Mid/SeniorDynamic Programming
Count Number of Ways to Place Houses
There is a street with n * 2 plots, where there are n plots on each side of the street. The plots on each side are numbered from 1 to n. On each plot, a house can be placed.
Return the number of ways houses can be placed such that no two houses are adjacent to each other on the same side of the street. Since the answer may be very large, return it modulo 10^9 + 7.
Note that if a house is placed on the i^th plot on one side of the street, a house can also be placed on the i^th plot on the other side of the street.
Example 1
Input
n = 1Output
4There are four possible arrangements: all plots empty, one house on either side, or one house on each side.
Example 2
Input
n = 2Output
9There are 9 valid possible arrangements for two plots on each side of the street.
Constraints
- 1 <= n <= 10^4