<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>

#include <vector>

#define ll long long
#define vll vector<ll>
#define pb push_back
#define f(i,a,b) for(ll i=a; i<b; i++)

using namespace std;

class Solution {
public:
    vector<int> ans_hai;
    vector<ll> count_node;
    vector<ll> ans_node;
    vector<ll> sub_tree_ans;

    void preprocessing(vector<vector<ll>>& adj, vector<bool>& vis, ll node) {
        vis[node] = true;
        ll node_ans = 0;
        ll node_cnt = 1;
        for (auto &x : adj[node]) {
            if (!vis[x]) {
                preprocessing(adj, vis, x);
                node_cnt += count_node[x];
                node_ans += sub_tree_ans[x] + count_node[x];
            }
        }
        ans_node[node] = node_ans;
        count_node[node] = node_cnt;
        sub_tree_ans[node] = node_ans;
    }

    void final_ans(vector<vector<ll>>& adj, vector<bool>& vis, ll node, ll totalnodes, ll partial_ans) {
        vis[node] = true;
        ans_node[node] = partial_ans + sub_tree_ans[node] + (totalnodes - count_node[node]);
        for (auto x : adj[node]) {
            if (!vis[x]) {
                ll partial_ans_cntr_curr_node = ans_node[node] - (sub_tree_ans[x] + count_node[x]);
                final_ans(adj, vis, x, totalnodes, partial_ans_cntr_curr_node);
            }
        }
    }

    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        vector<vector<ll>> adj(n + 1);
        for (auto edge : edges) {
            adj[edge[0]].push_back(edge[1]);
            adj[edge[1]].push_back(edge[0]);
        }

        count_node.resize(n + 1);
        ans_node.resize(n + 1);
        sub_tree_ans.resize(n + 1);

        vector<bool> vis(n + 1, false);
        preprocessing(adj, vis, 1);
        fill(vis.begin(), vis.end(), false);
        final_ans(adj, vis, 1, n, 0);

        for (int i = 0; i < n; ++i) {
            ans_hai.push_back(static_cast<int>(ans_node[i]));
        }
        
        return ans_hai;
    }
};
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