Codeforces 1060E(dfs计数)

题目链接

题意

给一棵树，对于一个节点，与它相邻的结点可以连一条边，求所有点对间距离之和

思路

任意两点间的距离被优化为$\left \lceil \frac{s}{2} \right \rceil$，转化为任意两点间距加间距为奇数的路径数，即$\frac{\sum_{i\in G,j\in G,i<j}dis[i][j]+\sum_{i\in G,j\in G,i<j[dis[i][j]=1(mod 2)]}}{2}$，奇数路径可由深度奇偶性不同的点数相乘得到，即$\sum_{i\in G}dep[i]=1(mod 2)*\sum_{i\in G}dep[i]=0(mod2)$

代码

//#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <stack>
#include <cstdio>
#include <vector>
#include <cassert>
#include <cstring>
#include <iostream>
#include <algorithm>
 
#define IOS    ios::sync_with_stdio(0),cin.tie(0);
#define DBG(x) cerr << #x << " = " << x << endl;
 
using namespace std;
 
typedef long long LL;
typedef long double LD;
typedef unsigned long long ULL;
 
const int inf = 0x3f3f3f3f;
const int mod = 1000000007;
const double eps = 1e-8;
const double pi  = acos(-1.0);
 
void file(){
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
}
 
const int maxn = 2e5+5;
const int maxm = 4e5+5;
 
int n;
int head[maxn],tot;
int dep[maxn],vis[maxn];
LL cnt0,cnt1;
LL siz[maxn];
 
struct edgenode{
    int to,next;
}edge[maxm];
 
void addedge(int u,int v){
    edge[tot].to=v;
    edge[tot].next=head[u];
    head[u]=tot++;
}
 
void dfs(int x,int dep){
    siz[x]=1;
    if(vis[x] == inf){
        vis[x]=dep;
        if(abs(dep)%2 == 0)cnt0++;
        else cnt1++;
    }
    for(int i=head[x];i != -1;i=edge[i].next){
        int v=edge[i].to;
        if(vis[v] == inf){
            dfs(v,dep+1);
            siz[x]+=siz[v];
        }
    }
}
 
namespace BakuretsuMahou{
    void Explosion(){
        memset(head,-1,sizeof head);
        memset(vis,0x3f,sizeof vis);
        scanf("%d",&n);
        for(int i=1;i<n;i++){
            int a,b;
            scanf("%d%d",&a,&b);
            addedge(a,b);
            addedge(b,a);
        }
        dfs(1,0);
        LL ans=cnt0*cnt1;
        for(int i=1;i<=n;i++)
            ans+=siz[i]*(1LL*n-siz[i]);
        printf("%I64d\n",ans/2);
    }
}
 
int main(){
    //IOS
    //file();
    BakuretsuMahou::Explosion();
    return 0;
}