# https://leetcode.com/problems/distribute-coins-in-binary-tree/
"""
You are given the root of a binary tree with n nodes where each node in the tree has node.val coins. There are n coins in total throughout the whole tree.

In one move, we may choose two adjacent nodes and move one coin from one node to another. A move may be from parent to child, or from child to parent.

Return the minimum number of moves required to make every node have exactly one coin.

Example 1:
Input: root = [3,0,0]
Output: 2
Explanation: From the root of the tree, we move one coin to its left child, and one coin to its right child.

Example 2:
Input: root = [0,3,0]
Output: 3
Explanation: From the left child of the root, we move two coins to the root [taking two moves]. Then, we move one coin from the root of the tree to the right child.

Constraints:
The number of nodes in the tree is n.
1 <= n <= 100
0 <= Node.val <= n
The sum of all Node.val is n.
"""
from typing import Optional

from puzzles.utils import TreeNode


def distribute_coins(root: Optional[TreeNode]) -> int:
    steps = 0

    def dfs(root):
        nonlocal steps
        if not root:
            return 0
        l = dfs(root.left)
        r = dfs(root.right)
        steps = steps + abs(l) + abs(r)
        return root.val + l + r - 1

    dfs(root)
    return steps
