SDE - 1

You are playing a board game where you die when your hp (health points) becomes 0 or negative. Now you start with some initial hp, and start moving in the board starting from the top-left corner. You have to reach the bottom right corner of the board by only moving right and down. Whenever you arrive on a cell in the board your hp may increase or decrease by the amount written on the cell. If the cell has a positive value it means your hp increases, if it has a negative value it means your hp decreases. You need to return the minimum initial health required so that you can reach the rightmost corner.

For Example:

In the example below, if we follow the path shown in the figure, then the minimum initial hp required will be 3.

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).

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