<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:
    vector<int> ans;
    vector<int> childCount;

    void f(vector<vector<int>> &g, vector<vector<int>> &graph, int par, int cur) {
        for(auto x: graph[cur]) {
            if(x != par) {
                g[cur].push_back(x);
                childCount[cur]++;
                f(g, graph, cur, x);
                childCount[cur] += childCount[x];
            }
        }
    }

    vector<vector<int>> makeTree(int n, vector<vector<int>>& edges) {
        vector<vector<int>> graph(n);
        for(auto x: edges) {
            graph[x[1]].push_back(x[0]);
            graph[x[0]].push_back(x[1]);
        }
        vector<vector<int>> g(n);
        f(g, graph, -1, 0);
        return g;
    }

    void initf(vector<vector<int>> &graph, int cur) {
        if(!childCount[cur]) {
            ans[cur] = 0;
        }

        int sum = 0;
        for(auto x : graph[cur]) {
            initf(graph, x);
            sum += ans[x];
            sum += 1 + childCount[x];
        }
        ans[cur] = sum;
    }

//TODO
    void initl(vector<vector<int>> &graph, int cur, int carry) {
        ans[cur] += carry;  //carry = curAns - xAns - 2ChildX - 2 + n
        int nextCarry = ans[cur] + childCount.back() - 2;   //ans[cur] + n - 2
        for(auto x: graph[cur]) {
            int temp = nextCarry - ans[x] - 2 * childCount[x];
            cout<<endl<<cur<<" "<<temp;
            initl(graph, x, temp);
        }
    }

    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        ans = vector<int> (n, 0);
        childCount = vector<int> (n+1, 0);
        childCount.back() = n;
        vector<vector<int>> graph = makeTree(n, edges);

        initf(graph, 0);
        for(auto x : graph) {
            for(auto y : x) {
                cout<<y<<" ";
            }
            cout<<endl;
        }
        cout<<endl;
        for(auto x : childCount) {
            cout<<x<<" ";
        }
        cout<<endl;
        for(auto x : ans) {
            cout<<x<<" ";
        }

        initl(graph, 0, 0);
        cout<<endl;
        for(auto x : childCount) {
            cout<<x<<" ";
        }
        cout<<endl;
        for(auto x : ans) {
            cout<<x<<" ";
        }

        return ans;
    }
};
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