分析:
Dijkstra求最短路树,在最短路树上进行操作,详情可见上一篇博客:http://www.cnblogs.com/Winniechen/p/9042937.html
我觉得这个东西不压行写出了有点丑...之后写了一个压行后更丑的...
附上压行后的代码:
#include <cstdio> #include <algorithm> #include <cmath> #include <cstdlib> #include <cstring> #include <iostream> #include <queue> using namespace std; #define N 200005 #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 #define inf 0x3f3f3f3f struct node { int to,next,val; }E[N<<2],e[N<<1]; int head[N],head1[N],cnt,cnt1,fa[N],a[N]; int dep[N],anc[N],siz[N],son[N],idx[N],b[N]; int dis[N],minn[N<<2],cov[N<<2],n,vis[N],c[N]; void add1(int x,int y,int z){E[cnt1].to=y;E[cnt1].next=head1[x];E[cnt1].val=z;head1[x]=cnt1++;} void add(int x,int y,int z){e[cnt].to=y;e[cnt].next=head[x];e[cnt].val=z;head[x]=cnt++;} void Dijkstra() { memset(dis,0x3f,sizeof(dis));int num=0; priority_queue<pair<int ,int > >q;dis[1]=0;q.push(make_pair(0,1)); while(!q.empty()) { if(num==n)break; int x=q.top().second;q.pop(); if(vis[x])continue;vis[x]=1;num++; for(int i=head1[x];i!=-1;i=E[i].next) { int to1=E[i].to; if(dis[to1]+E[i].val==dis[x])add(to1,x,E[i].val),add(x,to1,E[i].val); } for(int i=head1[x];i!=-1;i=E[i].next) { int to1=E[i].to; if(dis[x]+E[i].val<dis[to1]) { dis[to1]=dis[x]+E[i].val; q.push(make_pair(-dis[to1],to1)); } } } } void dfs1(int x,int from) { fa[x]=from,dep[x]=dep[from]+1,siz[x]=1; for(int i=head[x];i!=-1;i=e[i].next) { int to1=e[i].to; if(to1!=from) { dfs1(to1,x);siz[x]+=siz[to1]; if(siz[son[x]]<siz[to1])son[x]=to1; } } } int tims; void dfs2(int x,int top) { anc[x]=top;idx[x]=++tims; if(son[x])dfs2(son[x],top); for(int i=head[x];i!=-1;i=e[i].next) { int to1=e[i].to; if(to1!=fa[x]&&to1!=son[x])dfs2(to1,to1); } } void PushDown(int rt) { if(cov[rt]!=inf) { int t=cov[rt]; cov[rt<<1]=min(cov[rt<<1],t); minn[rt<<1]=min(minn[rt<<1],t); cov[rt<<1|1]=min(cov[rt<<1|1],t); minn[rt<<1|1]=min(minn[rt<<1|1],t); cov[rt]=inf; } } void build(int l,int r,int rt) { minn[rt]=cov[rt]=inf; if(l==r)return ;int m=(l+r)>>1; build(lson);build(rson); } void Update(int L,int R,int c,int l,int r,int rt) { if(L<=l&&r<=R) { minn[rt]=min(minn[rt],c);cov[rt]=min(cov[rt],c); return ; } PushDown(rt);int m=(l+r)>>1; if(L<=m)Update(L,R,c,lson); if(m<R)Update(L,R,c,rson); } int query(int x,int l,int r,int rt) { if(l==r)return minn[rt]; PushDown(rt);int m=(l+r)>>1; if(m>=x)return query(x,lson); else return query(x,rson); } void get_lca(int x,int y,int c) { while(anc[x]!=anc[y]) { if(dep[anc[x]]<dep[anc[y]])swap(x,y); Update(idx[anc[x]],idx[x],c,1,n,1);x=fa[anc[x]]; } if(dep[x]>dep[y])swap(x,y); if(x!=y)Update(idx[x]+1,idx[y],c,1,n,1); } int main() { int m;memset(head,-1,sizeof(head));memset(head1,-1,sizeof(head1));scanf("%d%d",&n,&m); for(int i=1;i<=m;i++) { int x,y,z;scanf("%d%d%d",&x,&y,&z); add1(x,y,z);add1(y,x,z);a[i]=x,b[i]=y,c[i]=z; } Dijkstra();dfs1(1,0);dfs2(1,1);build(1,n,1); for(int i=1;i<=m;i++) { if(abs(dis[a[i]]-dis[b[i]])==c[i])continue; get_lca(a[i],b[i],dis[a[i]]+dis[b[i]]+c[i]); } for(int i=2;i<=n;i++) { int t=query(idx[i],1,n,1); t==inf?printf("-1 "):printf("%d ",t-dis[i]); } return 0; }