Change DP (ah ah ah)

Portal

Ideas ：

  *  The first is the conventional dfs Find the sum of the distance from the root node to all other points . If so x Root node ,y by x Immediate child nodes of , that y Subtree pair x The contribution of dis[y]+cnt[y],dis[y] by y To y Is the sum of the distances of all subtree nodes of the root node ,cnt[y] by y The number of all subtree nodes as the root node .

  *  Then change the root dp Handle . After the root node is removed from x Move to y When ,dp[y] = dp[x]-cnt[y]+(n-cnt[y); Among them -cnt[y] Is to y Extended cnt[y] All paths -1, and +(n-cnt[y]) Yes, from x The extended does not include y The other paths are +1.

Code implementation ：

#include<bits/stdc++.h>
#define endl '\n'
#define null NULL
#define ll long long
#define int long long
#define pii pair<int, int>
#define lowbit(x) (x &(-x))
#define ls(x) x<<1
#define rs(x) (x<<1+1)
#define me(ar) memset(ar, 0, sizeof ar)
#define mem(ar,num) memset(ar, num, sizeof ar)
#define rp(i, n) for(int i = 0, i < n; i ++)
#define rep(i, a, n) for(int i = a; i <= n; i ++)
#define pre(i, n, a) for(int i = n; i >= a; i --)
#define IOS ios::sync_with_stdio(0); cin.tie(0);cout.tie(0);
const int way[4][2] = {
   {1, 0}, {-1, 0}, {0, 1}, {0, -1}};
using namespace std;
const int  inf = 0x3f3f3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-6;
const ll   mod = 1e9+7;
const int  N = 1e6+10;

inline void read(int &x){
    char t=getchar();
    while(!isdigit(t)) t=getchar();
    for(x=t^48,t=getchar();isdigit(t);t=getchar()) x=x*10+(t^48);
}

int n, dis[N], cnt[N], dp[N], vis[N];
vector<int> ve[N];

void dfs(int x){
    vis[x] = 1;
    int sum = 0;
    for(int i = 0; i < ve[x].size(); i ++){
        int y = ve[x][i];
        if(!vis[y]){
            dfs(y);
            sum += cnt[y];
            dis[x] += dis[y]+cnt[y];
        }
    }
    cnt[x] = sum+1;
}

void DP(int x){
    vis[x] = 1;
    for(int i = 0; i < ve[x].size(); i ++){
        int y = ve[x][i];
        if(!vis[y]){
            dp[y] = dp[x]-cnt[y]+(n-cnt[y]);
            DP(y);
        }
    }
}

signed main()
{
    IOS;

    cin >> n;
    for(int i = 1; i < n; i ++){
        int a, b; cin >> a >> b;
        ve[a].push_back(b);
        ve[b].push_back(a);
    }
    me(vis); dfs(1); me(vis);
    for(int i = 1; i <= n; i ++)
        dp[i] = dis[i];
    DP(1);
    int ans = inf;
    for(int i = 1; i <= n; i ++)
        ans = min(ans, dp[i]);

    cout << ans << endl;

    return 0;
}