E. Paths and Trees
time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Little girl Susie accidentally found her elder brother's notebook. She has many things to do, more important than solving problems, but she found this problem too interesting, so she wanted to know its solution and decided to ask you about it. So, the problem statement is as follows.

Let's assume that we are given a connected weighted undirected graph G = (V, E) (here V is the set of vertices, E is the set of edges). The shortest-path tree from vertex u is such graph G1 = (V, E1) that is a tree with the set of edges E1 that is the subset of the set of edges of the initial graph E, and the lengths of the shortest paths from u to any vertex to G and to G1 are the same.

You are given a connected weighted undirected graph G and vertex u. Your task is to find the shortest-path tree of the given graph from vertex u, the total weight of whose edges is minimum possible.

Input

The first line contains two numbers, n and m (1 ≤ n ≤ 3·105, 0 ≤ m ≤ 3·105) — the number of vertices and edges of the graph, respectively.

Next m lines contain three integers each, representing an edge — ui, vi, wi — the numbers of vertices connected by an edge and the weight of the edge (ui ≠ vi, 1 ≤ wi ≤ 109). It is guaranteed that graph is connected and that there is no more than one edge between any pair of vertices.

The last line of the input contains integer u (1 ≤ u ≤ n) — the number of the start vertex.

Output

In the first line print the minimum total weight of the edges of the tree.

In the next line print the indices of the edges that are included in the tree, separated by spaces. The edges are numbered starting from 1 in the order they follow in the input. You may print the numbers of the edges in any order.

If there are multiple answers, print any of them.

Examples
input
3 3
1 2 1
2 3 1
1 3 2
3
output
2
1 2
input
4 4
1 2 1
2 3 1
3 4 1
4 1 2
4
output
4
2 3 4
Note

In the first sample there are two possible shortest path trees:

  • with edges 1 – 3 and 2 – 3 (the total weight is 3);
  • with edges 1 – 2 and 2 – 3 (the total weight is 2);

And, for example, a tree with edges 1 – 2 and 1 – 3 won't be a shortest path tree for vertex 3, because the distance from vertex 3 to vertex 2 in this tree equals 3, and in the original graph it is 1.

题目链接:点击传送

题意:给你n个点,m条边,让你求u到所有点的都是最短路,并且使得图的总权值最小;

思路:dij+堆优化,在求最短路的时候多存两个pos,跟w,在保证最短路的情况下,使得w更小即可;

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<iostream>
#include<cstdio>
#include<cmath>
#include<string>
#include<queue>
#include<algorithm>
#include<stack>
#include<cstring>
#include<vector>
#include<list>
#include<set>
#include<map>
using namespace std;
#define ll long long
#define pi (4*atan(1.0))
#define eps 1e-14
#define bug(x) cout<<"bug"<<x<<endl;
const int N=3e5+,M=1e6+,inf=;
const ll INF=1e18+,mod=;
struct is
{
int v,next,w,pos;
}edge[N<<];
int head[N],edg;
void init()
{
memset(head,-,sizeof(head));
edg=;
}
void add(int u,int v,int w,int pos)
{
edg++;
edge[edg].v=v;
edge[edg].w=w;
edge[edg].pos=pos;
edge[edg].next=head[u];
head[u]=edg;
}
struct mmp
{
int s,pos,w;
ll dis;
mmp(){}
mmp(int ss,ll d,int p,int ww){s=ss,dis=d;pos=p;w=ww;}
bool operator <(const mmp &b)const
{
if(dis!=b.dis)
return dis>b.dis;
return w>b.w;
}
};
ll ans[N],sum;
int vis[N];
priority_queue<mmp>q;
vector<int>out;
void dij(int s)
{
ans[s]=;
q.push(mmp(s,0LL,,));
while(!q.empty())
{
mmp now = q.top();
q.pop();
if(vis[now.s])continue;
sum+=now.w;
out.push_back(now.pos);
vis[now.s]=;
for(int i = head[now.s]; i !=-; i = edge[i].next)
{
int v=edge[i].v;
ll w=edge[i].w;
int p=edge[i].pos;
if(ans[v] >=ans[now.s] + w)
{
q.push(mmp(v,ans[now.s]+w,p,w));
ans[v]=ans[now.s]+w;
}
}
}
}
int main()
{
init();
int n,m;
scanf("%d%d",&n,&m);
for(int i=;i<=m;i++)
{
int u,v,w;
scanf("%d%d%d",&u,&v,&w);
add(u,v,w,i);
add(v,u,w,i);
}
int s;
scanf("%d",&s);
for(int i=;i<=n;i++)
ans[i]=INF;
dij(s);
printf("%lld\n",sum);
sort(out.begin(),out.end());
for(int i=;i<out.size();i++)
printf("%d ",out[i]);
return ;
}
 
