Question

Consider a maze representation in which a maze is represented in a grid where each location in the grid had possible outgoing paths. Say that a maze is constructed correctly if (1) there is one path from the start to the finish, (2) the entire maze is reachable from the start, and (3) there are no cycles. Describe an algorithm that takes in an N x M maze represented in a grid and outputs true if the maze is constructed correctly and false otherwise. Analyze the runtime of the algorithm.

Answer 1

Algorithm that takes in an N×M maze represented in a grid is given as following types--

We will perform the depth first search (DFS). now ,We will start with the start point. As
we go on visiting the grid cells .l,after marked as visited we will be putting them in stack .

When we stuck, then we will keep on poping the grid cells from the
stack .and we will repeat same activity after looking all available options.

In the case if we get to the finish at
any point we can stop the process at that time.

In the worst case we have to visit all the cells, so the complexity of the
algorithm will be O(n) ,here it is assumed that we will not visit the visited node again except while
backtracking.If there is a path , we will definitly get that and in the case when the stack
becomes empty, it means there is no solutuon.

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