Dynamic Programming Approach

The time complexity issue for our problem can be reduced to an extent if we use the dynamic programming approach. It breaks down this complex, large problem into smaller subproblems that can be solved optimally.

For this problem, we will use the bottom-up dynamic programming approach (through tabulation). This approach requires us to initialize a 2D grid so that we can store the result of each subproblem and reference it later in constant time. This ensures that similar subproblems are not recomputed.