E. Paths and Trees
time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Little girl Susie accidentally found her elder brother's notebook. She has many things to do, more important than solving problems, but she found this problem too interesting, so she wanted to know its solution and decided to ask you about it. So, the problem statement is as follows.

Let's assume that we are given a connected weighted undirected graph G = (V, E) (here V is the set of vertices, E is the set of edges). The shortest-path tree from vertex u is such graph G1 = (V, E1) that is a tree with the set of edges E1 that is the subset of the set of edges of the initial graph E, and the lengths of the shortest paths from u to any vertex to G and to G1 are the same.

You are given a connected weighted undirected graph G and vertex u. Your task is to find the shortest-path tree of the given graph from vertex u, the total weight of whose edges is minimum possible.

Input

The first line contains two numbers, n and m (1 ≤ n ≤ 3·105, 0 ≤ m ≤ 3·105) — the number of vertices and edges of the graph, respectively.

Next m lines contain three integers each, representing an edge — ui, vi, wi — the numbers of vertices connected by an edge and the weight of the edge (ui ≠ vi, 1 ≤ wi ≤ 109). It is guaranteed that graph is connected and that there is no more than one edge between any pair of vertices.

The last line of the input contains integer u (1 ≤ u ≤ n) — the number of the start vertex.

Output

In the first line print the minimum total weight of the edges of the tree.

In the next line print the indices of the edges that are included in the tree, separated by spaces. The edges are numbered starting from 1 in the order they follow in the input. You may print the numbers of the edges in any order.

If there are multiple answers, print any of them.

Examples
input
3 3
1 2 1
2 3 1
1 3 2
3
output
2
1 2
input
4 4
1 2 1
2 3 1
3 4 1
4 1 2
4
output
4
2 3 4
Note

In the first sample there are two possible shortest path trees:

  • with edges 1 – 3 and 2 – 3 (the total weight is 3);
  • with edges 1 – 2 and 2 – 3 (the total weight is 2);

And, for example, a tree with edges 1 – 2 and 1 – 3 won't be a shortest path tree for vertex 3, because the distance from vertex 3 to vertex 2 in this tree equals 3, and in the original graph it is 1.

 

Codeforces Round #303 (Div. 2)E. Paths and Trees 最短路的更多相关文章

  1. Codeforces Round #303 (Div. 2) E. Paths and Trees 最短路+贪心

    题目链接: 题目 E. Paths and Trees time limit per test 3 seconds memory limit per test 256 megabytes inputs ...

  2. Codeforces Round #303 (Div. 2) E. Paths and Trees Dijkstra堆优化+贪心(!!!)

    E. Paths and Trees time limit per test 3 seconds memory limit per test 256 megabytes input standard ...

  3. 水题 Codeforces Round #303 (Div. 2) D. Queue

    题目传送门 /* 比C还水... */ #include <cstdio> #include <algorithm> #include <cstring> #inc ...

  4. DP Codeforces Round #303 (Div. 2) C. Woodcutters

    题目传送门 /* 题意:每棵树给出坐标和高度,可以往左右倒,也可以不倒 问最多能砍到多少棵树 DP:dp[i][0/1/2] 表示到了第i棵树时,它倒左或右或不动能倒多少棵树 分情况讨论,若符合就取最 ...

