Quality Testing Intern

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).

You are given a sorted array of ‘N’ distinct integers that are in the Arithmetic Progression sequence except for one element which is missing from the sequence. You have to find that missing number from the given sequence.

Note:

1. A sequence [arr0, arr1,…, arr(n-1)] is called an Arithmetic progression if for each 'i' ( 0 ≤ i < n - 1) the value arr[i+1] − arr[i] is the same. 
2. There is exactly one missing number in the given sequence.
3. All the numbers present in the sequence are distinct.
4. It is the guarantee that the first and last elements of the sequence are not missing elements.

Follow Up

The overall run time complexity should be O(log(N)).

There are 25 horses. We are allowed to conduct multiple races among the horses and based on the result, we need to find the fastest 5 horses among them. Find what is the minimum number of races to be organized to find the required result.

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