Is Minimum Flips in Binary Tree to Get Result easy or hard?

Minimum Flips in Binary Tree to Get Result is classified as Hard. The difficulty comes from modeling the boolean operators correctly and designing a tree DP that tracks both possible evaluation states. Once the DP state is defined, the implementation becomes a structured DFS with operator-specific case analysis.

Minimum Flips in Binary Tree to Get Result Python/Java solution

Implement a DFS that returns a pair of values: flips_to_zero and flips_to_one for each node. Leaf nodes return costs based on whether their value matches the target. Internal nodes combine child results using operator rules for AND, OR, XOR, and NOT. The same logic works in Python, Java, C++, Go, and TypeScript.

How to solve Minimum Flips in Binary Tree to Get Result in O(n)?

Run a postorder DFS and maintain two DP values for each node: the minimum flips needed for the subtree to evaluate to 0 and to 1. For leaves, the cost depends on whether the value matches the target. For internal nodes, combine children using operator logic (e.g., OR requires at least one child equal to 1). Each node performs constant work, leading to O(n) time.

What is the best approach for Minimum Flips in Binary Tree to Get Result?

Tree dynamic programming with a postorder DFS is the most efficient approach. For each node, compute the minimum flips needed for the subtree to evaluate to 0 and 1. Combine child states using operator-specific rules (AND, OR, XOR, NOT). This processes every node once for an overall O(n) time complexity.

Is Minimum Flips in Binary Tree to Get Result asked at Google/Amazon/Meta?

Boolean expression tree problems and tree dynamic programming patterns frequently appear in interviews at companies like Google, Amazon, and Meta. Variants involving expression evaluation, DP on trees, and minimizing operations are common in high-level system and algorithm interviews.

What data structure is used in Minimum Flips in Binary Tree to Get Result?

The core data structure is a binary tree representing a boolean expression. The algorithm uses depth-first search along with dynamic programming states stored per node, tracking the minimum flips required for the subtree to evaluate to both possible boolean outcomes.

What is the time complexity of Minimum Flips in Binary Tree to Get Result?

The optimal Tree DP solution runs in O(n) time where n is the number of nodes in the tree. Each node is visited exactly once during a DFS traversal, and only constant-time case analysis is performed per node. Space complexity is O(h) due to the recursion stack, where h is the tree height.

Description Hints 3 Solution Video 10:26

2313. Minimum Flips in Binary Tree to Get Result

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You are given the root of a binary tree with the following properties:

Leaf nodes have either the value 0 or 1, representing false and true respectively.
Non-leaf nodes have either the value 2, 3, 4, or 5, representing the boolean operations OR, AND, XOR, and NOT, respectively.

You are also given a boolean result, which is the desired result of the evaluation of the root node.

The evaluation of a node is as follows:

If the node is a leaf node, the evaluation is the value of the node, i.e. true or false.
Otherwise, evaluate the node's children and apply the boolean operation of its value with the children's evaluations.

In one operation, you can flip a leaf node, which causes a false node to become true, and a true node to become false.

Return the minimum number of operations that need to be performed such that the evaluation of root yields result. It can be shown that there is always a way to achieve result.

A leaf node is a node that has zero children.

Note: NOT nodes have either a left child or a right child, but other non-leaf nodes have both a left child and a right child.

Example 1:

Input: root = [3,5,4,2,null,1,1,1,0], result = true
Output: 2
Explanation:
It can be shown that a minimum of 2 nodes have to be flipped to make the root of the tree
evaluate to true. One way to achieve this is shown in the diagram above.

Example 2:

Input: root = [0], result = false
Output: 0
Explanation:
The root of the tree already evaluates to false, so 0 nodes have to be flipped.

Constraints:

The number of nodes in the tree is in the range [1, 10⁵].
0 <= Node.val <= 5
OR, AND, and XOR nodes have 2 children.
NOT nodes have 1 child.
Leaf nodes have a value of 0 or 1.
Non-leaf nodes have a value of 2, 3, 4, or 5.

Asked at 1 company

Google

Topics

Hints open one at a time

Hint 1

Try using tree DP to solve this problem.

Hint 2

Find the minimum operations to change each subtree to true and to false separately.

Hint 3

For nodes representing boolean operations, find the minimum operations by trying all combinations of values to which the child nodes can evaluate.

10:26

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