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📗 (Fall 2018 Midterm Q1) A search tree has levels (the root is at level 0), and every internal node has children. Suppose there is no goal node. How many goal checks will depth first search perform? Include the initial node (the root).
📗 Note: we "goal check" every time we expand a node (i.e. not when putting them into the queue or stack).
📗 Hint: a tree with only the root has 0 level, and a decision stump has 1 level.
📗 Answer: .
📗 (Fall 2018 Midterm Q2) Let the search space be integers. Each state \(n\) has successors . Write down the shortest path (i.e. the sequence of states) from the initial state 1 to the goal state .
📗 Answer: .
📗 (Fall 2018 Midterm Q3) Consider a 3-puzzle where, like in the usual 8-puzzle game, a tile can only move to an adjacent empty space. Tiles cannot move diagonally. Which of the following initial states can reach the goal state (0 means "no tile")?
📗 Choices:
📗 (Fall 2018 Midterm Q4) Consider Depth First Search on a tree, where the nodes are denoted by numbers. Write down the sequence depth first search visited in the order they are expanded (i.e. expansion path). 0 is the initial state and is the goal state.
📗 (Fall 2018 Midterm Q4) Consider Iterative Deepening Search on a tree, where the nodes are denoted by numbers. Iterative deepening search visited the following sequence of nodes (expansion path): . Reconstruct one possible tree. 0 is the initial state and is the goal state. You must include all nodes from 0 to .
📗 Answer:
📗 Note: to use the eraser, drag it from one node to another to remove the (directed) edge in between. This answer cannot be saved and loaded using the "download" and "load" buttons at the bottom of the page.
📗 (Fall 2017 Final Q24) Consider n + 1 = + 1 states. The initial state is 1, the goal state is n. State 0 is a dead-end state with no successors. For each non-0 state i, it has two successors: i + 1 and 0. There is no cycle check nor CLOSED list (this means we may expand (or goal-check) the same nodes many times, because we do not keep track of which nodes are checked previously). How many goal-checks will be performed by Breadth First Search? Break ties by expanding the node with the smaller index first.
📗 Answer: .
📗 (Fall 2017 Final Q10) Consider a search graph which is a tree, and each internal node has children. The only goal node is at depth (root is depth 0). How many total goal-checks will be performed by Iterative Deepening Search in the luckiest case (i.e. the smallest number of goal-checks)? If a node is checked multiple times you should count that multiple times.
📗 Answer: .
📗 (Fall 2016 Final Q2) Recall in uniform-cost search, each node has a path-cost from the initial node (sum of edge costs along the path), and the search expands the least path-cost node first. Consider a search graph with \(n\) = nodes: \(1, 2, ..., n\). For all \(1 \leq i < j \leq n\), there is a directed edge from \(i\) to \(j\) with an edge cost . The initial node is 1, and the goal node is \(n\). How many (unique) goal-checks (the same nodes expanded twice is counted only once) with uniform-cost search perform? Break ties by expanding the node with the smaller index first.
📗 Answer: .
📗 On the PathFinding page: Link and try to "take two minutes to design a maze that takes one minute to solve" (not literally, and no need to do anything crazy). Try different search algorithms. Post a screen shot on Piazza.
📗 The number of operations used with A* (you can find the information on the bottom left corner of page): and I have participated in the discussion on Piazza.
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📗 Answer: .
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