 
class GFG
{
 
// Function to find the minimum and the
// maximum possible length of the third
// side of the given triangle
static void find_length(int s1, int s2)
{
 
    // Not a valid triangle
    if (s1 <= 0 || s2 <= 0)
    {
        System.out.print(-1);
        return;
    }
    int max_length = s1 + s2 - 1;
    int min_length = Math.max(s1, s2) - Math.min(s1, s2) + 1;
 
    // Not a valid triangle
    if (min_length > max_length)
    {
        System.out.print(-1);
        return;
    }
 
    System.out.println("Max = " + max_length);
    System.out.print("Min = " + min_length);
}
 
// Driver code
public static void main (String[] args)
{
    int s1 = 8, s2 = 5;
    find_length(s1, s2);
}
}
 
// This code is contributed by anuj_67..

Python3




# Python3 implementation of the approach
 
# Function to find the minimum and the
# maximum possible length of the third
# side of the given triangle
def find_length(s1, s2) :
 
    # Not a valid triangle
    if (s1 <= 0 or s2 <= 0) :
        print(-1, end = "");
        return;
         
    max_length = s1 + s2 - 1;
    min_length = max(s1, s2) - min(s1, s2) + 1;
 
    # Not a valid triangle
    if (min_length > max_length) :
        print(-1, end = "");
        return;
 
    print("Max =", max_length);
    print("Min =", min_length);
 
 
# Driver code
if __name__ == "__main__" :
 
    s1 = 8;
    s2 = 5;
     
    find_length(s1, s2);
     
# This code is contributed by AnkitRai01

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
// Function to find the minimum and the
// maximum possible length of the third
// side of the given triangle
static void find_length(int s1, int s2)
{
 
    // Not a valid triangle
    if (s1 <= 0 || s2 <= 0)
    {
        Console.Write(-1);
        return;
    }
    int max_length = s1 + s2 - 1;
    int min_length = Math.Max(s1, s2) - Math.Min(s1, s2) + 1;
 
    // Not a valid triangle
    if (min_length > max_length)
    {
        Console.WriteLine(-1);
        return;
    }
 
    Console.WriteLine("Max = " + max_length);
    Console.WriteLine("Min = " + min_length);
}
 
// Driver code
public static void Main ()
{
    int s1 = 8, s2 = 5;
    find_length(s1, s2);
}
}
 
// This code is contributed by anuj_67..

Javascript




<script>
// javascript implementation of the approach
 
    // Function to find the minimum and the
    // maximum possible length of the third
    // side of the given triangle
    function find_length(s1 , s2)
    {
 
        // Not a valid triangle
        if (s1 <= 0 || s2 <= 0)
        {
            document.write(-1);
            return;
        }
        var max_length = s1 + s2 - 1;
        var min_length = Math.max(s1, s2) - Math.min(s1, s2) + 1;
 
        // Not a valid triangle
        if (min_length > max_length)
        {
            document.write(-1);
            return;
        }
 
        document.write("Max = " + max_length+"<br/>");
        document.write("Min = " + min_length);
    }
 
    // Driver code
    var s1 = 8, s2 = 5;
    find_length(s1, s2);
 
// This code is contributed by todaysgaurav
</script>

Output: 

Max = 12
Min = 4

 

Time Complexity: O(1)

Auxiliary Space: O(1)


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