Given a circular ring which has marking from 1 to N. Given two numbers A and B, you can stand at any place(say X) and count the total sum of the distance(say Z i.e., distance from X to A + distance from X to B). The task is to choose X in such a way that Z is minimized. Print the value of Z thus obtained. Note that X cannot neither be equal to A nor be equal to B.
Input: N = 6, A = 2, B = 4
Choose X as 3, so that distance from X to A is 1, and distance from X to B is 1.
Input: N = 4, A = 1, B = 2
Choose X as 3 or 4, both of them gives distance as 3.
Approach: There are two paths between the positions A and B on the circle, one in clockwise direction and another in anti-clockwise. An optimal value for Z is to choose X as any point on the minimum path between A and B then Z will be equal to the minimum distance between the positions except for the case when both the positions are adjacent to each other i.e. the minimum distance is 1. In that case, X cannot be chosen as the point between them as it must be different from both A and B and the result will be 3.
Below is the implementation of the above approach:
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- Minimum numbers needed to express every integer below N as a sum
- Minimum positive integer to divide a number such that the result is an odd
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