input: def compute_edit_distance(string1: str, string2: str) -> int:
      """Compute the edit distance between two strings.
      The edit distance is the minimum number of operations (insertions, deletions, or substitutions)
      required to change one string into the other.
      >>> compute_edit_distance("kitten", "sitting")
      3
      >>> compute_edit_distance("Saturday", "Sunday")
      3
      """
      m, n = len(string1), len(string2)
      dp = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
  
      for i in range(m + 1):
          dp[i][0] = i
  
      for j in range(n + 1):
          dp[0][j] = j
  
      for i in range(1, m + 1):
          for j in range(1, n + 1):
              if string1[i - 1] == string2[j - 1]:
                  dp[i][j] = dp[i - 1][j - 1]
              else:
                  dp[i][j] = 1 + min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1])
  
      return dp[m][n]
output:     m, n = len(string1), len(string2)
      dp = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
  
      for i in range(m + 1):
          dp[i][0] = i
  
      for j in range(n + 1):
          dp[0][j] = j
  
      for i in range(1, m + 1):
          for j in range(1, n + 1):
              if string1[i - 1] == string2[j - 1]:
                  dp[i][j] = dp[i - 1][j - 1]
              else:
                  dp[i][j] = 1 + min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1])
  
      return dp[m][n]