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