思路就是尽量连相距远的叶节点，然后如果有落单的叶节点就把这个叶节点连到根上，为什么有的点没过？

#include <iostream>
#include <cstring>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <vector>
#include <queue>
using namespace std;
const int N = 5e5+5;
int n;
int tot = 0 , head[N];
int dfn[N] , sz[N] , idx = 0 , dep[N] , dp;
struct edge{
    int to , nxt;
}e[N*2];
struct leaf{
    int id , val;
}lf[N];

void add( int u , int v ){
    e[++tot].to = v;
    e[tot].nxt = head[u];
    head[u] = tot;
}

void dfs( int u , int fa ){
    //sz[u] = 1;
    dfn[u] = ++idx;
    dep[u] = dep[fa] + 1;
    for( int i = head[u] ; i ; i = e[i].nxt ){
        int v = e[i].to;
        if( v == fa ) continue;
        dfs( v , u );
        //sz[u] += sz[v];
    }
}

bool cmp( leaf a , leaf b ){
    return a.val < b.val;
}

int main( ) {
    cin >> n;
    for( int i = 1 , a , b ; i < n ; i++ ){
        cin >> a >> b;
        add( a , b );
        add( b , a );
        sz[a]++;
        sz[b]++;
    }
    //dep[1] = 1;
    dfs( 1 , 0 );
    int ans  = 0;
    for( int i = 1 ; i <= n ; i++ ){
        if( sz[i] == 1 ){
            lf[++ans].id = i;
            lf[ans].val = dfn[i];
        }
        dp = max( dp , dep[i] );
    }
    sort( lf + 1 , lf + ans + 1 , cmp );
    cout << ans-ans/2 <<endl;
    int l = 1 , r = ans;
    while( l < r ){
        if( lf[l].id > lf[r].id ) swap( lf[l].id , lf[r].id );
        cout << lf[l].id << " " << lf[r].id <<endl;
        l++;
        r--;
    }
    if( ans&1 ){
        if( dp > 2  ) cout << 1 <<" "<< lf[l].id <<endl;
        else cout << lf[l-1].id <<" "<< lf[r].id <<endl;
    }
    return 0;
}