(Solved): The Manhattan distance heuristic is a commonly used method for estimating the distance between two ...

The Manhattan distance heuristic is a commonly used method for estimating the distance between two points in a gridlike environment, such as a puzzle or a maze. It is named after the grid-like street layout of Manhattan in New York City. In the context of a puzzle or a maze, the Manhattan distance heuristic is used to estimate the number of moves required to reach a goal state from a given initial state. Specifically, the Manhattan distance between two points is defined as the sum of the absolute differences of their coordinates along each axis. Assume the 8-puzzle problem where initial and goal states are defined as follows: Initial State Goal State Assume the cost function $$(g(x))$$ to be 1 for each move. answer the following two questions: 3- What is the Manhattan distance of the initial state shown above. 4- what is the value of cost function $$(f(x)=g(x)+h(x))$$ of the next node to be selected by using $$A^{?}$$ algorithm.