SDE - Intern

The city of Ninjaland is analogous to the unweighted graph. The city has ‘N’ houses numbered from 1 to ‘N’ respectively and are connected by M bidirectional roads. If a road is connecting two houses ‘X’ and ‘Y’ which means you can go from ‘X’ to ‘Y’ or ‘Y’ to ‘X’. It is guaranteed that you can reach any house from any other house via some combination of roads. Two houses are directly connected by at max one road.

A path between house ‘S’ to house ‘T’ is defined as a sequence of vertices from ‘S’ to ‘T’. Where starting house is ‘S’ and the ending house is ‘T’ and there is a road connecting two consecutive houses. Basically, the path looks like this: (S , h1 , h2 , h3 , ... T). you have to find the shortest path from ‘S’ to ‘T’.

For example

In the below map of Ninjaland let say you want to go from S=1 to T=8, the shortest path is (1, 3, 8). You can also go from S=1 to T=8  via (1, 2, 5, 8)  or (1, 4, 6, 7, 8) but these paths are not shortest.

You are given a matrix having ‘N’ rows and ‘M’ columns. Each cell of the matrix is either ‘X’ or ‘O’. You need to flip all those regions of ‘O’ which are surrounded by ‘X’ i.e. you need to change all ‘O’s which are present in the region to ‘X’.

Note

1. Surrounded regions shouldn’t be on the border, which means that any 'O' on the border of the matrix is not flipped to 'X'. 
2. Any ‘O’ or group of connected ‘O’ are said to be surrounded by ‘X’ when all cells touching the boundary of the group of ‘O’ must contain ‘X’.

For example