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2313. Minimum Flips in Binary Tree to Get Result 👍

  • Time: $O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  int minimumFlips(TreeNode* root, bool result) {
    return dp(root, result);
  }

 private:
  struct PairHash {
    template <class T1, class T2>
    std::size_t operator()(const std::pair<T1, T2>& p) const {
      return std::hash<T1>{}(p.first) ^ std::hash<T2>{}(p.second);
    }
  };

  unordered_map<pair<TreeNode*, bool>, int, PairHash> mem;

  // Returns the minimum flips to make the subtree become the target.
  int dp(TreeNode* root, bool target) {
    const pair<TreeNode*, bool> key{root, target};
    if (const auto it = mem.find(key); it != mem.cend())
      return it->second;
    if (root->val == 0 || root->val == 1)  // the leaf
      return root->val == target ? 0 : 1;
    if (root->val == 5)  // NOT
      return dp(root->left == nullptr ? root->right : root->left, !target);

    vector<pair<int, int>> nextTargets;
    if (root->val == 2)  // OR
      nextTargets = target ? vector<pair<int, int>>{{0, 1}, {1, 0}, {1, 1}}
                           : vector<pair<int, int>>{{0, 0}};
    else if (root->val == 3)  // AND
      nextTargets = target ? vector<pair<int, int>>{{1, 1}}
                           : vector<pair<int, int>>{{0, 0}, {0, 1}, {1, 0}};
    else  // root.val == 4 (XOR)
      nextTargets = target ? vector<pair<int, int>>{{0, 1}, {1, 0}}
                           : vector<pair<int, int>>{{0, 0}, {1, 1}};

    int ans = INT_MAX;
    for (const auto& [leftTarget, rightTarget] : nextTargets)
      ans = min(ans, dp(root->left, leftTarget) + dp(root->right, rightTarget));
    return mem[key] = ans;
  }
};

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class Solution:
  def minimumFlips(self, root: TreeNode | None, result: bool) -> int:
    @functools.lru_cache(None)
    def dp(root: TreeNode | None, target: bool) -> int:
      """Returns the minimum flips to make the subtree root become target."""
      if root.val in (0, 1):  # the leaf
        return 0 if root.val == target else 1
      if root.val == 5:  # NOT
        return dp(root.left or root.right, not target)
      if root.val == 2:  # OR
        nextTargets = [(0, 1), (1, 0), (1, 1)] if target else [[0, 0]]
      elif root.val == 3:  # AND
        nextTargets = [(1, 1)] if target else [(0, 0), (0, 1), (1, 0)]
      else:  # root.val == 4 XOR
        nextTargets = [(0, 1), (1, 0)] if target else [(0, 0), (1, 1)]
      return min(dp(root.left, leftTarget) + dp(root.right, rightTarget)
                 for leftTarget, rightTarget in nextTargets)

    return dp(root, result)