Backtracking / search problems tend to be O(2^n). That’s slow.
But many of them have shared subproblems. If we can exploit that, we can go much faster.
Robber Problem (or Fib) #
Robber problem:
- There’s a street with houses along one side.
- You have a list of the value of the stuff you could steal from the houses, in order.
- You’d get caught if you rob two houses next to each other
- Maximize the value of the houses that you rob.
Basic strategy:
- Either include a house or don’t.
- If we do include a house, the next legal house is i + 2.
- Problem: Best set of houses to rob up to some index i.
Steps:
- Recursive
- Memoize
- Table
- prev0, prev1
Longest Increasing Subsequence #
- We’ve got a list of numbers.
- We want to find the longest increasing subsequence.
- Recursive problem:
- Best subsequence that ends with the number at index ii.
- Then we can expand by one by scanning through for the best compatible previous subsequence, so O(n^2) total.
Work through some variants #
- Recursive
- Memoize
- Table
- Must retain table
