🌐 Implicit vs. Explicit State Spaces
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# 🌐 Implicit vs. Explicit State Spaces ## 1.
🌐 Implicit vs. Explicit State Spaces
1. 🎯 Learning Objectives
- Distinguish implicit (generated) from explicit (stored) graphs
- Explain why most AI problems use implicit representation
- Design MoveGen for implicit graph generation
2. 📖 Core Content
3.1 Explicit Graphs
Entire graph stored in memory. Adjacency list or matrix. Pros: O(1) neighbor lookup, easy random access. Cons: O(|V|+|E|) memory. Infeasible for large spaces. Use when: Graph is small, static, and known upfront (road networks).
3.2 Implicit Graphs
States generated on-the-fly via MoveGen. No explicit storage of entire graph. Pros: O(bd) memory (only frontier). Works for infinite or huge spaces. Cons: Repeated state generation possible without memoization. Use when: State space is large, dynamic, or infinite (chess, 8-puzzle, planning).
3.3 Hybrid Approach
Cache generated states in a transposition table (hash table) for faster re-expansion. Used in game engines (chess) where same positions arise via different move orders.
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