679: Solution with step by step explanation
Intuition\n Describe your first thoughts on how to solve this problem. \n\n# Approach\n1. Define a helper function called "generate" that takes in two float val
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\n\n# Approach\n1. Define a helper function called "generate" that takes in two float values "a" and "b" and returns a list of float values that represent all possible arithmetic combinations of "a" and "b".\n2. Define another helper function called "dfs" that takes in a list of float values "nums" and returns a boolean value.\n3. In the "dfs" function, check if the length of the input list is equal to 1. If it is, return True if the absolute difference between the first element in the list and 24.0 is less than 0.001, else return False.\n4. Iterate through all possible pairs of indices in the input list using two nested loops.\n5. For each pair of indices, call the "generate" function to get a list of all possible arithmetic combinations of the values at the two indices.\n6. For each value in the list generated in step 6, create a new list called "nextRound" that contains the value from step 6 and all the other values in the input list except the ones at the indices used in step 5.\n7. Recursively call the "dfs" function with the "nextRound" list as the input.\n8. If the recursive call in step 8 returns True, return True in the current call, else continue with the loop in step 5.\n9. If none of the recursive calls in step 8 returned True, return False after the loops in step 5 have completed.\n10. In the "judgePoint24" function, call the "dfs" function with the input list "nums" and return the result.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\n\n# Code\n```\nclass Solution:\n  def judgePoint24(self, nums: List[int]) -> bool:\n    def generate(a: float, b: float) -> List[float]:\n      return [a * b,\n              math.inf if b == 0 else a / b,\n              math.inf if a == 0 else b / a,\n              a + b, a - b, b - a]\n\n    def dfs(nums: List[float]) -> bool:\n      if len(nums) == 1:\n        return abs(nums[0] - 24.0) < 0.001\n\n      for i in range(len(nums)):\n        for j in range(i + 1, len(nums)):\n          for num in generate(nums[i], nums[j]):\n            nextRound = [num]\n            for k in range(len(nums)):\n              if k == i or k == j:\n                continue\n              nextRound.append(nums[k])\n            if dfs(nextRound):\n              return True\n\n      return False\n\n    return dfs(nums)\n```
['Array', 'Math', 'Backtracking', 'Python', 'Python3']