How do you solve Distribute Coins in Binary Tree on LeetCode?

Distribute Coins in Binary Tree (LeetCode #979) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The total number of coins is equal to the number of nodes, ensuring that redistribution is always possible.

What is the time complexity of Distribute Coins in Binary Tree?

The optimal solution for Distribute Coins in Binary Tree runs in O(n) time and uses O(n) space. The complexity is O(n) because we visit each node exactly once during the DFS traversal.

What is the brute force solution for Distribute Coins in Binary Tree?

The brute force approach for Distribute Coins in Binary Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking every possible way to move coins between nodes until each node has exactly one coin. This is inefficient as it requires multiple passes through the tree. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Distribute Coins in Binary Tree?

Distribute Coins in Binary Tree uses the following concepts: Tree, Depth-First Search, Binary Tree. The recommended patterns to study are: Depth-First Search, Tree Traversal.

What are the interview tips for Distribute Coins in Binary Tree?

Always clarify the problem constraints and edge cases before diving into the solution. Explain your thought process as you work through the problem, especially when transitioning from brute-force to optimal solutions. Practice DFS and tree traversal techniques, as they are commonly used in tree-related problems.

What are common mistakes when solving Distribute Coins in Binary Tree?

Failing to account for the net balance of coins at each node, leading to incorrect move counts. Not considering the tree structure when calculating moves, which can lead to overestimating the number of moves needed.

#979

Distribute Coins in Binary Tree

Medium

TreeDepth-First SearchBinary TreeDepth-First SearchTree Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal approach uses Depth-First Search (DFS) to calculate the number of coins that need to be moved up or down the tree, minimizing the total moves required.

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Algorithm

3 steps

1Step 1: Perform a DFS traversal of the tree.
2Step 2: For each node, calculate the excess or deficit of coins compared to 1 coin per node.
3Step 3: Accumulate the absolute values of excess/deficit to count the total moves.

solution.py19 lines

1# Full working Python code
2class TreeNode:
3    def __init__(self, val=0, left=None, right=None):
4        self.val = val
5        self.left = left
6        self.right = right
7
8class Solution:
9    def distributeCoins(self, root: TreeNode) -> int:
10        self.moves = 0
11        def dfs(node):
12            if not node:
13                return 0
14            left = dfs(node.left)
15            right = dfs(node.right)
16            self.moves += abs(left) + abs(right)
17            return node.val + left + right - 1
18        dfs(root)
19        return self.moves

ℹ

Complexity note: The complexity is O(n) because we visit each node exactly once during the DFS traversal.

1The total number of coins is equal to the number of nodes, ensuring that redistribution is always possible.
2DFS is a powerful technique for tree problems, allowing us to efficiently traverse and calculate values.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.