Uniform-cost search

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Uniform-cost search (UCS) is an uninformed search strategy that is used to find the lowest-cost path from a starting state to a goal state. It is similar to breadth-first search (BFS), but with the added consideration of the cost of each action taken.

In UCS, each node in the search tree is associated with a cost, which is the sum of the costs of the actions taken to reach that node from the starting state. The cost of each action is defined by a cost function that is provided as part of the problem definition. The cost function assigns a non-negative cost to each action, and the cost of a path is the sum of the costs of the actions in that path.

UCS explores the search tree by maintaining a priority queue of the nodes to be expanded. The priority of a node is its total cost from the starting state. UCS always expands the node with the lowest total cost first. If there are multiple nodes with the same total cost, UCS breaks the tie arbitrarily.

UCS is guaranteed to find the lowest-cost path to the goal state, as long as the cost function satisfies certain conditions, such as the non-negativity and monotonicity of the cost of each action. However, UCS can be very slow if the cost of each action is large or if there are many possible paths to the goal state. In addition, UCS requires a lot of memory to store the priority queue, which can be a limitation in large search spaces.

One variation of UCS is A* search, which combines UCS with a heuristic function that estimates the cost of reaching the goal state from each node. A* search is usually faster than UCS and can be more memory-efficient, but it requires a good heuristic function that provides accurate estimates of the cost of reaching the goal state.

Overall, UCS is a powerful search algorithm that is widely used in many AI applications, including route planning, logistics, and scheduling. Its ability to find the lowest-cost path makes it suitable for problems where the cost of each action is important, but its memory and time requirements can be a limitation in some contexts

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