What is the range of the third side of a triangle?

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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:

s1 + s2 > s3
s1 + s3 > s2
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:

#include <iostream>
using namespace std;
void find_length(int s1, int s2)
{
    if (s1 <= 0 || s2 <= 0) {
        cout << -1;
        return;
    }
    int max_length = s1 + s2 - 1;
    int min_length = max(s1, s2) - min(s1, s2) + 1;
    if (min_length > max_length) {
        cout << -1;
        return;
    }
    cout << "Max = " << max_length << endl;
    cout << "Min = " << min_length;
}
int main()



{
    int s1 = 8, s2 = 5;
    find_length(s1, s2);
    return 0;
}

import java.io.*;
class GFG
{
static void find_length(int s1, int s2)
{
    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;
    if (min_length > max_length)
    {
        System.out.print(-1);
        return;
    }
    System.out.println("Max = " + max_length);
    System.out.print("Min = " + min_length);
}



public static void main (String[] args)
{
    int s1 = 8, s2 = 5;
    find_length(s1, s2);
}
}

def find_length(s1, s2) :
    if (s1 <= 0 or s2 <= 0) :
        print(-1, end = "");
        return;
    max_length = s1 + s2 - 1;
    min_length = max(s1, s2) - min(s1, s2) + 1;
    if (min_length > max_length) :
        print(-1, end = "");
        return;
    print("Max =", max_length);
    print("Min =", min_length);
if __name__ == "__main__" :
    s1 = 8;
    s2 = 5;
    find_length(s1, s2);

using System;
class GFG
{
static void find_length(int s1, int s2)
{
    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;
    if (min_length > max_length)
    {
        Console.WriteLine(-1);
        return;
    }
    Console.WriteLine("Max = " + max_length);
    Console.WriteLine("Min = " + min_length);
}
public static void Main ()
{
    int s1 = 8, s2 = 5;
    find_length(s1, s2);
}
}

<script>
    function find_length(s1 , s2)
    {
        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;
        if (min_length > max_length)
        {
            document.write(-1);
            return;
        }
        document.write("Max = " + max_length+"<br/>");
        document.write("Min = " + min_length);
    }
    var s1 = 8, s2 = 5;
    find_length(s1, s2);
</script>

Time Complexity: O(1)

Auxiliary Space: O(1)

Q&A What

What is the range of the third side of a triangle?

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