input: from typing import Any
  
  def compare_heuristic_algorithms(
      data1: Any, data2: Any, algorithm1: Any, algorithm2: Any
  ) -> str:
      """ Compare the performance of two heuristic algorithms by evaluating the time
      taken to process the given input data.
      
      >>> compare_heuristic_algorithms(data1, data2, heuristics_algorithm1, heuristics_algorithm2)
      'Algorithm 2 is faster than algorithm 1'
      """
      import time
  
      start = time.time()
      result1 = algorithm1.run(data1)
      end = time.time()
      time1 = end - start
  
      start = time.time()
      result2 = algorithm2.run(data2)
      end = time.time()
      time2 = end - start
  
      if time1 < time2:
          return "Algorithm 1 is faster than algorithm 2"
      elif time2 < time1:
          return "Algorithm 2 is faster than algorithm 1"
      else:
          return "Both algorithms have the same performance time"
output:     import time
  
      start = time.time()
      result1 = algorithm1.run(data1)
      end = time.time()
      time1 = end - start
  
      start = time.time()
      result2 = algorithm2.run(data2)
      end = time.time()
      time2 = end - start
  
      if time1 < time2:
          return "Algorithm 1 is faster than algorithm 2"
      elif time2 < time1:
          return "Algorithm 2 is faster than algorithm 1"
      else:
          return "Both algorithms have the same performance time"