Final answer:
To reduce A* Search to UCS, set the heuristic function to zero, making the A* algorithm's path cost function equal to that of UCS. This change makes A* operate exactly as the UCS algorithm, which always considers the lowest path cost and is optimal but potentially slower without heuristic guidance.
Step-by-step explanation:
The A* Search algorithm (A*) can be reduced to Uniform Cost Search (UCS) by modifying the heuristic function it uses. In A*, the cost of a path to a node is estimated by a function f(n) which is a sum of two components: the exact cost of the path from the start node to the current node, denoted by g(n), and a heuristic estimate of the cost from n to the goal, denoted by h(n).
To reduce A* to UCS, you simply set the heuristic function h(n) to zero for all nodes. When h(n) = 0, the function f(n) just considers the path cost g(n), which is exactly how UCS operates. UCS is essentially A* search without any heuristic information guiding it towards the goal. It expands nodes based on the lowest path cost, ignoring any potential future costs.
This means that UCS is optimal as long as the cost between nodes represents an actual cost, such as distance or time, and you are seeking the cheapest solution. However, without a heuristic to guide it, UCS might be slower than A* in reaching the goal, as it does not prioritize paths that appear to lead closer to the goal.