【思维题 并查集 图论】bzoj1576: [Usaco2009 Jan]安全路经Travel

有趣的思考题

Description

Input

* 第一行: 两个空格分开的数, N和M

* 第2..M+1行: 三个空格分开的数a_i, b_i,和t_i

Output

* 第1..N-1行: 第i行包含一个数:从牛棚_1到牛棚_i+1并且避免从牛棚1到牛棚i+1最短路经上最后一条牛路的最少的时间.如果这样的路经不存在,输出-1.

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题目分析

做法一

暴力树剖线段树

做法二

并查集[bzoj1576] [Usaco2009 Jan]安全路经Travel

 #include<bits/stdc++.h>
 const int maxn = ;
 const int maxm = ;

 int n,m,dis[maxn];
 struct cmp
 {
     bool operator ()(int a, int b) const
     {
         return dis[a] > dis[b];
     }
 };
 struct Edge
 {
     int y,val;
     Edge(int a=, int b=):y(a),val(b) {}
 }edges[maxm];
 struct EdgeSv
 {
     int x,y,dis;
     bool operator < (EdgeSv a) const
     {
         return dis < a.dis;
     }
     EdgeSv(int a=, int b=, int c=):x(a),y(b),dis(c) {}
 }edgeSv[maxm];
 int fa[maxn],fat[maxn],tag[maxn],dep[maxn];
 bool disVis[maxn],treeTag[maxm];
 int edgeTot,svTot,nxt[maxm],pre[maxm],head[maxn];
 std::priority_queue<int, std::vector<int>, cmp> q;

 int read()
 {
     char ch = getchar();
     int num = ;
     bool fl = ;
     for (; !isdigit(ch); ch = getchar())
         if (ch=='-') fl = ;
     for (; isdigit(ch); ch = getchar())
         num = (num<<)+(num<<)+ch-;
     if (fl) num = -num;
     return num;
 }
 void addedge(int u, int v)
 {
     int c = read();
     edges[++edgeTot] = Edge(v, c), nxt[edgeTot] = head[u], head[u] = edgeTot;
     edges[++edgeTot] = Edge(u, c), nxt[edgeTot] = head[v], head[v] = edgeTot;
 }
 int get(int x){return fa[x]==x?x:fa[x]=get(fa[x]);}
 int main()
 {
     memset(dis, 0x3f3f3f3f, sizeof dis);
     memset(head, -, sizeof head);
     n = read(), m = read();
     for (int i=; i<=n; i++) fa[i] = i;
     for (int i=; i<=m; i++) addedge(read(), read());
     dis[] = , q.push();
     while (q.size())
     {
         int tt = q.top();
         q.pop();
         for (int i=head[tt]; i!=-; i=nxt[i])
             if (dis[edges[i].y] > dis[tt]+edges[i].val){
                 dis[edges[i].y] = dis[tt]+edges[i].val;
                 dep[edges[i].y] = dep[tt]+, pre[edges[i].y] = i, fat[edges[i].y] = tt;
                 q.push(edges[i].y);
             }
     }
     for (int i=; i<=n; i++) treeTag[pre[i]] = ;
     for (int i=; i<=edgeTot; i+=)
         if (!treeTag[i]&&!treeTag[i+]){
             int u = edges[i].y, v = edges[i+].y;
             edgeSv[++svTot] = EdgeSv(u, v, edges[i].val+dis[u]+dis[v]);
         }
     std::sort(edgeSv+, edgeSv+svTot+);
     for (int i=; i<=svTot; i++)
     {
         int u = edgeSv[i].x, v = edgeSv[i].y, lstu = , lstv = ;
         int topu = get(u), topv = get(v);
         while (topu!=topv)
         {
             if (dep[topu] < dep[topv])
                 std::swap(u, v), std::swap(lstu, lstv), std::swap(topu, topv);
             if (!tag[u]){
                 tag[u] = i;
                 if (lstu) fa[lstu] = u;
             }else if (lstu) fa[lstu] = topu;
             lstu = topu, u = fat[topu], topu = get(u);
         }
     }
     for (int i=; i<=n; i++)
         if (!tag[i]) puts("-1");
         else printf("%d\n",edgeSv[tag[i]].dis-dis[i]);
     return ;
 }

END