input: def optimize_equation(equation: str) -> str:
      """
      Optimize an equation by reducing like terms. Each term in the equation is of the form 'variable count',
      where 'variable' is a single character and 'count' is an integer. The function combines like terms
      and returns the optimized equation.
  
      >>> optimize_equation('x + x + y + y + y')
      'x^2 + y^3'
      >>> optimize_equation('a + a + a + b')
      'a^3 + b^1'
      """
      from collections import defaultdict
  
      variables = defaultdict(int)
      for term in equation.split('+'):
          var = term.strip()
          variables[var] += 1
  
      new_equation = ""
      for var, count in variables.items():
          new_equation += (var + '^' + str(count)) + ' + '
      return new_equation[:-3]
output:     from collections import defaultdict
  
      variables = defaultdict(int)
      for term in equation.split('+'):
          var = term.strip()
          variables[var] += 1
  
      new_equation = ""
      for var, count in variables.items():
          new_equation += (var + '^' + str(count)) + ' + '
      return new_equation[:-3]