Given integers i, j, k and n where (i, j) is the initial position of the Knight on a n * n chessboard, the task is to find the number of positions the Knight can move to in exactly k moves.
Input: i = 5, j = 5, k = 1, n = 10
Input: i = 0, j = 0, k = 2, n = 10
The knight can see total 10 different positions in 2nd move.
Approach: Use a recursive approach to solve the problem.
First find all the possible positions where the knight can move to so if the initial position is i, j. Get to all valid locations in single move and recursively find all the possible positions where knight can move to in k – 1 steps from there. The base case of this recursion is when k == 0 (no move to make) then we will mark the position of the chessboard as visited if it is unmarked and increase the count. Finally, display the count .
Below is the implementation of the above approach: