input: from typing import List, Tuple
  
  def knapSack(W: int, wt: List[int], val: List[int], n: int) -> int:
      """
      Find the optimal solution to solve a knapsack problem using dynamic programming.
      >>> knapSack(50, [10, 20, 30], [60, 100, 120], 3)
      220
      >>> knapSack(30, [10, 20], [60, 100], 2)
      160
      """
  
      # Base Case 
      if n == 0 or W == 0 : 
          return 0
    
      # If weight of the nth item is more 
      # than Knapsack capacity W, then 
      # this item cannot be included in the optimal solution 
      if (wt[n-1] > W): 
          return knapSack(W, wt, val, n-1) 
    
      # return the maximum of two cases: 
      # (1) nth item included 
      # (2) not included 
      else: 
          return max(val[n-1] + knapSack(W-wt[n-1], wt, val, n-1), 
                      knapSack(W, wt, val, n-1))
output:     
      # Initialize a table to store results of subproblems 
      K = [[0 for x in range(W + 1)] for x in range(n + 1)] 
    
      # Build table K[][] in bottom up manner 
      for i in range(n + 1): 
          for w in range(W + 1): 
              if i == 0 or w == 0: 
                  K[i][w] = 0
              elif wt[i-1] <= w: 
                  K[i][w] = max(val[i-1] + K[i-1][w-wt[i-1]],  K[i-1][w]) 
              else: 
                  K[i][w] = K[i-1][w] 
    
      return K[n][W]
  