<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>

#define ll long long
class Solution {
public:

    pair<ll,ll> dfs(vector<vector<ll>>&g,ll idx, vector<ll>& leafs, map<pair<ll,ll>,pair<ll,ll> >& hmap, vector<ll>& vis){
        ll c = 0;
        vis[idx] = 1;
        ll dis = 0;
        ll num = 1;
        for(ll i=0; i<g[idx].size();i++){
            ll end = g[idx][i];
            if(vis[end]==0){
                c++;
                pair<ll,ll> p = dfs(g,end,leafs,hmap,vis);
                num += p.second;
                dis += p.first+ p.second;
                hmap[{idx,end}] = p;
            }
        }
        if(c==0){
            leafs.push_back(idx);
        }
        pair<ll,ll> req = {dis,num};
        return req;
    }

    void recur(vector<vector<ll>>&g,ll idx, vector<int>& dis, map<pair<ll,ll>,pair<ll,ll> >& hmap, vector<ll>& vis, ll curval, ll curnum){
        vis[idx] = 1;
        dis[idx] = curval+curnum;
        ll num = 1;
        ll childrenvals = 0;
        ll childrenum = 0;
        for(ll i=0; i<g[idx].size();i++){
            ll end = g[idx][i];
            if(vis[end]==0){
                pair<ll,ll> p = hmap[{idx,end}];
                childrenvals += p.second+p.first;
                childrenum += p.second;
            }
        }
        dis[idx] += childrenvals;
        // cout<<idx<<" "<<childrenvals<<" "<<childrenum<<"\n";
        // cout<<curval<<" "<<curnum<<"\n";
        // cout<<" --------------- \n";
        for(ll i=0; i<g[idx].size();i++){
            ll end = g[idx][i];
            if(vis[end]==0){
                pair<ll,ll> p = hmap[{idx,end}];
                // cout<<idx<<" "<<end<<" "<<p.first<<" "<<p.second<<"\n";
                ll leftsum = childrenvals - p.second-p.first;
                ll leftnum = childrenum - p.second+1;
                recur(g,end,dis,hmap,vis,leftsum+curval+curnum,leftnum+curnum);
            }
        }
        return;
    }

    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        vector<vector<ll> > g(n);
        for(ll i=0; i<edges.size();i++){
            ll a = edges[i][0];
            ll b = edges[i][1];
            g[a].push_back(b);
            g[b].push_back(a);
        }
        map<pair<ll,ll>,pair<ll,ll> > hmap;
        vector<ll> leafs;
        vector<ll> vis(n,0);
        dfs(g,0,leafs,hmap,vis);
        vector<int> dis(n,0);
        vector<ll> vis1(n,0);
        recur(g,0,dis,hmap,vis1,0,0);
        return dis;
    }
};
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