1. Chapter 10: Algorithm Design Techniques
Mark Allen Weiss: Data Structures and Algorithm Analysis in Java
Chapter 10: Algorithm Design Techniques
Backtracking
Lydia Sinapova, Simpson College

2. Backtracking How to solve a problem by search Generate and Test
What is Backtracking
Example

3. The Idea Problem solving: search in a space of possible states.
Initial state
Target state2
Target state1

4. Generate and Test Method
Take a state
Generate next states by applying relevant rules
(not all rules are applicable for a given state!)
Test to see if the goal state is reached.
If yes - stop
  If no - add the generated states into a stack/queue (do not add if the state has already been generated) and repeat the procedure.
To get the solution: Record the paths

5. Search Methods Breadth-first vs depth-first search
Exhaustive search (brute force) vs informative (constraint-based, heuristic) search
Backtracking

6. Backtracking
rejecting the currently reached state as a dead-end state,
going back to some previous level in the state-space tree/graph
proceeding with the exploration of other paths toward the target state
Backtracking occurs in depth-first search

7. Example
Replace the letters with distinct digits such that the addition is correct
Decide on:
State representation
Operators
Constraints
Initial state
Target state
  LOAN
+ LOAN
LOAN
DEBT