Solution 3 for Scaler Topics Fortnightly Contest - 6

This article is part of the Scaler Topics Fortnightly Contest - 6.

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Solution Approach

• We can use Dynamic Programming here to solve this problem, as we have reached some cell we only care about the last move used to reach this cell.
• There are 5 kinds of moves possible in the game so we can keep track of the moves by assigning them a value.
• Let DP[i][j][k] represent the number of ways to reach the destination if we start at (i, j) cell, with the last move being represented by k, from state (i, j, k) we can make all possible moves not equal to k.

Time Complexity: O(A × B × K × K) where K represents the possible number of moves which is 5 in our case.

Space Complexity:- O(A × B × K)

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