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

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 = 6Output:

Max = 8

Min = 4Input:s1 = 5, s2 = 8Output:

Max = 12

Min = 4

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**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:

## 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