<p>There is an undirected connected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code> and <code>n - 1</code> edges.</p>

<p>You are given the integer <code>n</code> and the array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p>

<p>Return an array <code>answer</code> of length <code>n</code> where <code>answer[i]</code> is the sum of the distances between the <code>i<sup>th</sup></code> node in the tree and all other nodes.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist1.jpg" style="width: 304px; height: 224px;" />
<pre>
<strong>Input:</strong> n = 6, edges = [[0,1],[0,2],[2,3],[2,4],[2,5]]
<strong>Output:</strong> [8,12,6,10,10,10]
<strong>Explanation:</strong> The tree is shown above.
We can see that dist(0,1) + dist(0,2) + dist(0,3) + dist(0,4) + dist(0,5)
equals 1 + 1 + 2 + 2 + 2 = 8.
Hence, answer[0] = 8, and so on.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist2.jpg" style="width: 64px; height: 65px;" />
<pre>
<strong>Input:</strong> n = 1, edges = []
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist3.jpg" style="width: 144px; height: 145px;" />
<pre>
<strong>Input:</strong> n = 2, edges = [[1,0]]
<strong>Output:</strong> [1,1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>edges.length == n - 1</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>The given input represents a valid tree.</li>
</ul>

class Solution:
    def sumOfDistancesInTree(self, n: int, edges: List[List[int]]) -> List[int]:
        G = defaultdict(list)
        for edge in edges:
            u, v = edge
            G[u].append(v)
            G[v].append(u)
        tree = defaultdict(list)  # with root =0
        # tree[0] = []
        # tree[0]+=G[0]
        self.constructTree(G, tree)
        SIZE = {}
        SUM = {}
        self.calculateSize(tree, SIZE, 0)
        self.calculateSum(tree, SUM, SIZE, 0)
        self.calculateSumDistances(0, SIZE, SUM, tree)
        L = []
        for i in range(n):
            L.append(SUM[i])
        return L

    def calculateSumDistances(self, root, SIZE, SUM, tree):
        if root in tree:
            for child in tree[root]:
                    SUM[child] = SUM[root] + SIZE[root] - SIZE[child] - SIZE[child] - 1
                    SIZE[child] = SIZE[root]
                    self.calculateSumDistances(child, SIZE, SUM, tree)

    def constructTree(self, G, tree):
        queue = [0]
        visited = set()
        while len(queue) != 0:
            node = queue.pop(0)
            visited.add(node)
            for v in G[node]:
                if not v in visited:
                    tree[node].append(v)
                    queue.append(v)

    def calculateSize(self, tree, SIZE, root):
        nodeSize = 0
        if root in tree:
            for v in tree[root]:
                nodeSize += 1 + self.calculateSize(tree, SIZE, v)
        SIZE[root] = nodeSize
        return nodeSize

    def calculateSum(self, tree, SUM, SIZE, root):
        nodeSum = 0
        # Size[2] + SUM[2] + 1, 1 + SUM[0] + SIZE[0]
        if root in tree:
            for v in tree[root]:
                nodeSum = nodeSum + 1 + self.calculateSum(tree, SUM, SIZE, v) + SIZE[v]
        SUM[root] = nodeSum
        return nodeSum

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