<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 {
vector<int>tree[30001];
int sub[30001];
int subdis[30001];
vector<int>ans;
void dfs(int src,int par){
    int ans=0;
    int ansdis=0;
    for(auto &c:tree[src]){
        if(c!=par)dfs(c,src);

    }
    for(auto &c:tree[src]){
        if(par!=c){
            int num=sub[c];
            int dis=subdis[c];
            ansdis+=dis+num;
            ans+=num;
        }
    }
    sub[src]=(ans+1);
    subdis[src]=ansdis;
    return;


}
void solve(int src,int par,int parAns){
    if(par!=-1)
    ans[src]=parAns+sub[0]-sub[src];
    else ans[src]=0;
    // cout<<src<<" N "<<parAns<<endl;
    vector<int>pre,suff;
    for(auto &c:tree[src]){
        if(c!=par){
            pre.push_back(subdis[c]+sub[c]);
            suff.push_back(subdis[c]+sub[c]);
            // cout<<c<<' '<<subdis[c]<<' '<<sub[c]<<endl;;

        }
    }
    int size=(int)(pre.size());
    // cout<<size<<endl;
    for(int i=1;i<(int)pre.size();i++){
        pre[i]=pre[i]+pre[i-1];
        // cout<<pre[i]<<' ';
    }
    // cout<<endl;
    for(int i=(int)pre.size()-2;i>=0;i--){
        suff[i]=suff[i]+suff[i+1];
    }
    int c_no=0;
    for(auto &c:tree[src]){
        if(c!=par){
            int lc=((c_no==0)?0:pre[c_no-1]);
            int rc=((c_no==((int)pre.size()-1))?0:suff[c_no+1]);
            // cout<<lc<<' '<<rc<<' '<<c<<endl;;
            // cout<<src<<' '<<c<<' '<<ans[src]+lc+rc<<endl;
            solve(c,src,ans[src]+lc+rc);
            c_no++;
        }
    }
    // if(src==3)cout<<ans[src]<<endl;
    ans[src]+=((size==0)?0:suff[0]);
}

public:
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        memset(sub,0,sizeof(sub));
        memset(subdis,0,sizeof(subdis));
        for(auto &edge:edges){
            int u=edge[0];
            int v=edge[1];
            tree[u].push_back(v);
            tree[v].push_back(u);
        }
        dfs(0,-1);
        // for(int i=0;i<n;i++){
        //     cout<<sub[i]<<' '<<subdis[i]<<endl;
        // }
        ans.resize(n,0);
        solve(0,-1,0);
        return ans;

    }
};
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