<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 {
public:
    map <pair <int, int>, int> mp;
    int N;
    int dfs(int parent, int child, vector <int> &sum, vector <int> &nodes, vector <vector <int> > &graph){
        
        int count = 0, temp, down = 0;
        vector <int> distances;
        for (auto node : graph[child]){
            if (parent == node) continue;
            temp = dfs(child, node, sum, nodes, graph) + nodes[node];
            distances.push_back(temp);
            count += temp;
            down += nodes[node];
            // cout << parent << " " << child << " " << temp << endl;
            // cout << node << " " << child << " " << temp << endl;
        }
        int curr = 0;
        for (int i=0; i<graph[child].size(); i++){
            if (graph[child][i] == parent) continue;
            mp[{child, graph[child][i]}] = count - distances[curr];
            curr++;
        }
        sum[child] = count;
        nodes[child] = down + 1;
        return count;
    }

    void dfs2(int parent, int child, vector <int> &ans, vector <int> &sum, vector <int> &nodes, vector <vector <int> > &graph, int pass){
        ans[child] = sum[child] + pass;
        // cout << parent << " " << child << " " << pass << endl;
        for (auto node : graph[child]){
            if (node == parent) continue;
            dfs2(child, node, ans, sum, nodes, graph, pass + mp[{child, node}] + N - nodes[node]);
        }
    }

    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        N = n;
        vector <vector <int> > graph(n+1);
        for (int i=0; i<n-1; i++){
            graph[edges[i][0]].push_back(edges[i][1]);
            graph[edges[i][1]].push_back(edges[i][0]);
        }
        vector <int> sum(n+1, 0), nodes(n+1, 0);
        dfs(-1, 0, sum, nodes, graph);
        vector <int> ans(n+1, 0);
        ans[0] = sum[0];
        // for (auto i : sum) cout << i << " ";
        // cout << endl;
        // for (auto i : nodes) cout << i << " ";
        // cout << endl;
        dfs2(-1, 0, ans, sum, nodes, graph, 0);
        ans.pop_back();
        return ans;
    }
};
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