Last time: We looked at a problem called subset sum.
This time, a broad algorithm design strategy for that kind of problem: backtracking.
Search Problems #
- We have a series of choices we need to make.
- Whether or not to include a number in our subset.
- Which road to take when finding a path on a map.
- Which move to make in a game.
- Once we have a proposed sequence, we can validate it.
- Correct / Wrong
- Score (e.g. # of bins)
Basic plan:
- Make the first choice in the series.
- Recurse find the rest of the choices in the series.
- At each level, if we know we have the best answer then we’re done.
- If we may not have the best answer, try another choice.
How efficient was our subset sum algorithm? #
- Not great.
Example: Game Trees #
Tic-Tac-Toe is too complicated. So let’s do a simpler game.
- There’s a 1D array of squares of some length.
- Players take turns placing X’s in the squares.
- Whoever makes 3 in a row wins.
Who wins for each board size?
- n = 1, 2 - No winner
- n = 3?
Let’s write a program to do the search in general.
