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Yes, Paint Fence is a common interview problem used to test understanding of dynamic programming and state transitions. Variations of this problem may appear in interviews at large tech companies.
The optimal approach uses dynamic programming by tracking two states: when the current post has the same color as the previous one and when it has a different color. By updating these states iteratively, we can compute the total number of valid colorings efficiently.
Dynamic programming is used because the number of ways to paint a post depends on the results of previous posts. By storing and reusing these intermediate results, we avoid redundant calculations and improve efficiency.
A few integer variables or a small DP array is sufficient. Since only the previous state values are needed, the solution can be optimized to constant space using simple variables.