Chapter 10: Algorithm Design Techniques

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Chapter 10 Algorithm Design Techniques
Mark Allen Weiss Data Structures and Algorithm
Analysis in Java

• Backtracking

Lydia Sinapova, Simpson College
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Backtracking

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

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The Idea
Problem solving search in a space of possible
states.
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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

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Search Methods

• Breadth-first vs depth-first search
• Exhaustive search (brute force) vs informative
  (constraint-based, heuristic) search
• Backtracking

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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

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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
LOAN ------- DEBT