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CodeForces 1029E :Tree with Small Distances 思维

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题目描述

给定一颗有根树(根节点为 1 1 1)。要求往树中加入一些边使得从根节点到其他节点的距离至多是 2 2 2。 求加入边的最小数量。(边全部都是无向的)

分析

我们首先 d f s dfs dfs维护每一个节点距离跟节点的距离以及他们的前驱节点,然后把距离大于 2 2 2的点排序,从距离远到距离近一次处理,每一次把节点周围打上标记即可

代码

#pragma GCC optimize(3)
#include <bits/stdc++.h>
#define debug(x) cout<<#x<<":"<<x<<endl;
#define dl(x) printf("%lld\n",x);
#define di(x) printf("%d\n",x);
#define _CRT_SECURE_NO_WARNINGS
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> PII;
typedef vector<int> VI;
const int INF = 0x3f3f3f3f;
const int N = 4e5 + 10;
const ll mod = 1000000007;
const double eps = 1e-9;
const double PI = acos(-1);
template<typename T>inline void read(T &a) {
	char c = getchar(); T x = 0, f = 1; while (!isdigit(c)) {if (c == '-')f = -1; c = getchar();}
	while (isdigit(c)) {x = (x << 1) + (x << 3) + c - '0'; c = getchar();} a = f * x;
}
int gcd(int a, int b) {return (b > 0) ? gcd(b, a % b) : a;}
int n,d[N];
int h[N],e[N],ne[N],idx;
int f[N];

void add(int x,int y){
	ne[idx] = h[x],e[idx] = y,h[x] = idx++;
}
bool cmp(int x,int y){
	return d[x] > d[y];
}

void dfs(int u,int fa){	
	f[u] = fa;
	for(int i = h[u];~i;i = ne[i]){
		int j = e[i];
		if(j == fa) continue;
		d[j] = d[u] + 1;
		dfs(j,u);
	}
}

int main() {
	memset(h,-1,sizeof h);
	read(n);
	for(int i = 1;i < n;i++){
		int x,y;
		read(x),read(y);
		add(x,y);
		add(y,x);
	}
	dfs(1,-1);
	VI nums;
	int res = 0;
	for(int i = 1;i <= n;i++) if(d[i] > 2) nums.pb(i);
	sort(all(nums),cmp);
	for(auto x:nums){
		if(d[x] <= 2) continue;
		res++;
		int p = f[x];
		d[p] = 0;
		for(int i = h[p];~i;i = ne[i]){
			int j = e[i];
			d[j] = 0;
		}
	}
	di(res);
	return 0;
}

/**
*  ┏┓   ┏┓+ +
* ┏┛┻━━━┛┻┓ + +
* ┃       ┃
* ┃   ━   ┃ ++ + + +
*  ████━████+
*  ◥██◤ ◥██◤ +
* ┃   ┻   ┃
* ┃       ┃ + +
* ┗━┓   ┏━┛
*   ┃   ┃ + + + +Code is far away from  
*   ┃   ┃ + bug with the animal protecting
*   ┃    ┗━━━┓ 神兽保佑,代码无bug 
*   ┃        ┣┓
*    ┃        ┏┛
*     ┗┓┓┏━┳┓┏┛ + + + +
*    ┃┫┫ ┃┫┫
*    ┗┻┛ ┗┻┛+ + + +
*/
 

标签:Distances,const,idx,int,Tree,CodeForces,dfs,read,节点
来源: https://blog.csdn.net/tlyzxc/article/details/118343580