Pictures on the Wall#539

Solution

The pictures occupy $n \cdot w$ units of the wall's length. This leaves $l - n \cdot w$ units for the gaps.

There are $n - 1$ gaps between $n$ pictures. Including the gaps at both edges of the wall, there are $n + 1$ n+1 gaps.

All gaps must have the same integer length. Therefore, an arrangement exists if and only if $l - n \cdot w$ l-n \cdot w is divisible by $n + 1$ n+1. Print YES in this case and NO otherwise.

The guarantee $n \cdot w \leq l$ n \cdot w \le l ensures that the gap length is non-negative. If the pictures occupy the entire wall, all gaps have length zero, which is allowed.

Complexity

The time complexity is $O (1)$ and the extra space is $O (1)$ .