SDE - 1

You are given a matrix 'MAT' with ‘N’ rows and ‘N’ columns, and an ant is initially sitting on a coordinate given to you. The ant moves in an interesting way. If the ith row and jth column value are 1, it rotates 90 degrees in the right direction and moves 1 step forward. If the value at the ith row and jth column are 0, it rotates 90 degrees in the left direction and moves 1 step forward.

Your task is to find the final coordinates of the ant.

Note:

The ant initially faces toward the east side. Every time an ant moves from a block, it inverts it, i.e., changes 0 to 1 and 1 to 0.

If the ant exits the matrix just return -1,-1.

For example,

If ‘N’ = 2    
mat[2][2] = {{1, 1},
             {0, 0}}
startingRow = 0 , startingColumn = 0
moves = 1
The ant is initially facing the east side, it will take a right turn and move 1 stop in the south.    
The output will be 1 0.

You have been given a square chessboard of size ‘N x N’. The position coordinates of the Knight and the position coordinates of the target are also given.

Your task is to find out the minimum steps a Knight will take to reach the target position.

Example:

knightPosition: {3,4}
targetPosition: {2,1}

The knight can move from position (3,4) to positions (1,3), (2,2) and (4,2). Position (4,2) is selected and the ‘stepCount’ becomes 1. From position (4,2), the knight can directly jump to the position (2,1) which is the target point and ‘stepCount’ becomes 2 which is the final answer. 

Note:

1. The coordinates are 1 indexed. So, the bottom left square is (1,1) and the top right square is (N, N).

2. The knight can make 8 possible moves as given in figure 1.

3. A Knight moves 2 squares in one direction and 1 square in the perpendicular direction (or vice-versa).

Bob lives with his wife in a city named Berland. Bob is a good husband, so he goes out with his wife every Friday to ‘Arcade’ mall.

‘Arcade’ is a very famous mall in Berland. It has a very unique transportation method between shops. Since the shops in the mall are laying in a straight line, you can jump on a very advanced trampoline from the shop i, and land in any shop between (i) to (i + Arr[i]), where Arr[i] is a constant given for each shop.

There are N shops in the mall, numbered from 0 to N-1. Bob's wife starts her shopping journey from shop 0 and ends it in shop N-1. As the mall is very crowded on Fridays, unfortunately, Bob gets lost from his wife. So he wants to know, what is the minimum number of trampoline jumps from shop 0 he has to make in order to reach shop N-1 and see his wife again. If it is impossible to reach the last shop, return -1.

How to design Splitwise?