# Minimum distance of a number from origin.

• Given a number line from -infinity to +infinity. You start at 0 and can go either to the left or to the right. The condition is that in i’th move, you take i steps.

1. Find if you can reach a given number x
2. Find the most optimal way to reach a given number x, if we can indeed reach it. For example, 3 can be reached in 2 steps, (0, 1) (1, 3) and 4 can be reached in 3 steps (0, -1), (-1, 1) (1, 4)

• One can always reach any of the numbers...
Right,left,right,left
Or left, right, left, right...
Every left and right, you move right one step...

• The condition is that in i’th move, you take i steps.

[...]

4 can be reached in 3 steps (0, -1), (-1, 1) (1, 4)

In three moves, not in three steps.

Find the most optimal way to reach a given number x

Just always walk towards it. Or one step away if you have to complete moves (it's not clear, but I guess you have to because otherwise it makes no sense to talk about moves at all) and are in the middle of a move and already on the goal. For example, to reach 11:

First move: 0 -> 1
Second move: 1 -> 2 -> 3
Third move: 3 -> 4 -> 5 -> 6
Fourth move: 6 -> 7 -> 8 -> 9 -> 10
Fifth move: 10 -> 11 -> 10 -> 11 -> 10 -> 11

So that took eleven steps and five moves (not clear what you're counting, what "optimal" means).

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