http://www.programcreek.com/2014/03/leetcode-house-robber-java/
This project solves the House Robber problem in 2 Dimensions. In a city there are R rows and C columns of houses aligned on a grid. We know the total amount of valuables in each house. The goal is to rob houses to maximize the amount of valuables. However robbing two adjacent houses will raise an alarm.
This is solved in two ways. A generalized solution is given using Dynamic Programming. Restricting the problem to positive integers greater than or equal to zero allows for the problem to be represented as a maximum flow / min cut problem.
Benchmark and Analysis
The DP solution has a runtime of O(N*φ^N) ( Actually, O(R*φ^C) ),
while the flow algorithm is O(N^2).
The benchmarks below are for finding the optimum value.
| Solver Function | Grid Shape (Row x Col) | runtime (ms) |
|---|---|---|
| DP-Rectangle | 3,000,000 x 6 | 1,611 |
| Flow-Rectangle | 20,000,000 x 6 | 2,040 |
| DP-Square | 447 x 447 | 25,704 |
| Flow-Square | 10,000 x 10,000 | 1,639 |
Results were generated using the go benchmark tool. The grid sizes are not the same, so this is not exactly comparing apples to apples. However the results are pretty clear. The optimized Flow solution allows for processing significantly larger problems.