  5. 贪心 Codeforces Round #303 (Div. 2) B. Equidistant String

    题目传送门 /* 题意:找到一个字符串p,使得它和s,t的不同的总个数相同 贪心:假设p与s相同,奇偶变换赋值,当是偶数,则有答案 */ #include <cstdio> #includ ...

  6. 水题 Codeforces Round #303 (Div. 2) A. Toy Cars

    题目传送门 /* 题意:5种情况对应对应第i或j辆车翻了没 水题:其实就看对角线的上半边就可以了,vis判断,可惜WA了一次 3: if both cars turned over during th ...

  7. Codeforces Round #303 (Div. 2)

    A.Toy Cars 题意:给出n辆玩具车两两碰撞的结果,找出没有翻车过的玩具车. 思路:简单题.遍历即可. #include<iostream> #include<cstdio&g ...

  8. Codeforces Round #303 (Div. 2)(CF545) E Paths and Trees(最短路+贪心)

    题意 求一个生成树,使得任意点到源点的最短路等于原图中的最短路.再让这个生成树边权和最小. http://codeforces.com/contest/545/problem/E 思路 先Dijkst ...

  9. Codeforces Round #303 (Div. 2) D. Queue 傻逼题

    C. Woodcutters Time Limit: 20 Sec  Memory Limit: 256 MB 题目连接 http://codeforces.com/contest/545/probl ...

随机推荐

  1. Spark On Yarn Cluster生产环境下JVM的OOM和Stack Overflow问题

    1.Spark on Yarn下JVM的OOM问题及解决方式 2.Spark中Driver的Stack Overflow的问题及解决方式 Spark on Yarn cluster mode: 此时有 ...

  2. [py]django强悍的数据库接口(QuerySet API)-增删改查

    django强悍的数据库接口(QuerySet API) 4种方法插入数据 获取某个对象 filter过滤符合条件的对象 filter过滤排除某条件的对象- 支持链式多重查询 没找到排序的 - 4种方 ...

  3. 畅通工程续 (SPFA模板Floy模板)

    http://acm.hdu.edu.cn/showproblem.php?pid=1874 SPFA #include <iostream> #include <stdio.h&g ...

  4. 面经:Google两轮背靠背

    如题,谷歌两轮背靠背电面.两轮都是废话不多说直奔coding,虽然第一轮的中国大哥还是花了一点点时间了解了一下我的背景.毕业时间.research方向.说好的research面呢? 中国大哥出的题: ...

  5. 018-DNS解析过程与配置DNS服务

  6. SQL Server报“GUID应包含带4个短划线的32位数”

    转自:http://www.seayee.net/article/info_106.html 最近在配置一台服务器的MS SQL Server 2005的维护计划自动备份数据库,能创建维护计划,但设置 ...

  7. 让前端独立于后端进行开发,模拟数据生成器Mock.js

    让前端独立于后端进行开发,模拟数据生成器Mock.jsMock.js 是一款模拟数据生成器,旨在帮助前端攻城师独立于后端进行开发,帮助编写单元测试. Home · nuysoft/Mock Wiki ...

  8. Nginx启动SSL功能

    Nginx启动SSL功能,并进行功能优化,你看这个就足够了 一:开始Nginx的SSL模块 1.1 Nginx如果未开启SSL模块,配置Https时提示错误 nginx: [emerg] the &q ...

  9. oracle_存储过程小记

    # 刷新会员标签函数 {color:red} fun_refresh_code{color} {noformat}CREATE OR REPLACE FUNCTION fun_refresh_code ...

  10. Antlr4 入门

    一.ANTRL 是什么 ANTLR 是用JAVA写的语言识别工具,它用来声明语言的语法,简称为“元语言”(meta-language). ANTLR 语法识别一般分为二个阶段: 1.词法分析阶段 (l ...