[Codeforces 545E] Paths and Trees
[题目链接]
https://codeforces.com/contest/545/problem/E
[算法]
首先求 u 到所有结点的最短路
记录每个节点最短路径上的最后一条边
答案即为以u为根的一棵最短路径生成树
时间复杂度 : O(NlogN)
[代码]
#include<bits/stdc++.h>
using namespace std;
const int MAXN = 3e5 + ;
const long long INF = 1e60; struct edge
{
int to , w , nxt;
} e[MAXN << ]; int n , m , s , tot;
int head[MAXN],u[MAXN],v[MAXN],w[MAXN],last[MAXN];
long long dist[MAXN];
bool visited[MAXN],vis[MAXN << ]; template <typename T> inline void chkmax(T &x,T y) { x = max(x,y); }
template <typename T> inline void chkmin(T &x,T y) { x = min(x,y); }
template <typename T> inline void read(T &x)
{
T f = ; x = ;
char c = getchar();
for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
for (; isdigit(c); c = getchar()) x = (x << ) + (x << ) + c - '';
x *= f;
}
inline void addedge(int u,int v,int w)
{
tot++;
e[tot] = (edge){v,w,head[u]};
head[u] = tot;
}
inline void dijkstra(int s)
{
priority_queue< pair<long long,int> , vector< pair<long long,int> > ,greater< pair<long long,int> > > q;
for (int i = ; i <= n; i++)
{
dist[i] = INF;
visited[i] = false;
}
dist[s] = ;
q.push(make_pair(,s));
while (!q.empty())
{
int cur = q.top().second;
q.pop();
if (visited[cur]) continue;
visited[cur] = true;
for (int i = head[cur]; i; i = e[i].nxt)
{
int v = e[i].to , w = e[i].w;
if (!visited[v] && dist[cur] + w <= dist[v])
{
if (dist[cur] + w < dist[v]) last[v] = i;
else if (w < e[last[v]].w) last[v] = i;
dist[v] = dist[cur] + w;
q.push(make_pair(dist[v],v));
}
}
}
} int main()
{ read(n); read(m);
for (int i = ; i <= m; i++)
{
read(u[i]); read(v[i]); read(w[i]);
addedge(u[i],v[i],w[i]);
addedge(v[i],u[i],w[i]);
}
read(s);
dijkstra(s);
for (int i = ; i <= n; i++) vis[last[i]] = true;
vector< int > ans;
long long res = ;
for (int i = ; i <= tot; i += )
{
if (vis[i] || vis[i - ])
{
ans.push_back(i >> );
res += e[i].w;
}
}
printf("%I64d\n",res);
for (unsigned i = ; i < ans.size(); i++)
if (i == ) printf("%d",ans[i]);
else printf(" %d",ans[i]);
printf("\n"); return ; }
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