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Depth-First Search (DFS) Properties

Depth-First Search (DFS) Properties. Non-optimal solution path Incomplete unless there is a depth bound Exponential time Linear space. BFS. Comments on Iterative Deepening Search. Complexity Space complexity = O( bd ) Time Complexity

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Depth-First Search (DFS) Properties

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  1. Depth-First Search (DFS) Properties • Non-optimal solution path • Incomplete unless there is a depth bound • Exponential time • Linear space

  2. BFS

  3. Comments on Iterative Deepening Search • Complexity • Space complexity = O(bd) • Time Complexity • = O(bd) (i.e., asymptotically the same as BFS or DFS in the the worst case) • The overhead in repeated searching of the same subtrees is small relative to the overall time • e.g., for b=10, only takes about 11% more time than DFS • A useful practical method • combines • guarantee of finding an optimal solution if one exists (as in BFS) • space efficiency, O(bd) of DFS • But still has problems with loops like DFS

  4. Time requirements for depth-first iterative deepening on binary tree Nodes at each level 1 2 4 8 16 32 64 128 Nodes searched by DFS 1 +2 = 3 +4 = 7 +8 = 15 +16 = 31 +32 = 63 +64 = 127 +128 = 255 Nodes searched by iterative DFS 1 +3 = 4 +7 = 11 +15 = 26 +31 = 57 +63 = 120 +127 = 247 +255 = 502

  5. Homework

  6. Example

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