Distribute Coins in Binary Tree

Medium

Solution

A tricky problem that can be solved with single recursion.

Calculate numbers of expected remaining coins for each left and right subtree recursively.
Calculate expected movements for the current subtree by abs(leftCoins) + abs(rightCoins). This means that
- If the number of remaining coins is negative, the amount of coins should be moved to the subtree.
- If it is positive, the amount of coins should be drained from the subtree.
Return the number of expected remaining coins while discounting 1 coin for the current node by leftCoins + rightCoins + this.val - 1

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.