<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>

#pragma GCC optimize("O3", "unroll-loops")
static const int _ = []() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    return 0;
}();

class Solution {
public:
    //keeps track of which nodes each node is directly connected to
    map<int, vector<int>> edgeMap;
    int global_n;
    //distances will keep track of the distance between the current node and all other nodes
    // we populate each level of the tree by adding 1 with each dfs call
    // we also need to keep track of how many child nodes each node has
    void dfs(vector<int>& distances, int parent_node, int current_node, vector<int>& child_nodes){
        child_nodes[current_node] = 1;
        for(auto node: edgeMap[current_node]){
            if (node == parent_node) {continue;}
            distances[node] = distances[current_node]+1;
            dfs(distances, current_node, node, child_nodes);
            //the number of child nodes the current node has is equal to the sum of childs 
            child_nodes[current_node]+= child_nodes[node];
        }
    }

    void dfs2(int parent_node, int current_node, vector<int>& child_nodes, vector<int>& answer, int cur_sum){
        answer[current_node] = cur_sum;
        for(auto node: edgeMap[current_node]){
            if (node == parent_node) {continue;}
            // get the current node sum as the parent node sum
            // subtract distance of 1 for each child node of current node
            // add distance of 1 for all other nodes that aren't a child node
            int new_cur_sum = cur_sum - child_nodes[node] + (global_n - child_nodes[node]);
            dfs2(current_node, node, child_nodes, answer, new_cur_sum);
        }
    }

    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        global_n = n;
        for (auto edge: edges){
            if (edgeMap.find(edge[0]) == edgeMap.end()){
                vector<int> newvec = {edge[1]};
                edgeMap[edge[0]] = newvec;
            }
            else{
                edgeMap[edge[0]].push_back(edge[1]);
            }
            if (edgeMap.find(edge[1]) == edgeMap.end()){
                vector<int> newvec = {edge[0]};
                edgeMap[edge[1]] = newvec;
            }
            else{
                edgeMap[edge[1]].push_back(edge[0]);
            }

        }
        vector<int> answers(n,0), distances(n,0), child_nodes(n,0);
        dfs(distances, -1, 0, child_nodes);
        int sum_zero =accumulate(distances.begin(), distances.end(), 0);
        dfs2(-1,0,child_nodes, answers, sum_zero);
        return answers;
    }
};
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