add distribute coins (TheAlgorithms#7975)

* add distribute coins

* updating DIRECTORY.md

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* fix review notes

* fix typehint

* fix type in TreeNode

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Author: 3 people

DIRECTORY.md

@@ -173,6 +173,7 @@
     * [Binary Tree Path Sum](data_structures/binary_tree/binary_tree_path_sum.py)
     * [Binary Tree Traversals](data_structures/binary_tree/binary_tree_traversals.py)
     * [Diff Views Of Binary Tree](data_structures/binary_tree/diff_views_of_binary_tree.py)
+    * [Distribute Coins](data_structures/binary_tree/distribute_coins.py)
     * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py)
     * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py)
     * [Is Bst](data_structures/binary_tree/is_bst.py)

data_structures/binary_tree/distribute_coins.py

@@ -0,0 +1,135 @@
+"""
+Author  : Alexander Pantyukhin
+Date    : November 7, 2022
+
+Task:
+You are given a tree root of a binary tree with n nodes, where each node has
+node.data coins. There are exactly n coins in 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:
+
+   3
+  / \
+ 0   0
+
+Result: 2
+
+Example 2:
+
+   0
+  / \
+ 3   0
+
+Result 3
+
+leetcode: https://leetcode.com/problems/distribute-coins-in-binary-tree/
+
+Implementation notes:
+User depth-first search approach.
+
+Let n is the number of nodes in tree
+Runtime: O(n)
+Space: O(1)
+"""
+
+from __future__ import annotations
+
+from collections import namedtuple
+from dataclasses import dataclass
+
+
+@dataclass
+class TreeNode:
+    data: int
+    left: TreeNode | None = None
+    right: TreeNode | None = None
+
+
+CoinsDistribResult = namedtuple("CoinsDistribResult", "moves excess")
+
+
+def distribute_coins(root: TreeNode | None) -> int:
+    """
+    >>> distribute_coins(TreeNode(3, TreeNode(0), TreeNode(0)))
+    2
+    >>> distribute_coins(TreeNode(0, TreeNode(3), TreeNode(0)))
+    3
+    >>> distribute_coins(TreeNode(0, TreeNode(0), TreeNode(3)))
+    3
+    >>> distribute_coins(None)
+    0
+    >>> distribute_coins(TreeNode(0, TreeNode(0), TreeNode(0)))
+    Traceback (most recent call last):
+     ...
+    ValueError: The nodes number should be same as the number of coins
+    >>> distribute_coins(TreeNode(0, TreeNode(1), TreeNode(1)))
+    Traceback (most recent call last):
+     ...
+    ValueError: The nodes number should be same as the number of coins
+    """
+
+    if root is None:
+        return 0
+
+    # Validation
+    def count_nodes(node: TreeNode | None) -> int:
+        """
+        >>> count_nodes(None):
+        0
+        """
+        if node is None:
+            return 0
+
+        return count_nodes(node.left) + count_nodes(node.right) + 1
+
+    def count_coins(node: TreeNode | None) -> int:
+        """
+        >>> count_coins(None):
+        0
+        """
+        if node is None:
+            return 0
+
+        return count_coins(node.left) + count_coins(node.right) + node.data
+
+    if count_nodes(root) != count_coins(root):
+        raise ValueError("The nodes number should be same as the number of coins")
+
+    # Main calculation
+    def get_distrib(node: TreeNode | None) -> CoinsDistribResult:
+        """
+        >>> get_distrib(None)
+        namedtuple("CoinsDistribResult", "0 2")
+        """
+
+        if node is None:
+            return CoinsDistribResult(0, 1)
+
+        left_distrib_moves, left_distrib_excess = get_distrib(node.left)
+        right_distrib_moves, right_distrib_excess = get_distrib(node.right)
+
+        coins_to_left = 1 - left_distrib_excess
+        coins_to_right = 1 - right_distrib_excess
+
+        result_moves = (
+            left_distrib_moves
+            + right_distrib_moves
+            + abs(coins_to_left)
+            + abs(coins_to_right)
+        )
+        result_excess = node.data - coins_to_left - coins_to_right
+
+        return CoinsDistribResult(result_moves, result_excess)
+
+    return get_distrib(root)[0]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()