input: 
  def knapSack(W: int, wt: List[int], val: List[int], n: int) -> int:
      """ Solve the knapsack problem using dynamic programming.
      >>> knapSack(50, [10, 20, 30], [60, 100, 120], 3)
      220
      """
      if n == 0 or W == 0:
          return 0
      if wt[n-1] > W:
          return knapSack(W, wt, val, n-1)
      else:
          return max(val[n-1] + knapSack(W-wt[n-1], wt, val, n-1),
                     knapSack(W, wt, val, n-1))
  
output:     
      dp = [[0 for _ in range(W + 1)] for _ in range(n + 1)]
      for i in range(n + 1):
          for w in range(W + 1):
              if i == 0 or w == 0:
                  dp[i][w] = 0
              elif wt[i-1] <= w:
                  dp[i][w] = max(val[i-1] + dp[i-1][w-wt[i-1]], dp[i-1][w])
              else:
                  dp[i][w] = dp[i-1][w]
      return dp[n][W]
  